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Impact of humidity, temperature, and particulate fouling on membrane-based energy exchangers Engarnevis, Amin 2018

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  IMPACT OF HUMIDITY, TEMPERATURE, AND PARTICULATE FOULING ON MEMBRANE-BASED ENERGY EXCHANGERS  by  Amin Engarnevis  B.A.Sc., Ferdowsi University of Mashhad, 2008 M.A.Sc., K. N. Toosi University of Technology, 2011    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)    August 2018 © Amin Engarnevis, 2018    ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  IMPACT OF HUMIDITY, TEMPERATURE, AND PARTICULATE FOULING ON MEMBRANE-BASED ENERGY EXCHANGERS  submitted by Amin Engarnevis  in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering  Examining Committee: Steven N. Rogak Co-supervisor Sheldon I. Green Co-supervisor Savvas G. Hatzikiriakos Supervisory Committee Member Mu Chiao University Examiner Fariborz Taghipour University Examiner   Additional Supervisory Committee Members: Frank Ko Supervisory Committee Member Walter Merida Supervisory Committee Member    iii  ABSTRACT Membrane-based energy recovery ventilators (ERVs) improve building energy efficiency by transporting heat and moisture between incoming and outgoing air streams. Although long-term studies are not available due to the recent implementation of this technology, there are preliminary indications that moisture transport might degrade with the extended operation, possibly as the result of exposure to air pollution or other environmental stresses. The scope of this dissertation is to quantify the influence of environmental factors on the permeation properties of current-generation composite membranes and the overall performance of ERV exchanger cores. First, the impact of particulate fouling was investigated via accelerated membrane- and core-level fouling experiments. The core-level experiments showed minimal impact on the effectiveness of ERV cores from coarse dust loadings. However, membrane-level examination with aerosol nanoparticles indicated that moisture transport through membranes was especially impaired when particles were hygroscopic or contained liquids. These results suggest that the optimal protection by filters and the orientation of the membrane would depend on the nature of the indoor and outdoor aerosols. Second, the effects of relative humidity and temperature on the transport of water vapor and CO2 (as a surrogate for indoor air pollutants) was evaluated through a systematic study of some standard polymers suitable for ERV use. It was shown that the permeability and selectivity of membranes could vary up to an order of magnitude depending on the membrane material, the temperature and relative humidity on both feed and permeate sides of the membrane, as well as orientation in asymmetric composite membranes. A theoretical model for predicting permeability of composite membranes, based on a limited number of kinetic water vapor sorption tests of the selective coating polymer, was successfully developed and validated for a commercial membrane. This model was then coupled with a heat and mass transfer model of cross-flow ERV exchanger cores to interpret the membrane-level variations regarding ERV exchanger core performance. A study of the effects of outdoor air parameters showed that the effectiveness of ERV exchangers could increase or decrease significantly with outdoor air relative humidity, while outdoor air temperature had only a minimal influence on effectiveness parameters.    iv  LAY SUMMARY Energy recovery ventilators (ERVs) are used in modern building ventilation systems to recycle the energy in the exhausted air and use it to pre-condition the fresh outdoor air supplied to the building. This is especially beneficial in hot and humid climates where air conditioners consume large amounts of energy for cooling and dehumidifying air. A new generation of ERVs using moisture-permeable polymeric membranes are particularly promising due to their small footprint, simplicity, and reduced contaminant transfer between the exhaust and fresh air streams. However, there is little information on the effects of environmental factors on the performance and longevity of these systems. This study investigates the effects of in-service operating conditions, including air pollution, relative humidity, and temperature, on the performance of membrane-based ERVs. Experimental work provides guidelines for material selections, and developed modeling tools provide means for evaluation of the actual energy savings potential of such devices in building ventilation systems.     v  PREFACE This dissertation is an original intellectual product of the author, Amin Engarnevis. This dissertation is an integration of refereed or under review manuscripts in scholarly journals and conference proceedings as follows. Permissions were obtained from publishers for reproduction of previously published material. Manuscripts are slightly modified for the dissertation formatting style and coherence. Various results from chapters 2, 3, 4, and Appendix B of this dissertation have been presented as oral or poster presentations at ASHRAE 2016 Winter Conference, ASHRAE 2016 IAQ Conference, ASHRAE 2017 Annual Conference, AAAR 2016, and ICOM 2017. A version of Chapter 2 has been published. Engarnevis, A., Huizing, R., Green, S., Rogak, S. ‘Particulate fouling assessment in membrane-based air-to-air energy exchangers’ Energy and Buildings (2017), 150(1), 477-487. The author completed all of the experimental and analytical work, writing the manuscript, and incorporating co-authors’ comments. Dr. Rogak and Dr. Green provided direction and feedback on the work. Dr. Ryan Huizing from dPoint Technologies Inc. is the industry partner for this project. He contributed in providing the test enthalpy exchangers, commenting on the data analysis, and proofreading the paper. The aerosol wind tunnel test facility used for conducting dust fouling and deposition experiments in Chapter 2 was designed and built in the Aerosols laboratory at UBC by the author and three co-op students (Matthew Grant, Bastien Caron, and Hunarbir Singh) under the author’s supervision in 2014. A version of Chapter 3 has been submitted for publication in a peer-reviewed journal in July 2018.  A portion of SEM imaging of membrane samples presented in Chapter 3 was completed with the help of Dr. Ryan Huizing. Some of the nanoparticle loading and water vapor transport testing of membrane samples presented in this chapter were conducted under the author’s supervision by A visiting graduate intern, Mr. Ali Vaseghi, in 2015 and a Visiting International Research Student (VIRS), Julien Peret, in 2016. The author conducted this study by performing the majority of experiments and all of the data analysis and prepared the manuscript under the supervision of Dr. Steve Rogak and Dr. Sheldon Green. A version of Chapter 4 has been published. Engarnevis, A., Romani, S., Sylvester, A., Huizing, R., Green, S., Rogak, S. ‘The effects of temperature and humidity on the permeation properties of membrane transport media used in energy recovery ventilators’ ASHRAE (2017) Annual Conference Proceedings. The Mixed Gas Permeation (MGP) testing apparatus used for conducting simultaneous water vapor and CO2 permeation testing in this chapter was designed and built in the Aerosols laboratory at UBC by the author and a fellow MASc student, Alexander Sylvester. A coop student under the author’s supervision, Sarah Romani, fabricated and tested a portion of the membranes in Chapter 4. The author completed a portion of the experimental work and all of the data analysis and interpretation in this chapter. The author prepared the manuscript and accommodated the co-authors’ comments under the supervision of Dr. Rogak and Dr. Green. Dr. Ryan Huizing contributed in providing membrane material and proof reading the manuscript. A version of Chapter 5 has been submitted for publication in a peer-reviewed journal in August 2018. Water vapor sorption experiments presented in this chapter were conducted by the author vi  using TA Instruments Q5000 SA dynamic vapor sorption analyzer at dPoint Technologies material laboratory. The author developed the experimental plan, analyzed the collected data, and prepared the manuscript under the supervision of Dr. Rogak and Dr. Green. Dr. Ryan Huizing from dPoint Technologies Inc. contributed in providing membrane material, conducting a portion of water vapor permeability testing of PU-PEO polymer films, commenting on the data analysis, and proof reading the manuscript. A version of Chapter 6 has been published. Engarnevis, A., Huizing, R., Green, S., Rogak, S. ‘Heat and mass transfer modeling in enthalpy exchangers using asymmetric composite membranes,’ Journal of Membrane Science, 556 (2018) pp. 248-262. The data article associated with this published work is presented in Appendix F. ‘Dataset on water vapor transport properties of asymmetric composite membranes using hydrophilic PU-PEO copolymer active coating layers’ Data Br. (2018), in press. The heat and mass transfer model of enthalpy exchanger core was developed by the author and Dr. Rogak. The author completed all of the material testing and analytical work, running simulations, writing the manuscript, and incorporating co-authors’ comments under the supervision of Dr. Rogak and Dr. Green. Dr. Ryan Huizing contributed in providing the test results of enthalpy exchanger cores, and mercury intrusion porosimetry of the substrate sample, as well as commenting on the data analysis, and proofreading the manuscript. Performance testing of full enthalpy exchanger cores presented for validation of modeling work in Chapter 6 was conducted by dPoint Technologies by an AHRI 1060 certified test facility (Lucerne University (HSLU), Switzerland). Chapter 7 was written by the author with guidance from Dr. Rogak and Dr. Green. The discussed conclusions and recommendations for future work therein are the result of collaboration and conversations with the colleagues listed above throughout the development of this dissertation.    vii  TABLE OF CONTENTS   ABSTRACT .................................................................................................................................................... iii LAY SUMMARY ............................................................................................................................................ iv PREFACE ........................................................................................................................................................ v TABLE OF CONTENTS .................................................................................................................................. vii LIST OF TABLES ...........................................................................................................................................xiii LIST OF FIGURES ......................................................................................................................................... xiv LIST OF SYMBOLS AND ABBREVIATIONS ................................................................................................... xvii ACKNOWLEDGMENTS ................................................................................................................................ xxii DEDICATION .............................................................................................................................................. xxiii CHAPTER 1 - INTRODUCTION ........................................................................................................................ 1 1.1. BACKGROUND .............................................................................................................................. 1 1.1.1. Energy Recovery in Building Ventilation Systems .............................................................. 1 1.1.2. Membrane-Based Energy Recovery Ventilators ................................................................... 3 1.1.3. Transport in Polymeric Membranes ...................................................................................... 5 1.1.4. Air Quality Considerations ................................................................................................... 7 1.1.5. Membrane Fouling by Aerosols ............................................................................................ 8 1.1.6. Heat and Mass Transfer Modeling in Membrane-based ERVs............................................. 8 1.2. MOTIVATION ................................................................................................................................ 9 1.3. RESEARCH OBJECTIVES AND THESIS OUTLINE ....................................................................... 10 CHAPTER 2 - DUST FOULING OF FIXED-PLATE ENTHALPY EXCHANGERS ................................................. 13 2.1. OVERVIEW .................................................................................................................................. 13 2.2. INTRODUCTION........................................................................................................................... 14 2.3. EXPERIMENTAL METHODS ........................................................................................................ 15 2.3.1. Exchanger Core Samples .................................................................................................... 15 2.3.2. Test Apparatus .................................................................................................................... 16 2.3.3. Test Dust ............................................................................................................................. 17 2.3.4. Deposition Fraction and Dust Loading Test Procedures ..................................................... 18 2.3.5. ERV Core Performance ...................................................................................................... 19 2.3.6. Data Sampling and Uncertainty Analysis ........................................................................... 19 2.4. RESULTS AND DISCUSSION ....................................................................................................... 20 2.4.1. Deposition Fraction and Particle Fouling Rate ................................................................... 20 viii  2.4.2. Clean Performance Test ...................................................................................................... 21 2.4.3. Sensible and Latent Effectiveness ....................................................................................... 22 2.4.4. Mass Transfer Resistance Analysis ..................................................................................... 23 2.4.5. Core Pressure Drop ............................................................................................................. 25 2.5. CONCLUSIONS ............................................................................................................................ 26 CHAPTER 3 - MEMBRANE MEDIA FOULING BY AEROSOL NANOPARTICLES  .............................................. 27 3.1. OVERVIEW .................................................................................................................................. 27 3.2. INTRODUCTION........................................................................................................................... 28 3.3. THEORY AND HYPOTHESIS OF EXPERIMENTS .......................................................................... 29 3.3.1. Fouling in Composite Membranes ...................................................................................... 29 3.3.2. Water Vapor Transport in Composite Membranes ............................................................. 31 3.4. MATERIALS AND EXPERIMENTAL METHODS ........................................................................... 34 3.4.1. Membrane Materials ........................................................................................................... 34 3.4.2. Test Apparatus .................................................................................................................... 35 3.4.3. Membrane Module .............................................................................................................. 36 3.4.4. Membrane Sample Preparation ........................................................................................... 37 3.4.5. Particle Deposition and Loading Test Procedures .............................................................. 37 3.4.6. Weight Measurements ......................................................................................................... 38 3.4.7. Water vapor Flux and Permeance ....................................................................................... 39 3.4.8. Pressurized Air Leak Rate and Gas Permeance .................................................................. 40 3.4.9. Determination of Pore Structure of Substrate ..................................................................... 41 3.4.10. Microscopic Analysis .......................................................................................................... 42 3.5. RESULTS AND DISCUSSION ....................................................................................................... 42 3.5.1. Particle Deposition on Membrane Surfaces ........................................................................ 42 3.5.2. Impact of Fouling on Composite Membranes ..................................................................... 44 3.5.3. Pore Narrowing in Microporous Substrate ......................................................................... 49 3.5.4. Impact of Fouling on Microporous Substrate ..................................................................... 51 3.5.5. Fouling Mechanisms ........................................................................................................... 53 3.6. FOULING CONTROL IN MEMBRANE-BASED ENTHALPY EXCHANGERS .................................. 54 3.6.1. Upstream Filtration ............................................................................................................. 55 3.6.2. HVAC System Operation Control Strategy ........................................................................ 55 3.6.3. Orientation of Membrane .................................................................................................... 55 3.6.4. Membrane Cleaning and Flux Recovery............................................................................. 55 ix  3.7. CONCLUSIONS ............................................................................................................................ 56 CHAPTER 4 - THE EFFECTS OF TEMPERATURE AND HUMIDITY ON THE PERMEATION PROPERTIES OF MEMBRANE MEDIA ..................................................................................................................................... 57 4.1. OVERVIEW .................................................................................................................................. 57 4.2. INTRODUCTION........................................................................................................................... 58 4.2.1. Contaminant Transfer in ERVs ........................................................................................... 59 4.2.2. Membrane Requirements for ERV Exchangers .................................................................. 62 4.3. MATERIALS AND MEMBRANE FABRICATION ........................................................................... 64 4.3.1. Materials and Chemicals ..................................................................................................... 64 4.3.2. Composite Membrane Preparation ...................................................................................... 66 4.3.3. Coating Thickness ............................................................................................................... 67 4.4. MEASUREMENT OF MIXED GAS/WATER VAPOR PERMEATION .............................................. 68 4.4.1. Test Apparatus .................................................................................................................... 68 4.4.2. Permeation Test Cell ........................................................................................................... 70 4.4.3. Permeation Test Cell Boundary Layer Resistances ............................................................ 70 4.4.4. Data Analysis ...................................................................................................................... 75 4.5. RESULTS AND DISCUSSION ....................................................................................................... 77 4.5.1. Water Vapor Permeability .................................................................................................. 77 4.5.2. CO2 Permeability ................................................................................................................ 79 4.5.3. Membrane Selectivity ......................................................................................................... 80 4.5.4. Membrane Material Selection for ERVs ............................................................................. 81 4.6. CONCLUSIONS ............................................................................................................................ 83 CHAPTER 5 – MEASUREMENTS OF MOISTURE SORPTION ISOTHERMS AND DIFFUSION COEFFICIENTS IN DENSE POLYMERS ....................................................................................................................................... 84 5.1. OVERVIEW .................................................................................................................................. 84 5.2. INTRODUCTION........................................................................................................................... 85 5.3. THEORETICAL BACKGROUND ................................................................................................... 86 5.3.1. Equilibrium Sorption........................................................................................................... 86 5.3.2. Fickian Diffusion ................................................................................................................ 87 5.3.3. Permeability ........................................................................................................................ 88 5.4. EXPERIMENTAL METHODS AND MATERIALS ........................................................................... 89 5.4.1. Materials ............................................................................................................................. 89 5.4.2. Film Preparation .................................................................................................................. 89 5.4.3. Gravimetric Sorption Balance ............................................................................................. 90 x  5.4.4. Water Vapor Permeation ..................................................................................................... 92 5.5. RESULTS AND DISCUSSIONS...................................................................................................... 93 5.5.1. Equilibrium Sorption Isotherms .......................................................................................... 93 5.5.2. Sorption and Desorption Kinetics ....................................................................................... 95 5.5.3. Non-Fickian Diffusion ...................................................................................................... 100 5.5.4. Diffusion-Relaxation Model ............................................................................................. 101 5.5.5. Evaluation of Mutual Diffusion Coefficient at Equilibrium ............................................. 105 5.5.6. Steady-State Permeability ................................................................................................. 110 5.6. CONCLUSIONS ....................................................................................................................... 111 CHAPTER 6 - IMPACT OF OPERATING CONDITIONS ON THE PERFORMANCE OF ENTHALPY EXCHANGERS .................................................................................................................................................................. 112 6.1. OVERVIEW ................................................................................................................................ 112 6.2. INTRODUCTION......................................................................................................................... 113 6.3. COUPLED HEAT AND MASS TRANSFER THROUGH MEMBRANE ........................................... 114 6.3.1. Mass Transfer .................................................................................................................... 114 6.3.2. Heat Transfer..................................................................................................................... 119 6.3.3. Membrane Material ........................................................................................................... 121 6.3.4. Moisture Permeability Calculation Procedures ................................................................. 121 6.4. MATHEMATICAL ENTHALPY EXCHANGER CORE MODEL ..................................................... 121 6.4.1. Geometry ........................................................................................................................... 122 6.4.2. Assumptions ...................................................................................................................... 122 6.4.3. Governing Equations......................................................................................................... 123 6.4.4. Air-side Heat and Mass Transfer Coefficients .................................................................. 125 6.4.5. Solution Procedures .......................................................................................................... 126 6.4.6. Enthalpy Exchanger Performance ..................................................................................... 126 6.5. RESULTS AND DISCUSSION ..................................................................................................... 127 6.5.1. Moisture Permeation through Composite Membrane ....................................................... 127 6.5.2. Validation of Enthalpy Core Model .................................................................................. 129 6.5.3. Effect of Variable Membrane Permeability ...................................................................... 131 6.5.4. Effect of Operating Humidity and Temperatures .............................................................. 133 6.5.5. Membrane Surface Temperature Profiles ......................................................................... 137 6.5.6. Effect of Membrane Orientation ....................................................................................... 138 6.6. CONCLUSIONS .......................................................................................................................... 140 xi  CHAPTER 7 – SUMMARY OF CONCLUSIONS, CONTRIBUTIONS, AND RECOMMENDATIONS FOR FUTURE WORK ........................................................................................................................................................ 142 7.1. OVERVIEW ................................................................................................................................ 142 7.2. CONCLUSIONS AND CONTRIBUTIONS ..................................................................................... 142 7.2.1. Fouling by Coarse Aerosol Particles ................................................................................. 143 7.2.2. Fouling by Aerosol nanoparticles ..................................................................................... 143 7.2.3. CO2 Crossover ................................................................................................................... 144 7.2.4. Material-level Studies of Water Diffusion and Sorption in Membranes .......................... 145 7.2.5. A Comprehensive Model of Water Vapor Permeability in Asymmetric Composite Membranes ........................................................................................................................................ 146 7.2.6. A Full ERV Core Model Including Variable Membrane Properties ................................. 146 7.3. RECOMMENDATIONS FOR FUTURE WORK ............................................................................. 146 7.3.1. Field Investigation of Fouling ........................................................................................... 146 7.3.2. Fouling Control and Mitigation Measures ........................................................................ 147 7.3.3. Membrane Longevity and Degradation Mechanisms ....................................................... 147 7.3.4. Contaminant Transport in Membrane-based ERVs .......................................................... 148 7.3.5. Indoor Air Quality-Energy Trade-offs .............................................................................. 148 7.3.6. Moisture Permeation through Asymmetric Composite Membranes ................................. 148 7.3.7. Heat and Moisture Transfer Modeling in ERV Cores ...................................................... 149 BIBLIOGRAPHY .......................................................................................................................................... 150  TEST PROCEDURES FOR DUST LOADING OF ENTHALPY EXCHANGER CORES .............. 166 A. 1 Deposition Fraction Measurements .......................................................................................... 166 A. 2 Dust Loading Tests ................................................................................................................... 168  MEMBRANE FOULING AND CONTAMINANT CROSSOVER OF ENVIRONMENTAL TOBACCO SMOKE 170 B. 1 Overview ................................................................................................................................... 170 B. 2 Experimental Methodology....................................................................................................... 170 B.2.1. ETS Loading Experiments ................................................................................................ 170 B.2.2. Membrane Performance Testing ....................................................................................... 172 B. 3 Results and Discussion ............................................................................................................. 173 B.3.1. Water Vapor and Gas Transport ............................................................................................. 173 B.3.2. VOC Crossover Measurements .............................................................................................. 175 B. 4 Conclusions ............................................................................................................................... 176  DATA REDUCTION AND UNCERTAINTY ANALYSIS IN PERMEATION TESTS .................. 178 xii  C. 1 Steady-State Permeation Test Criterion .................................................................................... 178 C. 2 Mass Balance and Data Reduction Criteria .............................................................................. 179 C. 3 Uncertainty Analysis ................................................................................................................. 179  GAS MIXTURE PROPERTIES ........................................................................................... 182  SUPPLEMENTAL INFORMATION FOR CHAPTER 5 ........................................................... 184 E. 1 Sorption Equilibrium ................................................................................................................ 184 E. 2 Diffusion-Relaxation Model Fit Parameters ............................................................................. 186 E. 3 Boundary Conditions ................................................................................................................ 189 E. 4 Diffusion-Concentration Correlations ....................................................................................... 189 E. 5 Sorption and Desorption Curves for PU-PEO .......................................................................... 190  MODELING WATER VAPOR PERMEATION PROPERTIES OF PU-PEO COPOLYMER COATING FILMS 193 F. 1 Sorption Isotherms .................................................................................................................... 193 F. 2 Diffusion Coefficients ............................................................................................................... 194 F. 3 Substrate Pore Size Distribution ............................................................................................... 196  LIST OF PUBLICATIONS ................................................................................................. 198     xiii  LIST OF TABLES  Table 2.1. Geometrical specifications of the enthalpy exchanger cores ..................................................... 15 Table 2.2. Properties of ISO Medium test dust ........................................................................................... 17 Table 2.3. Summary of estimated uncertainties in measured and calculated values .................................. 19 Table 2.4. Repeatability performance measurements of the control enthalpy core .................................... 22 Table 3.1. Properties of membrane material samples ................................................................................. 35 Table 3.2. Pre- and Post-loading performance of dry-loaded composite membrane samples. ................... 45 Table 3.3. Pre- and Post-loading performance of wet-loaded composite membrane samples. ................... 48 Table 3.4. Pre- and Post-loading performance parameters of wet-loaded substrate samples. .................... 51 Table 3.5. Morphological parameters of SB and PC substrates evaluated using different methods ........... 53 Table 3.6. Morphological parameters of wet-loaded SB substrates evaluated using DGM method .......... 53 Table 4.1. The physical and chemical properties of indoor gas-phase contaminants ................................. 61 Table 4.2. Permeability data for water vapor and CO2 in various film-forming polymeric materials ........ 63 Table 4.3. Properties of Celgard® 2500 substrate used to make composite membranes ............................ 65 Table 4.4. Properties of membrane coating materials ................................................................................. 66 Table 4.5. Experimental and modeled water vapor boundary layer resistance inside permeation test cell 73 Table 4.6. Experimental and modeled CO2 boundary layer resistances inside permeation test cell ........... 73 Table 4.7. Effect of membrane orientation on water vapor flux through different membranes ................. 79 Table 4.8. CO2 permeability (crossover) (Barrer (%)) values in different membranes .............................. 79 Table 6.1.  Properties of membrane material sample ................................................................................ 121 Table 6.2.  Geometrical specifications of the enthalpy exchanger core tested in this study. .................... 129 Table 6.3. AHRI test conditions................................................................................................................ 129 Table 6.4.  Modeling and experimental results of validation test enthalpy exchanger core. .................... 131     xiv  LIST OF FIGURES  Figure 1.1. ERV function in cooling (summer) and heating (winter) modes of operation ........................... 2 Figure 1.2. The geometry of a typical cross-flow fixed-plate enthalpy exchanger core ............................... 3 Figure 1.3. Schematic presentation of asymmetric composite membranes .................................................. 4 Figure 1.4. Permeation process scheme in (a) Microporous membranes  (b) Dense membranes (re-adapted from [45]) ...................................................................................................................................................... 5 Figure 1.5. Schematic representation of the transport of small molecules in dense membranes [47] .......... 6 Figure 1.6. Thesis outline; showing the chapters and their connections. .................................................... 11 Figure 2.1. The geometry of the cross-flow fixed-plate enthalpy exchanger cores used for dust loading tests .................................................................................................................................................................... 14 Figure 2.2. Experimental test apparatus developed for ERV core fouling tests ......................................... 16 Figure 2.3. Size distribution of generated aerosol from dispersing ISO A3 dust inside fouling test apparatus; Dg=1.23 µm, σg=1.62. ................................................................................................................................ 18 Figure 2.4. Deposition fraction of ISO A3 medium dust particles in ERV core samples ........................... 20 Figure 2.5. Comparing measured deposition fractions before and after first dust insertion (~150 grams) at 0.5 m/s ......................................................................................................................................................... 21 Figure 2.6. Impact of dust loading on the sensible and latent effectiveness of cross-flow ERV cores ...... 23 Figure 2.7. Dust loaded membrane and mass transfer resistances to water vapor transport through the membrane .................................................................................................................................................... 24 Figure 2.8. Impact of dust loading on static pressure drop across cross-flow ERV cores .......................... 25 Figure 2.9. Evolution of the normalized core pressure drop during the loading test .................................. 26 Figure 3.1. Fouling mechanisms of asymmetric composite membranes .................................................... 30 Figure 3.2. Schematic representation of concentration profiles within the boundary layers and the composite membrane during water vapor transport ..................................................................................................... 32 Figure 3.3. Schematic of the experimental test apparatus used for aerosol nanoparticle loading and deposition measurements ............................................................................................................................ 36 Figure 3.4. Normalized particle mobility size distribution of SGG and NaCl nanoparticles generated for membrane loading and deposition tests. ..................................................................................................... 36 Figure 3.5. Membrane permeation module [132] ....................................................................................... 37 Figure 3.6. schematic of water vapor permeation test apparatus ................................................................ 39 Figure 3.7. Schematic of a constant pressure/variable volume apparatus for gas permeation measurements .................................................................................................................................................................... 40 Figure 3.8. Deposition fraction of NaCl and SGG particles on the uncoated side of MA membrane ........ 42 Figure 3.9. Scanning electron micrographs of the surface of dry-loaded membrane samples .................... 43 Figure 3.10. Effect of particle charge on deposit formation patterns on membrane surfaces ..................... 44 Figure 3.11. Water vapor permeance comparison of dry loaded membrane samples versus their pristine value ............................................................................................................................................................ 46 Figure 3.12. Impact of relative humidity changes on dry salt deposit ........................................................ 47 Figure 3.13. Water vapor permeance comparison of wet loaded membrane samples versus their pristine value ............................................................................................................................................................ 48 Figure 3.14. Changes in water vapor permeance of composite membrane samples resulted from dry and wet particle loading cycles ................................................................................................................................. 49 xv  Figure 3.15. Substrate pore narrowing during wet loading experiments; (a) dry deposit layer at elevated relative humidity, (b) condensed water droplets, (c) salt crystals formed after a wet loading cycle .......... 50 Figure 3.16. Comparison of the changes in water vapor permeance of composite membrane and substrate-only samples under wet loading cycles ....................................................................................................... 52 Figure 3.17. Summary of fouling mechanisms from aerosols in asymmetric composite membranes; (a) hygroscopic particles, (b) non-hygroscopic particles.................................................................................. 54 Figure 4.1. Water vapor flux vs water vapor/CO2 selectivity in various commercially used polymeric films .................................................................................................................................................................... 64 Figure 4.2. Scanning electron micrographs of Celgard® 2500 film at 5k and 20k (inset) magnifications .. 65 Figure 4.3. Cross-sectional SEM micrographs of a commercial asymmetric composite membrane [27] .. 67 Figure 4.4. Schematic presentation of the mixed gas permeation (MGP) test apparatus............................ 69 Figure 4.5. Schematic representation of permeation test cell ..................................................................... 70 Figure 4.6. Boundary Layer Resistance Calibration of the permeation test cell at 30⁰C and 50⁰C, 50% RH on the feed side, and 1SLPM flow rate on both sides. ................................................................................ 71 Figure 4.7. Permeation cell total boundary layer resistance predicted from Sherwood correlation at different flow rates; (a) temperature effect (feed and sweep side activity values are 0.5 and 0, respectively, (b) feed water vapor activity effect with dry sweep (activity at 0). .......................................................................... 74 Figure 4.8. Water vapor permeability of a) PEBAX®1074, b) SPEEK, c) PU-PEO, d) CA at 30°C and 50°C .................................................................................................................................................................... 77 Figure 4.9. Membrane permeability measurement configurations ............................................................. 78 Figure 4.10. Water vapor/CO2 selectivity for four tested membranes: (a) 30°C and (b) 50°C ................... 80 Figure 4.11. Comparison of the selective performance of rubbery vs. glassy membranes at 30°C (hollow symbols) and 50°C (filled symbols)............................................................................................................ 82 Figure 5.1. An infinite film with the thickness 2l ....................................................................................... 85 Figure 5.2. Schematic drawing of the gravimetric moisture analyzer ........................................................ 90 Figure 5.3. Measurement routine for determination of equilibrium sorption and diffusion coefficients as a function of water vapor activity. ................................................................................................................. 91 Figure 5.4. Equilibrium sorption (open symbols) and desorption (filled symbols) isotherms at varying water vapor activity and dry film thickness at a constant test temperature (25⁰C). .............................................. 93 Figure 5.5. Equilibrium sorption (open symbols) and desorption (filled symbols) isotherms at varying water vapor activity and test temperature for a constant film thickness: PU-PEO (245µm) and PEBAX® 1074 (95µm). ....................................................................................................................................................... 94 Figure 5.6. Sorption (solid lines) and desorption (dashed lines) curves for a typical activity step (0.55-0.6) at varying test temperature for a constant film thickness: PEO-PU (245µm) and PEBAX® 1074 (95µm). .................................................................................................................................................................... 96 Figure 5.7. Sorption (solid lines) and desorption (dashed lines) curves for a typical test temperature (35⁰C) at varying activity steps for a constant film thickness: PU-PEO (245µm). ................................................ 97 Figure 5.8. Reduced sorption (solid lines) and desorption (dashed lines) curves at varying water vapor activity and dry film thickness for PEO-PU (a-c) and PEBAX® 1074 (d-f). As indicated in the legend of the figures, thicker lines represent thicker film samples. ............................................................................ 98 Figure 5.9. Impact of film thickness on the diffusion coefficient evaluated using half-time method for PEBAX® 1074 at constant temperature 25⁰C. The data from Potreck et al. (2009) is at different temperatures of 20⁰C and 30⁰C, but close to the test conditions of this work. ........................................... 99 Figure 5.10. Comparison between experimental sorption data and different sorption models for PU-PEO at various film thickness and constant temperature 25⁰C ............................................................................. 103 Figure 5.11. Impact of dry film thickness on diffusion coefficient at constant temperature 25⁰C. .......... 106 xvi  Figure 5.12. Effect of film thickness on the concentration profile development at short-times of sorption at a typical activity step (0.55-0.6)................................................................................................................ 108 Figure 5.13. Effect of film thickness on the Integral equilibrium diffusion coefficients for PU-PEO films at constant temperature 25⁰C. Solid symbols represent values calculated from desorption curves while hollow symbols represent values from the sorption curves. ................................................................................. 109 Figure 5.14. Integral Diffusion coefficients and Diffusion-Concentration correlation for PEO-PU films at varying temperatures from 5⁰C to 55⁰C. ................................................................................................... 110 Figure 5.15. Comparison of the measured steady-state permeability values with estimated values using Solution-Diffusion model for PU-PEO films of various thickness at different temperatures................... 110 Figure 6.1. Schematic of heat and moisture transfer through the asymmetric composite membrane. ...... 116 Figure 6.2. Schematic of a pair of core layers separated by a membrane plate  in cross-flow arrangement used in the mathematical model ................................................................................................................ 122 Figure 6.3. Membrane permeance at various supply and exhaust side activities at T = 35°C. ................. 127 Figure 6.4. Effect of temperature on water vapor permeance at various supply side activities ................ 128 Figure 6.5. Variations of enthalpy exchanger performance with air flow rate. The experimental measurements are shown by symbols, and the corresponding model predictions are shown by the faired curves. ....................................................................................................................................................... 130 Figure 6.6. Variations of  enthalpy exchanger performance with outdoor air relative humidity; comparison of constant permeability model and composite membrane model with variable permeability ................. 132 Figure 6.7. Variations of moisture flux through membrane surface; comparison of constant permeability model (dashed curves) and composite membrane model with variable permeability (solid curves) at 50% outdoor relative humidity. ......................................................................................................................... 133 Figure 6.8. Variations of  enthalpy exchanger performance with outdoor air state in cooling mode (flowrate = 544 m3/hr) .............................................................................................................................................. 134 Figure 6.9. Variations of  enthalpy exchanger performance with outdoor air state in heating mode (flowrate = 544 m3/hr) .............................................................................................................................................. 135 Figure 6.10. Contours of local membrane moisture transfer resistance, R M (sm); solid and dashed lines indicate cooling (Toutdoor = 35°C) and heating (Toutdoor = 1.7°C) modes, respectively. (RHoutdoor = 30%) . 136 Figure 6.11. Variations of average membrane moisture transfer resistance with outdoor air state; hollow and black symbols indicate cooling and heating conditions, respectively. ............................................... 136 Figure 6.12. Contours of dimensionless temperature in bulk air; solid and dashed lines indicate supply and exhaust sides, respectively. ....................................................................................................................... 137 Figure 6.13. Contours of dimensionless membrane surface temperature; solid and dashed lines indicate supply and exhaust sides, respectively. ..................................................................................................... 138 Figure 6.14. Membrane orientation effect at various outdoor air relative humidities; outdoor air temperatures are 35°C and 1.7°C for cooling and heating modes, respectively. ...................................... 139 Figure 6.15. Membrane orientation effect at various outdoor air relative humidities and a constant operating flowrate (544 m3/hr). ................................................................................................................................. 140    xvii  LIST OF SYMBOLS AND ABBREVIATIONS  Abbreviations ACH Air Change Rate per Hour AHRI Air-Conditioning, Heating and Refrigeration Institute ASHRAE American Society of Heating, Refrigerating, and Air-Conditioning Engineers ARD Arizona Road Dust ASTM American Society for Testing and Materials AWT Aerosol Wind Tunnel CA Cellulose Acetate DCV Demand Control Ventilation DGM Dusty Gas Model EATR Exhaust Air Transfer Ratio ERV Energy Recovery Ventilation ETS Environmental Tobacco Smoke GHG Greenhouse Gas GPU Gas Permeance Unit HRV Heat Recovery Ventilation HVAC&R Heating, Ventilation, Air Conditioning, and Refrigeration IAQ Indoor Air Quality MGP Mixed Gas Permeation  MIP Mercury Intrusion Porosimetry NSERC Natural Sciences and Engineering Research Council of Canada OACF Outside Air Correction Factor OPS Optical Particle Spectrometer OSHA Occupational Safety and Health Administration PEBAX Polyether block amide PEO Poly(ethylene oxide) PU Polyurethane RER Recovery Efficiency Ratio SBS Sick Building Syndrome SBSP Sustainable Building Science Program SEM Scanning Electron Microscope SGG Spark-Generated Graphite SMPS Scanning Mobility Particle Sizer SPEEK Sulfonated poly(ether ether ketone) STP Standard Temperature and Pressure UWT Uniform Wall Temperature UWF Uniform Wall Flux VOC Volatile Organic Compound WVTR Water Vapor Transfer Rate     xviii  Greek Letters 𝜀  effectiveness, surface porosity 𝜓  deposition fraction 𝛿  thickness 𝜖  aspect ratio 𝛤  shape parameter 𝜔  humidity ratio (kg-w/kg-dry air) 𝜃  dimensionless temperature 𝛺  dimensionless humidity ratio, fin conductance 𝜒  crossover (%) 𝛼  membrane selectivity 𝜌  Density (kg/m3) 𝜇  dynamic viscosity (kg/(m.s)) 𝛾  activity coefficient, latent-to-sensible heat ratio 𝜙  water vapor activity 𝜂𝑓𝑖𝑛  fin correction factor σg  geometric standard deviation 𝜆  thermal conductivity, thickness correction factor 𝛹  pore size distribution 𝜏  pore tortuosity 𝛽  surface relaxation rate (s-1) 𝜏𝐷  characteristic diffusion time 𝜏𝑅  characteristic relaxation time  Alphabetical Symbols Symbol Unit Description 𝑎 - , 𝑚𝑚 water vapor activity, triangular channel height (pitch) 𝑏 𝑚𝑚 triangular channel base 𝐷𝑝 𝜇𝑚 particle diameter 𝑑𝑝𝑜𝑟𝑒 𝜇𝑚 pore diameter 𝑁 𝑚−2 number of pores per unit area 𝐶 𝑚−3 particle number concentration 𝑇 ℃ (𝐾) temperature  𝑝𝑣 𝑃𝑎 partial vapor pressure 𝑝𝑖 𝑃𝑎 partial pressure ?̅? 𝑃𝑎 average pore pressure 𝐶𝑖 𝑚𝑜𝑙 𝑚3 ⁄  permeant (water vapor, CO2) concentration 𝐶 𝑚3 𝐻2𝑂(𝑣) (𝑆𝑇𝑃)𝑚3 − 𝑝𝑜𝑙𝑦𝑚𝑒𝑟 water equilibrium concentration in the polymer 𝐶𝑝 𝐽𝑘𝑔. 𝐾⁄  specific heat capacity 𝑣 𝑚 𝑠⁄  air velocity 𝜈𝑣 𝑑𝑚3𝑚𝑜𝑙⁄  molar volume of water vapor xix  𝜈𝑎 𝑑𝑚3𝑚𝑜𝑙⁄  molar volume of air 𝑣𝑀 𝑚𝑠⁄  mean molecular velocity ?̇? 𝑘𝑔 𝑠⁄  mass flow rate 𝑄 𝑚3 𝑠⁄  volumetric flowrate ℎ𝑓𝑔, ∆𝐻𝑣 𝑘𝐽𝑘𝑔⁄  latent heat of vaporization or condensation 𝑞𝑎𝑑 𝑘𝐽𝑘𝑔⁄  heat of adsorption 𝐽 𝑚3(𝑆𝑇𝑃) 𝑚2 . 𝑠⁄  mass flux 𝐽0 𝑚3(𝑆𝑇𝑃) 𝑚2 . 𝑠⁄  initial flux through the unblocked membrane 𝑞 𝑘𝑊 𝑚2 ⁄  heat flux ∆𝑃 𝑃𝑎 pressure drop ℎ 𝑘𝑊 𝑚2 𝐾⁄ ,  𝑘𝐽𝑘𝑔⁄  convective heat transfer coefficient, enthalpy of humid air 𝑘 𝑚 𝑠⁄ , 𝑠−1 convective mass transfer coefficient, bulk relaxation constant 𝑅 𝑀 𝑠 𝑚⁄  mass transfer resistance 𝑅 𝐻 𝑚2 𝐾 𝑘𝑊⁄  heat transfer resistance 𝑚  flow exponent, mixing parameter 𝐴 𝑚2 area 𝐴0 𝑚2 unblocked membrane area 𝑅 𝐽𝑘𝑔. 𝐾⁄ , 𝑠𝑚⁄  specific gas constant, mass transfer resistance 𝑀 𝑘𝑔𝑚𝑜𝑙⁄  molecular weight 𝑉𝑚 22.414 𝑑𝑚3𝑚𝑜𝑙⁄  molar volume of gas at STP 𝐺 𝐺𝑃𝑈 = 10−6𝑐𝑚3(𝑆𝑇𝑃) 𝑐𝑚2 . 𝑠. 𝑐𝑚𝐻𝑔 permeance ℘ 𝐵𝑎𝑟𝑟𝑒𝑟= 10−10𝑐𝑚3(𝑆𝑇𝑃). 𝑐𝑚 𝑐𝑚2 . 𝑠. 𝑐𝑚𝐻𝑔 permeability 𝑆 𝑐𝑚3(𝑆𝑇𝑃) 𝑐𝑚3. 𝑐𝑚𝐻𝑔 solubility coefficient 𝐷 𝑚2𝑠⁄  diffusion coefficient 𝐷𝑣𝑎 𝑚2𝑠⁄  vapor diffusivity in air 𝐷𝐾𝑛 𝑚2𝑠⁄  Knudsen diffusion coefficient 𝐷𝑉𝑚 𝑚2𝑠⁄  measured diffusion coefficient 𝐷𝑉 𝑚2𝑠⁄  mutual  diffusion coefficient 𝐿 𝑚 membrane channel length 𝑙 𝑚 film thickness 𝐷ℎ 𝑚 hydraulic diameter xx  𝑊𝑐 𝑚 core width 𝐻𝑐 𝑚 core height 𝐷𝑐 𝑚 core depth 𝑅𝑒  Reynolds number 𝑆ℎ  Sherwood number 𝑓  fanning friction factor 𝐿𝑒  Lewis number 𝑃𝑟  Prandtl number 𝑥∗  dimensionless x coordinate 𝑦∗  dimensionless y coordinate 𝑍∗  dimensionless channel length 𝐷𝑔 𝜇𝑚 geometric mean particle diameter 𝐾0 𝑚 morphological parameter related to Knudsen diffusion 𝐵0 𝑚2 morphological parameter related to viscous flow 𝑞2  pore tortuosity 𝐹𝐹  fouling factor 𝐷𝐸𝐵𝑠  surface Deborah number 𝐷𝐸𝐵𝐵  bulk Deborah number 𝑀∗  fractional moisture uptake 𝑀∞ 𝜇𝑔 equilibrium moisture content 𝑀0 𝜇𝑔 initial moisture content 𝑆𝐼 𝑠−12⁄  initial slope 𝜙𝑉  volume fraction of water vapor in the swollen polymer 𝑀𝑑  fractional moisture uptake due to Fickian diffusion 𝑀𝑟  fractional moisture uptake due to polymer relaxation  𝑁𝑢𝛺𝑇   fully-developed Nusselt number based on fin conductance  Superscripts 𝑚 membrane surface, mass transfer ℎ heat transfer 𝑏 bulk air ∗ interface 𝑆 sensible 𝐴 adsorption 𝑣 vapor 𝐹 feed 𝑃 permeate 𝑀 mass transfer 𝐻 heat transfer 𝑐 coating    xxi  Subscripts 1 Feed inlet 2 Feed outlet 3 Sweep inlet 4 Sweep outlet 𝑐 coating 𝑚 membrane 𝑠𝑢𝑏 substrate 𝑠 supply, standard conditions 𝑒 exhaust, estimate ∗ interface 𝑆 sensible 𝐿 latent 𝑇 total 𝑖𝑛 inlet 𝑜𝑢𝑡 outlet 𝑞 heat transfer √𝐴 based on square root of flow area 𝑓 final 𝑤 water 𝑝 polymer 𝑎 air 𝑣 vapor 𝐹 feed 𝑃 permeate 𝐵𝐿 Boundary layer 𝑈𝑝 upstream 𝐷𝑜𝑤𝑛 downstream 𝐵 background 𝑚𝑖𝑛 minimum     xxii  ACKNOWLEDGMENTS I would like to express my gratitude to my supervisor Dr. Steven Rogak for his distinguished supervision, patience, and continuous encouragement. His enthusiasm and dedication to science have always kept me motivated. I would like to extend my gratitude to my co-supervisor Dr. Sheldon Green for his insightful guidance and constructive criticism throughout this research work. It was an honor for me to work with such a knowledgeable leader. Many thanks to my supervisory committee members, Dr. Frank Ko, Dr. Savas Hatzikiriakos, and Dr. Walter Mérida. Their valuable suggestions sharped my understanding and helped me improve my research findings. I would also like to acknowledge Dr. Ryan Huizing for his continuous support and productive discussions. His thoughtful suggestions helped me to address several challenges I faced during this research work. I would like to thank the R&D team at dPoint Technologies, especially Dr. Hao Chen, Frankie Wong, Scott Dornian, and David Kadylak. Their valuable technical support and scientific feedbacks were invaluable in conducting the experiments. My colleagues at Aerosol Lab, Alexander Sylvester, Ali Vaseghi, Raj Lankinen, Sarah Romani, Julien Peret, Sarah Crosby, Hunarbir Singh, Matt Grant, Bastien Caron, Guilhem deSteve, Charlie Guilloton, Loic Marduel. Your assistance was imperative toward the completion of this work. My friends especially Ramin Dastanpour, Pouyan Kheirkhah, and Pouyan Jahangiri. Thank you for all the laughs and the wonderful time we have had together. Thanks will not be enough for my parents, from whom I have constantly been away. Your unconditional love and unselfish support give me the strength to pursue my dreams. Special thanks to my lovely brother, Ali, for his moral support and emotional reinforcement. My love, Hoda, you have always been the emotional support at the difficult times of my PhD. Thank you for believing in me and providing balance in my life. I appreciate the financial support of Natural Sciences and Engineering Research Council of Canada (NSERC) through Sustainable Building Science Program (SBSP), an ENGAGE GRANT-EGP461388-13 and a CRD Grant-CRDPJ485151-15 – both sponsored by dPoint Technologies Inc., and ASHRAE through a grant-in-aid.      xxiii  DEDICATION      To my wife and parents, my inspiration and motivation       1  Chapter 1 - INTRODUCTION  1.  1.1.  BACKGROUND 1.1.1. Energy Recovery in Building Ventilation Systems The building sector is responsible for a significant fraction of total energy consumption and associated greenhouse gas (GHG) emissions worldwide [1]. Recent reports indicate that residential and commercial buildings account for 41% of the primary energy use in the United States [2] and 27% in Canada [3]. Heating, ventilation, and air conditioning (HVAC) systems are responsible for roughly 50% of the total energy consumption in the building sector in North America (48% in the United States [4] and 57% in Canada [3]). This means that over 8% of all GHG emissions in North America are associated with HVAC systems. The building air relative humidity and temperature need to be controlled to maintain occupant thermal comfort [5], [6], and health, as well as the service life of the building. Concerning occupant health, it has been shown that high relative humidity and potential moisture condensation facilitates the survival and growth of fungi and mites, which may increase the risk of respiratory infections and allergies. Also, the abundance of bacteria and viruses is directly dependent upon the relative humidity. The narrow range between 40-60%RH has been suggested to minimize the growth of these biological contaminants [7]. As for the building service life, the prolonged moisture accumulation at very high relative humidity may make the building materials susceptible to mold growth and bio-degradation [8]. Depending on the building application and geographical location, varying levels of space conditioning are required with two distinct processes; 1) addition or removal of “sensible energy” (i.e., heating or cooling air), and 2) addition or removal of “latent energy” (i.e., humidifying or dehumidifying air).  Furthermore, supplying adequate levels of fresh outdoor air to the building is necessary for maintaining indoor air quality [9], [10]. Although improved building design (e.g., air sealing and improved insulation) and operation (e.g., advanced occupancy-level sensor and control systems for demand control ventilation (DCV)) may achieve significant reductions in heating and cooling loads of buildings, there will always be a need for mechanical air conditioning systems. Fresh outdoor air will need to be conditioned and replaced with stale indoor air for continuous ventilation. This is increasingly important in modern buildings with higher levels of air-tightness. Also, heat and moisture generated by occupants and building equipment will need to be removed. Energy recovery devices could “recycle” the energy which has already been used to condition the exhaust air, making for a better trade-off between energy expenditure, thermal comfort, and air quality than conventional air conditioning systems. Air-to-air Heat Recovery Ventilation (HRV) and Energy Recovery Ventilation (ERV) devices have become an integral part of energy-efficient ventilation systems. HRV/ERV devices recycle the sensible and latent energy in the exhausted air and use it to pre-condition the fresh incoming outdoor air. HRVs use heat exchanger cores that allow heating of the cool incoming air by warm exhausted air (or vice versa if the building is cooled). ERVs use heat and mass exchanger cores Chapter 1 – Introduction 2  (also known as ‘enthalpy exchangers’) that can also exchange moisture between the two air streams. In ‘cooling conditions’ (as shown in Figure 1.1), incoming warmer, more humid air is cooled and dehumidified in an ERV, while in ‘heating conditions’, incoming cool and dry air is heated and humidified by exhaust air from the building [11].  Figure 1.1. ERV function in cooling (summer) and heating (winter) modes of operation  Incorporating HRVs/ERVs into HVAC systems not only reduces the operational cost of air conditioning (i.e., energy demand for the conditioning of incoming air) but also lowers the capital cost of the system as they allow down-sizing HVAC equipment due to the reduced air conditioning load. Additionally, as the ERV/HRV partially condition the incoming fresh air, they would allow increased fresh air supply and thus improved IAQ with a low energy penalty [12]–[15]. ERVs are especially beneficial over HRVs in hot and humid climates, where the latent load constitutes a significant fraction of the total air conditioning load [16]–[18]. It has been shown that heat and moisture recovery using high-efficiency ERVs could save up to 65% of the energy used for fresh air treatment and up to 20% of the total cooling load in hot and humid climates [13], [15], [19]. Even in heating conditions, particularly in cold climates like Canada, using ERVs are beneficial over HRVs. The condensed moisture in HRVs must be captured by a drain system while ERV membranes allow the transfer of this moisture to the dry incoming air. This improves the low indoor humidity levels often experienced in winter conditions with sub-freezing outdoor temperatures. Also, less defrosting cycles are needed using ERVs compared to HRV systems (i.e., saving energy), as the additional transport of moisture through membranes lowers the temperature at which frosting is initiated [20]. Chapter 1 – Introduction 3  1.1.2. Membrane-Based Energy Recovery Ventilators Air-to-air energy exchangers are categorized into different groups based on the geometry of the exchanger and the air flow arrangement, including plenum chambers, adsorptive switching chambers, rotary wheels, membrane-based exchangers, and twin tower energy recovery loops [21]. Increasing attention is paid to membrane-based technology because of small footprint, compactness and modular design, simplicity, and reduced contaminant crossover [19], [22], [23]. Membrane-based ERVs use water vapor permeable membranes in the construction of their exchanger cores to separate indoor and outdoor air streams. Fixed-plates and frame is the most common configuration of these exchanger cores [24]–[27]. However, hollow fiber membrane module designs have also been reported for this application [28], [29]. Possible flow arrangements in fixed-plate exchangers are cross-flow, counter-flow, or a combination of these flow arrangements (i.e., quasi-counter-flow). Due to their ease of manufacturing and installation, cross-flow is the most widely adopted flow arrangement. They can be efficiently made by stacking membrane plates together separated by some spacer (i.e., essentially plate-fin channels) or individual solid panel with several internal airstreams. Figure 1.2 shows the exchanger core of a typical cross-flow, plate-fin membrane-based ERV using corrugated spacer sheets. The supply and exhaust airstreams flow along the triangular plate-fin channels in a cross-flow pattern and exchange heat and moisture through the membrane. Alternate layers of membranes, separated and sealed, form the supply and exhaust airstream passages.  Figure 1.2. The geometry of a typical cross-flow fixed-plate enthalpy exchanger core  Chapter 1 – Introduction 4  The membrane media is the central functional component of a membrane-based ERV exchanger. Ideally, membranes used for ERVs should be highly water vapor permeable to achieve high effectiveness in a compact exchanger design (see Figure 1.3). They also need to be sufficiently selective for water vapor over other gases, VOCs, and contaminants that might be present in outgoing indoor air stream [30], [31]. This is essential for preventing cross-contamination issues between the exhaust and fresh intake air streams and meeting building codes requirements [9], [32].  Figure 1.3. Schematic presentation of asymmetric composite membranes  Researchers have converted fixed-plate sensible heat exchangers into membrane-based enthalpy exchangers more than 40 years ago, by replacing the heat-conductive plates with moisture-permeable paper plates [33]. Many commercially available membrane-based ERVs still use such paper-based material as the membrane media. More recent paper-based membrane materials have been improved over older generations by treatment methods such as impregnation with hygroscopic salts and desiccant materials [34]–[36]. Although paper-based ERV exchanger cores can be made inexpensively, they suffer from some practical issues, including low moisture transfer performance, relatively high contaminant crossover rates, poor longevity particularly under wet conditions and freeze-thaw cycles in cold climates, and susceptibility to biological fouling and degradation by mold and bacteria [27]. Alternative materials for ERVs are synthetic polymeric membranes. These membranes are typically characterized based on their pore structure; dense and porous with pore sizes in the order of 0.1 nm and 0.1 µm, respectively. Over the past decade, researchers have explored a number of different dense and porous polymeric membranes for ERV application [31], [36]–[42]. Using porous polymer membranes has been reported to result in high moisture transfer efficiencies in ERVs. However, they do not provide the desirable selective function as a porous membrane essentially transfers all gases and contaminants present in building exhaust air streams. Unlike the porous membranes, the transport in dense polymer membranes is moderated based on the amount of permeant species that absorb into the polymer and the rate at which they diffuse through the polymer. Very high water vapor/contaminant selectivity’s (>100) can be achieved du to large differences between the sorption and diffusion of moisture with those of contaminants. Dense membranes, however, need to be made sufficiently thick (>15µm) to provide mechanical and handling properties required for manufacturing ERV exchanger cores [27], which compromises Chapter 1 – Introduction 5  their moisture transfer rates. Free-standing films of dense hydrophilic polymer which are particularly interesting for ERV application, also suffer from dimensional stability due to their significant swelling by water at high relative humidity values [27]. Current-generation ERV membranes typically consist of a polymeric microporous layer as the support for a relatively thin (<2µm) perm-selective dense polymer film, resulting in an asymmetric composite configuration (See Figure 1.3) [43]. The substrate layer provides mechanical strength to the resultant membrane with minimal selectivity function, while the dense coating layer provides a true selective barrier. The substrate also provides dimensional stability to the selective coating layer where the coating layer is exposed to the potential swelling (i.e., high relative humidity, freezing, and condensing conditions). Such composite membranes can maintain a high water vapor transfer rate without allowing high levels of crossover of contaminants from outgoing to incoming air [30], [44]. 1.1.3. Transport in Polymeric Membranes A membrane, in principle, is an interface that moderates the permeation of species in contact with it when a driving force is applied (e.g., pressure, concentration, temperature or voltage gradient across the membrane) [45]. Isotropic membranes, based on their pore structure, are generally classified into two categories: microporous and dense. The structure and function of a microporous membrane are very similar to a conventional filter. They have large, permanent pores in their structure (size range 0.01-10μm) which allow the penetrant molecules (e.g., water vapor) to diffuse through the air/vapor mixture within the pore space. In contrast, dense membranes have no visible/well-defined pores in their structure, and penetrant molecules adsorb onto the polymer and diffuse through the polymer matrix on the molecular level [45].   (a) Microporous membranes; separate by molecular filtration (Pore-flow mechanism) (b) Dense membranes; separate due to differences in the solubility and diffusivity of permeants in the membrane material Figure 1.4. Permeation process scheme in (a) Microporous membranes  (b) Dense membranes (re-adapted from [45])  Figure 1.4 shows schematic representations of the two transport models used to describe the mechanism of permeation. The pressure-driven convective flow, known as pore-flow model, is Chapter 1 – Introduction 6  responsible for permeate transport through tiny pores of the microporous layer. Separation in a microporous membrane is achieved mainly based on the molecular size sieving mechanism. The mass transport through dense membranes is usually described by the solution-diffusion mechanism. The permeants dissolve into the membrane material and then diffuse through the membrane down a concentration gradient. Separation in dense membranes is achieved due to the differences in solubility and diffusivity of permeants in the membrane material. The underlying physics of solution-diffusion could be described by the "hopping" mechanism. A permeant molecule oscillates most of the time inside a microcavity formed of free volume elements between surrounding polymer chains. Thermally stimulated motions of these chains occasionally open a transient gap of sufficient size as a passage to permit the permeant to "jump" into an unoccupied neighboring microcavity (see Figure 1.5). These jumps, caused by the concentration gradient, are responsible for the direction of transport. The frequency and magnitude of the jumps depend on the size of the permeant molecules as well as on the free volume of the polymer and mobility of the polymer chains. The smaller the permeant molecules are, the more frequent and more extended are the jumps, and hence the diffusion rate of the permeant in the polymer is higher. The frequency of the jumps and the chain mobility increase with the temperature; therefore, the diffusivity also increases with increasing temperature [45], [46].  Figure 1.5. Schematic representation of the transport of small molecules in dense membranes [47]  The solution-diffusion model is described as follows [48] 𝑱𝒊 = ℘𝒊𝒑𝒊,𝑭 − 𝒑𝒊,𝑷𝜹 (1.1)  where, 𝐽𝑖 is the permeate flux of component i through the membrane, ℘𝑖 is the membrane permeability for component i, 𝑝𝑖,𝐹 and 𝑝𝑖,𝑃 indicate the permeate partial pressures at the feed and sweep sides of the membrane, respectively, and 𝛿 is the membrane thickness. Using the Fick’s first law of diffusion, one can define the permeability of component i through a dense polymer membrane as ℘𝒊 = 𝑫𝒊. 𝑺𝒊 (1.2)  where, 𝑆𝑖 is the solubility coefficient, a thermodynamic parameter accounting for the absorbed amount of permeating component i in the polymer, and 𝐷𝑖 is the diffusivity, a kinetic parameter determining the magnitude of permeability for the component [48]. Chapter 1 – Introduction 7  The selectivity of a dense membrane for component i over component j is consequently defined as the ratio of their permeability values. 𝜶𝒊𝒋⁄=℘𝒊℘𝒋=𝑺𝒊𝑺𝒋.𝑫𝒊𝑫𝒋 (1.3) 1.1.4. Air Quality Considerations Indoor air quality (IAQ) is the most significant factor in our exposure to environmental pollutants. Maintaining an acceptable level of IAQ is crucial for occupant health and comfort. Adverse effects of inadequate ventilation rates on the well-being and performance of occupants (e.g., the so-called Sick Building Syndrome (SBS)) are extensively reported in the literature [49]–[52]. The major factors determining thermal comfort and air quality indoors are temperature, humidity, and concentrations of airborne particulates and gas-phase pollutants. The trade-off between energy consumption and adequate ventilation is well-known to architects and engineers, but the nature of the trade-off has evolved with building and HVAC technology. Humidity control is typically achieved using vapor-compression heat pumps. These systems are inefficient as they cool the moist air until the moisture condenses out. The cooled air then needs re-heating to a comfortable temperature. In energy-efficient buildings with a well-designed envelope, controlling humidity with vapor-compression systems is more challenging. Energy improvements often reduce the building's sensible load (e.g., from improved insulation), but do not affect the latent load (e.g., from required ventilation or internal gains) [53]. The use of ERV systems allows increased fresh air supply with a low energy penalty. However, during winter, condensation may occur in the exhaust stream, while in warm, humid conditions, condensation may happen in the supply air side (i.e., fresh air stream). Condensation and high humidity can contribute to the microbial growth and unhealthy indoor conditions [7]. Building standards such as ASHRAE 62.1 and 62.2 [9], [10] regulate minimum-required-ventilation rates for an acceptable indoor air quality based on different space use and occupant densities. With IAQ becoming a more significant concern, air change rates per hour (ACH) as high as 0.5 h-1 for new residential houses are recommended by some studies [54] and building standards [10], [55]. The requirement for improved indoor air quality necessitates the use of almost 100% fresh air in HVAC systems for specific buildings, such as hospitals, labs, casinos, and gaming spaces, resulting in a significant increase in the building cooling/heating loads [56]. HVAC systems in such spaces require a significant amount of outdoor air (up to 30 ACH) to dilute highly contaminated indoor air and to achieve the standard building code mandate, making them extremely demanding of energy. The use of ERVs in such a setting has the potential to reduce the energy cost of the ventilation system substantially. However, ERV use could potentially recycle some of the contaminants through contacting incoming and outgoing air streams and negatively impact IAQ. ERV exchangers with polymeric membranes are typically more selective than desiccant wheels and paper-based exchangers (i.e., the incumbent technology), but under some circumstances, crossover of unwanted gases (e.g., CO2), offensive odors, and toxic contaminants (e.g. VOCs with short- and long-term adverse health effects, such as Formaldehyde and Benzene) could be Chapter 1 – Introduction 8  significant. Examples are recovery from class 2 and class 3 return air streams, such as restrooms, kitchens, dry cleaners, beauty salons, and laboratories [9]. Increasing ventilation flowrate can minimize or completely mitigate contaminant crossover, but this reduces the net energy recovery achieved by latent heat recovery in an ERV. Furthermore, membrane-based ERVs might become suited for broader indoor spaces if sufficiently low crossover can be guaranteed. 1.1.5. Membrane Fouling by Aerosols Although membrane-based ERVs are commercial products, membrane durability and useful lifetime of the exchanger cores are still unclear. As no report has been found in the literature addressing the in-field longevity of membrane-based ERVs, questions have arisen about the consequences of air pollution and other environmental stresses on their performance [11]. Fouling is considered as one of the challenges in membrane-based separations and has been studied extensively in microfiltration (MF), ultrafiltration (UF), nanofiltration (NF), reverse osmosis (RO) and evaporative systems [57]. The membrane-based ERVs for HVAC applications are expected to have less fouling issues compared to these industrial membrane filtration processes, where pressure forcibly pushes water and foulant particles through the membrane. However, research is needed to understand the effects of environmental conditions and pollutants on the extent of potential air-side fouling and consequently on the useful life of the membrane in ERV exchanger cores. Deposition of aerosol particles on the surfaces of asymmetric membranes may result in degradation of water vapor permeability. This is mainly due to partial or complete pore blockage of the porous substrate, or failure of the dense layer when aerosols are water-soluble or chemically active [58]. In particular, for highly contaminated exhaust air streams, such as industrial kitchen exhaust streams, lab fume hoods, casinos and smoking lounges, a high concentration of aerosols containing liquids and condensable VOCs (e.g., cooking oils and tobacco smoke) could be detrimental to membrane performance. Building standards currently restrict energy recovery from some of these applications. However, ERVs with highly selective polymeric membranes could result in significant energy savings in these applications if potential fouling can be mitigated or controlled by proper measures such as adequate filtration and scheduled cleaning. 1.1.6. Heat and Mass Transfer Modeling in Membrane-based ERVs The performance of an air-to-air ERV exchanger core is defined by ANSI/ASHRAE standard 84-2013 [32] in terms of sensible (heat transfer) and latent (moisture transfer) effectiveness, supply and exhaust air-friction pressure drops, exhaust air transfer ratio-EATR (i.e. bulk crossover leakage of air and unwanted gases within the core due to pressure differences and carry-over), outside air correction factor-OACF (i.e. bulk air mass flow differences between the inlet and outlet of supply outdoor air), and recovery efficiency ratio-RER (i.e., the ratio of the energy recovered divided by the operational energy expended). Core-level effectiveness depends on the flow patterns in the core and the membrane characteristics. Sensible effectiveness is mainly dominated by the flow characteristics and arrangement in the exchanger channels. The overall thickness of the composite membrane is thin enough to have negligible thermal resistance. However, the transport resistance to water vapor is substantial Chapter 1 – Introduction 9  (similar magnitude to the air-side resistance of the core), and the thin selective coating completely dominates the resistance to transport of other gases. Core-level latent effectiveness is complicated by the variable moisture permeability of the membrane which varies with relative humidity, material properties, and aging. Water vapor transport is much higher at the warm, humid end of the core, where flow design would be most critical. These observations indicate that the overall ERV performance depends on more than the membrane transport characteristics, and it is imperative to have predictive models that can link membrane characteristics to ERV performance. The modeling attempts to solve the coupled heat and moisture transport in the ERV cores have been developed in two main categories. The first category considers the use of shortcut effectiveness-NTU equations [13], [34], [35], [59]–[62]. This method provides a fast estimate of the sensible, latent and enthalpy effectiveness, specific to the operating flow rates and the design of the system. However, it fails to provide insight into the mechanisms of heat and mass transport in the exchanger core. The second modeling category is based on discretizing the partial differential equations of heat and mass transfer into a system of algebraic equations and solve them iteratively [63]–[69]. In full CFD simulations, the governing equations of mass, momentum, and energy conservation are solved simultaneously [70]–[73]. However, when applicable, the empirical/analytical correlations have been used to approximate some components of the flow without significantly compromising the accuracy of the modeling [63], [65]–[67], [74]. A number of parameters may affect the complexity of the aforementioned modeling categories, such as considering spacer-filled channels over the bare parallel plate channels  [75]–[77], quasi-counter-flow arrangement over the cross-flow arrangement [78], and assessing the effect of heat of adsorption on energy and mass flows across a membrane [65]–[67], [78]–[80]. 1.2.  MOTIVATION Energy recovery systems are becoming a more critical part of building engineering. In the last two decades, many countries have introduced new regulations, standards, and codes for the incorporation of air-to-air energy recovery devices into building HVAC systems [81], [82]. ERVs using water vapor permeable membranes have great promise but are relatively new. Results of long-term field studies are not available due to the recent implementation of this technology. However, there are preliminary indications that water vapor transport might degrade with the extended operation, possibly as a result of exposure to air pollution (i.e., particle fouling), or other environmental stresses [11]. We have not found any reported study on the impact of airborne particulate fouling on water vapor transfer through membranes and the overall performance of fixed-plate ERV exchangers. ERVs may be used in different climates spanning a wide range of operating temperature and humidity. It is well-documented in the membrane gas separation literature that permeation properties of polymeric membranes, particularly for water vapor and larger, highly condensable permeant molecules such as organic vapors, vary significantly with the operating temperature and vapor pressures on feed and permeate sides of the membrane [83]–[85]. The diffusivity of water vapor may increase or decrease with the amount of water in the polymer [86]. Depending on membrane material, increased chain mobility due to moisture-induced swelling and concurrent plasticization (softening) of polymer matrix at different temperature and relative humidity levels Chapter 1 – Introduction 10  [87], [88], as well as clustering effects of water molecules [89], are reported reasons. Nonlinear sorption properties of moisture in polymers have also been extensively studied [88]–[92]. As a result, the moisture permeability of current-generation, asymmetric composite ERV membranes is a function of operating conditions (temperature and relative humidity) on both membrane sides [85]. It is therefore essential to quantify the effects of operating conditions on the moisture permeability of membranes and thus the overall effectiveness of exchanger cores in ERV systems. The membrane selectivity for water vapor over indoor contaminants may also depend on environmental factors, although even for laboratory conditions the unwanted transport of gases and VOCs is not well understood.  Recent reports indicate that transport of certain gaseous and vapor species in polymer membranes may be strongly affected by membrane moisture uptake at various humidity levels and by the temperature of working airstreams [88], [93]–[95]. Current methods for evaluating ERV contaminant crossover in building standards, such as ASHRAE 84-2013, focus on the measurement of the EATR based on inert tracer gas tests and single test conditions. Although this method might be appropriate for measuring defects and leakage in exchangers, it may not account for the permeation phenomena involved in the crossover of indoor contaminants through polymeric systems. The current tracer gas method of testing EATR in ASHRAE Standard 84 based on non-condensable SF6 gas appears to be insufficient to predict crossover of all contaminants in membrane-based ERVs [30]. Understanding the transport phenomena involved in the crossover of contaminants at different operating conditions will provide guidelines for future material development. The membrane-based ERVs might also be used in a broader range of applications if crossover can be guaranteed to be sufficiently low. 1.3.  RESEARCH OBJECTIVES AND THESIS OUTLINE Driven by the stated motivations, the scope of this dissertation is to measure the influence of environmental factors including airborne particulate matter, relative humidity, and temperature on the permeation properties of the membrane media and the performance of full energy exchanger cores of membrane-based ERV systems. The first goal of this Ph.D. study is to assess the potential particulate fouling via investigating different permutations of operating conditions and atmospheric aerosols of different chemistry that may be experienced by ERVs in HVAC systems. It is postulated that such an investigation would be beneficial in determining the optimal operation and fouling control strategies such as filtration selection in different environments with indoor and outdoor aerosols of different nature. The second goal is to address the impacts of in-service operating conditions (humidity and temperature) on both membrane media permeation properties and exchanger core effectiveness. A full experimental evaluation of these variations, even at a material-level, is cumbersome and often takes several hours for each such test to reach steady state conditions. It is postulated that the performance variations of a membrane-based energy exchanger may be predicted by conducting a limited number of transient material permeation tests. This fundamental understanding will also allow for optimal operation of ERV systems, leading to improved overall efficiency of building ventilation. With this framework in mind, the research objectives are as follows: Chapter 1 – Introduction 11  1) Measure the impact of particulate fouling on the performance of membrane-based ERVs both at the exchanger and material scales for coarse (>1μm) and fine (~ 0.1μm) aerosols. 2) Investigate the impact of aerosol chemistry and hygroscopic properties on fouling behavior of asymmetric composite membranes and provide recommendations to control and minimize airborne particulate fouling that can guide design and operations. 3) Measure mixed gas permeation properties of water vapor and CO2 for various ERV membranes at different levels of humidity and temperature. We expect that different membrane materials (e.g., glassy vs. rubbery) will be better or worse for some applications. 4) Develop a modeling framework for evaluating moisture permeation in composite membranes with various physical properties under variable operating conditions. 5) Develop a computationally fast model of coupled heat and mass transfer to investigate the effects of variable operating conditions the performance of fixed-plate, membrane-based enthalpy exchangers.  Figure 1.6. Thesis outline; showing the chapters and their connections. Chapter 1 – Introduction 12   Figure 1.6 depicts an outline of this dissertation with the subjects addressed in each chapter and their relations. Chapter 1 (this chapter) provides relevant background information, underlying motivation, and overall objectives of this research. Chapter 2 addresses the first objective of this research by conducting accelerated core-level fouling experiments in an Aerosol Wind Tunnel (AWT) test facility. The impact of coarse dust accumulation on the performance of ERV cores is investigated by comparing pre- and post-fouling measurements of the sensible and latent effectiveness of residential-size enthalpy exchangers. In Chapter 3, the second objective of this research is addressed. The effects of fouling with aerosol nanoparticles on the membrane material performance and physical properties are examined. Accelerated membrane-level experiments determine the fouling rate and initial and post-fouling performance of three commercial membrane samples. Furthermore, microscopic analysis is used to provide details of membrane fouling and particle deposit morphology relative to membrane pores. The results of a case of extreme fouling with environmental tobacco smoke (ETS) are also presented in Appendix B to support the findings of Chapter 3. Chapter 4 aims to address the third objective of this work. It reports on mixed gas water vapor/CO2 permeation measurements through a series of standard polymers at different levels of humidity and temperature. Recommendations for selection of membrane material are provided for applications where a high latent performance or minimal contaminant crossover are desired. Chapter 5 provides methods and experimental data of moisture permeation properties (diffusion, solubility, and permeability coefficients) of two highly water vapor permeable polymers suitable for fabrication of membrane media for ERV exchangers. This chapter also provides a fundamental understanding of the variations of such permeation properties under various operating temperatures, and relative humidity required for modeling and evaluation of the performance of both membrane and enthalpy exchanger in the following chapter. Chapter 6 combined with Chapter 5 address the last two objectives of this research. It presents a generalized approach for modeling moisture permeation through asymmetric composite membranes by combining pore-flow and solution-diffusion flux models. A mathematical model of membrane-based ERV exchangers is also developed that can relate the material properties to the exchanger performance. In this model, the composite membrane permeability model is coupled with a finite difference scheme for modeling coupled heat and mass transfer in a cross-flow exchanger core. Impact of variable operating conditions, specifically the temperature and humidity of the air streams, on the exchanger effectiveness are studied. Chapter 7 summarizes the results and contributions of this study. It also provides recommendations for implementation of the current results and an outlook on future research work.   13  Chapter 2 - DUST FOULING OF FIXED-PLATE ENTHALPY EXCHANGERS1  2.  2.1. OVERVIEW This chapter addresses the first objective of this study. A test facility and experimental procedures, developed for fouling assessment of full-size ERV cores, comprised of deposition fraction measurements, accelerated loading tests, and pre- and post-loading performance measurements are described in this chapter. The impact of air-side particulate fouling on the performance of typical membrane-based, fixed-plate enthalpy exchangers is investigated for both fine and coarse (0.3-10µm) aerosols. Two residential size cross-flow enthalpy exchanger cores were fouled with ISO A3 medium test dust (also known as Arizona road dust). It was found that coarse dust loading, equivalent to that of a few years of exposure in a heavily polluted environment, has minimal impact on the performance of ERV exchanger cores. In both cases, the sensible and latent effectiveness were actually slightly enhanced due to potential boundary layer thinning and additional flow recirculation on the fouled air-side caused by the dust deposit layer. Heavy dust loadings, in the absence of appropriate filtration upstream, may result in a fan energy penalty (~50%) due to the added pressure drop across the exchanger cores.                                                                1 This chapter has been part of the following publication: “Particulate fouling assessment in membrane based air-to-air energy exchangers”. Energy and Buildings, Volume 150, 1 September 2017, Pages 477-487. Copyright © 2017 Elsevier B.V. All rights reserved. Reprinted with permission. Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 14  2.2. INTRODUCTION Membrane fouling may occur on the airside of membrane-based ERVs as airborne particulate fouling, or biological fouling [96]. The sensitivity of the enthalpy exchanger to air-side fouling is strongly dependent on the details of its geometry and operating conditions [97].  Cross-flow parallel-plate channels separated by some corrugated spacers are the most common configuration of enthalpy exchangers (See Figure 2.1). They typically use microporous membranes either directly as the transport media or indirectly as the support for a perm-selective dense coating layer in a laminate membrane (Figure 2.1 (c)). The composite membrane media has an asymmetric structure with two surfaces and different properties; one smooth surface without visible pores, and one microporous surface with a high surface roughness that may be more susceptible to particulate fouling [98]. The two sides of the membrane are referred to as ‘coated’ and ‘uncoated’ sides.  (a) cross-flow core, (b) spacer-filled membrane channels, (c) scanning electron micrograph of the asymmetric composite membrane cross-section [43] Figure 2.1. The geometry of the cross-flow fixed-plate enthalpy exchanger cores used for dust loading tests   Very limited information is available on the impact of airborne particulate fouling on water vapor transfer through membranes and the overall performance of ERV exchangers. Charles et al. [96] characterized the air-side particulate fouling of a hollow-fiber membrane during a membrane evaporative cooling process. They found significant biological growth and wetting on the membrane fibers, but only minor impacts on water vapor transfer – not surprising because the fouling was from the fairly clean air (3084 particles/cm3; with 760 particulates/ cm3 between 55 and 800 nm and the balance below 55nm) over only 350 hours. Air-side fouling of ERVs occurs due to the accumulation of dust or condensates on exchanger surfaces and reduces the exchanger performance by increasing resistance to airflow, interfering Exhaust Air OutletExhaust Air Inlet (Indoor stale air)Supply Air Inlet (Outdoor fresh air)Supply Air Outlet(a)(b)(c)Coating layer: 1-5 µm thickMicroporous substrate: ~100 µm thickMembraneSpacerChapter 2 – Dust fouling of fixed-plate enthalpy exchangers 15  with vapor transfer, and generally decreasing heat and mass transfer coefficients [21].  Spacer-filled fixed-plate ERV exchangers, owing to their compact geometry, relatively low airflow rates, and the rough surfaces of the porous membranes, might be considerably fouled by the deposition of airborne particulate matter on the membrane surfaces. In these exchangers, large particles (>10µm) typically accumulate on the frontal surfaces and can be effectively removed by conventional filtration measures. However, smaller particles (<10µm), especially in the sub-micron size range, are likely to penetrate through filters and deposit onto the membrane surfaces throughout the depth of the exchanger core. This deposit layer may pose an additional vapor transport resistance comparable to those of composite membrane layers.  Moreover, deposition of ultrafine aerosol particles (~100nm) on porous membrane surfaces may result in complete or partial blockage of pores  (2nm<dpore<1000nm) [23] that are required for moisture transport, leading to effective porosity reduction and therefore degradation of water vapor transport.   The first part of this dissertation (chapters 2 and 3) investigates the impact of accelerated particulate fouling on the performance of membrane-based enthalpy exchangers. This chapter reports on fouling experiments with coarse dust particles carried out for full-size cross-flow ERV exchanger cores inside an aerosol wind tunnel. A material-level examination of fouling with aerosol nanoparticles and changes to the physical properties of membrane transport media used in commercial ERV cores will be discussed in Chapter 3. 2.3.  EXPERIMENTAL METHODS Fouling assessment of full-size ERV cores with coarse dust particles comprising deposition fraction measurements, accelerated loading tests, and initial and post-loading performance measurements are described in the following sections. 2.3.1. Exchanger Core Samples Two cross-flow ERV cores with membrane plate size of 12”×12” and 14” depth with a spacing of 2.42mm were provided by dPoint Technologies Inc. for use in this study. Table 2.1 summarizes the specifications of these cores. The membrane media used in these cores is a laminate composed of a dense water vapor selective copolymer film coated on a microporous polyethylene based substrate, distributed by dPoint Technologies under MX4TM [43]. In both exchangers, corrugated aluminum fins are used to separate membrane plates and enhance heat and moisture transfer in membrane channels (See Figure 2.1). The two cores are hereafter referred to as cores A and B, loaded on uncoated and coated sides, respectively. Table 2.1. Geometrical specifications of the enthalpy exchanger cores Footprint (DxW) (mmx mm) 305x305 Height (H) (mm) 290 Membrane area (m2) 9.42 Membrane  MX4 Flow spacer Corrugated  Aluminum sheet Number of layers 112 Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 16  Number of channels per layer 42 Pitch (a) (mm) 2.4±0.1 Base (b) (mm) 7.4±0.1 Apex angle (α) (degree) 54±2 Pressure drop @170m3/h (in. W.C.) 0.18±0.02 EATR @ 0.00 differential pressure (%) <0.5 Membrane thickness, 𝛿 (µm) 110±5 Membrane water vapor diffusivity, 𝐷𝑤𝑣 (m2/s) 2.0 × 10-6 ± 3 × 10-7 Membrane thermal conductivity, 𝑘𝑚 (W/m/K) 0.44  2.3.2. Test Apparatus The test apparatus developed for conducting dust loading tests of the enthalpy exchanger cores is shown in Figure 2.2. This test facility was designed to study particulate fouling of full-size ERV cores according to the requirements of ASHRAE standard 52.2-2012 [99].  Figure 2.2. Experimental test apparatus developed for ERV core fouling tests  There are two air streams in this apparatus flowing through two separate open-loop ducts that cross one another in a test section that holds ERV core samples (Figure 2.2 (b)). This simulates the real operating conditions of a typical ERV unit in building HVAC systems. Primary airstream from fan A, mimicking outdoor fresh intake air, is first pre-conditioned in a heating and humidifying section Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 17  and then passed through a HEPA filter (Flanders SF24-8-G2-GG-F with a 99.99% filtration efficiency at 0.3µm) to remove pre-existing particles from supply room air. Downstream of the HEPA filter, particles of known properties are introduced into the primary airstream using a fluidized-bed aerosol generator (TSI model 3400A). It produces a poly-disperse aerosol with moderate concentration (~104 particles/cm3) by dispersing Arizona road test dust.  Afterward, particles are mixed with the air flow and passed through the test section and the enthalpy core sample from Sin to Soot.  A TSI Optical Particle Sizer (OPS 3330) is used to measure the aerosol concentration in the air upstream and downstream of the test section. To accelerate loading, very high concentrations of dust particles (up to 150 mg/m3 at 136m3/h) are dispersed into the primary airstream using another custom-built aerosol generator (Figure 2.2 (c)). Measurement of high aerosol concentrations in loading tests is conducted using a TSI DUSTTRAK DRX. The secondary air stream generated by fan B simulates air exhausted from an indoor space. This airstream is room air that is passed through a high-efficiency MERV-14 pleated air filter upstream of the test section. The secondary air stream then passes through the enthalpy core from Ein to Eout. The flow rate of both airstreams, and the temperature and relative humidity of the primary air stream can be controlled between 60 - 600cfm, 8.3-50°C, and 17-90%, respectively. 2.3.3. Test Dust Actual fouling materials encountered by HVAC systems vary with application and operating environment. Typical HVAC ERV cores may encounter particles sizes in the range of 0.37 to 20 micron [100]. The test dust used in this study is ISO Medium test dust (12103-1, A3 dust provided by Powder Technology Inc). This test dust, also known as Arizona road dust (ARD), is primarily composed of silica (SiO2) and Alumina (Al2O3) with a bulk density of 1025 kgm-3, and D50=14.73 μm. The compositional information of ISO A3 test dust is summarized in Table 2.2. Typical size distribution of the dispersed test dust inside the test apparatus is shown in Figure 2.3. Table 2.2. Properties of ISO Medium test dust Component Quantity (%) Silica (fine dust) 69-77 Aluminium oxide  8-14 Calcium oxide (mineral) 2.5-5.5 Potassium oxide (mineral) 2-5 Sodium oxide (mineral) 1-4 Iron (III) oxide (hematite)  4-7 Magnesium oxide 1-2 Titanium oxide 0-1  Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 18   Figure 2.3. Size distribution of generated aerosol from dispersing ISO A3 dust inside fouling test apparatus; Dg=1.23 µm, σg=1.62.   2.3.4. Deposition Fraction and Dust Loading Test Procedures The general procedures of the dust fouling tests, including ‘deposition fraction’ and ‘loading,’ is similar to that described in ASHRAE standard 52.2 for testing the efficiency of air cleaners [99]. These procedures are summarized as follows (See Appendix A for the details of deposition fraction and dust loading test procedures). Dust loading: Each of the enthalpy cores was loaded at 136m3/h air flow rate with approximately 600 g of the A3 test dust in four steps. In each step, batches of 150 grams of the test dust were loaded to the high throughput Aerosol generator (Figure 2.2(c)) and dispersed into the test apparatus over the course of 2 hours. Cumulative dust loadings on these cores were equivalent to a few years (2 to 7) of operation in a highly polluted environment with 200 µg/m3 PM10 concentration. Deposition fraction: Deposition fraction measurements are completed for enthalpy cores at three air flow rates (136, 170, 204 m3/h), before and after completion of each step of a dust loading test. The size-resolved concentration of particles in the air upstream and downstream of the test section is measured at fixed intervals and used in the following correlation to determine particle deposition fraction.  𝝍(𝑫𝒑) = 𝟏 −𝑪𝑫𝒐𝒘𝒏 − ?̅?𝑫𝒐𝒘𝒏,𝑩𝑪𝑼𝒑,𝒆 − ?̅?𝑼𝒑,𝑩 (2.1)  Where 𝐷𝑝 is particle size, 𝐶𝐷𝑜𝑤𝑛 is the downstream concentration of particles, 𝐶𝑈𝑝,𝑒 is the upstream concentration of particles (estimated by averaging two consecutive samples of upstream separated by a downstream sample), and 𝐶?̅?𝑝,𝐵 and 𝐶?̅?𝑜𝑤𝑛,𝐵 are averaged up- and down-stream background counts, respectively. 0204060801000.1 1 10dN/dlogDp (#/cm3)Aerodynamic diameter (µm)Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 19  2.3.5. ERV Core Performance The performance parameters of the exchanger core samples, evaluated pre- and post-dust loading tests, include, sensible effectiveness, latent effectiveness, and supply and exhaust air-friction pressure drops. The effectiveness parameters are determined by measuring the inlet/outlet air temperature and relative humidity of the two air streams across the membrane exchanger core [32]:   𝜺𝑺 =(?̇?𝑪𝒑)𝒔(𝑻𝒔,𝒊𝒏 − 𝑻𝒔,𝒐𝒖𝒕) + (?̇?𝑪𝒑)𝒆(𝑻𝒆,𝒐𝒖𝒕 − 𝑻𝒆,𝒊𝒏)𝟐(?̇?𝑪𝒑)𝒎𝒊𝒏(𝑻𝒔,𝒊𝒏 − 𝑻𝒆,𝒊𝒏) (2.2)   𝜺𝑳 =(?̇?𝒉𝒇𝒈)𝒔(𝝎𝒔,𝒊𝒏 − 𝝎𝒔,𝒐𝒖𝒕) + (?̇?𝒉𝒇𝒈)𝒆(𝝎𝒆,𝒐𝒖𝒕 − 𝝎𝒆,𝒊𝒏)𝟐(?̇?𝒉𝒇𝒈)𝒎𝒊𝒏(𝝎𝒔,𝒊𝒏 − 𝝎𝒆,𝒊𝒏) (2.3)  where, 𝜀𝑆 and 𝜀𝐿 are sensible and latent effectiveness, respectively, 𝑇 is dry-bulb temperature, 𝜔 is the humidity ratio, ℎ𝑓𝑔 is latent heat of evaporation, 𝐶𝑝 is specific heat of dry air, and ?̇? is the air mass flowrate. The values of ?̇?𝐶𝑝 and ?̇?ℎ𝑓𝑔 for both supply (𝑠) and exhaust (𝑒) air streams are averaged between inlet and outlet conditions. The performance of enthalpy cores was evaluated under AHRI cooling (summer) test conditions [101] with supply air (primary airstream) inlet at 35ºC dry-bulb/26ºC wet-bulb, and exhaust air (secondary airstream) inlet at 24ºC dry-bulb/17ºC wet-bulb. The measured pressure drop is standardized for air density and viscosity using the following equation:  ∆𝑷𝒔 = ∆𝑷 [𝝆𝝆𝒔] [𝝁𝝁𝒔]𝒎 (2.4)  where ∆𝑃 is the tested pressure drop, ∆𝑃𝑠 is the standardized pressure drop, 𝑚 is the flow exponent (evaluated using the method of [32]), 𝜌𝑠 and 𝜇𝑠 are air density and viscosity at standard conditions, and  𝜌 and 𝜇 are air density and viscosity as tested, respectively. 2.3.6. Data Sampling and Uncertainty Analysis Table 2.3 summarizes the uncertainties in the measured and calculated parameters. Table 2.3. Summary of estimated uncertainties in measured and calculated values Parameter Accuracy  (±) Repeatability  (±) 95% CI (±) Temperature (℃) 0.2 0.03 0.2-0.3 Relative Humidity (RH (%)) 1.2-1.5 1.0 1.6-2 Volumetric air flowrate ((?̇? (𝑆𝐶𝐹𝑀))   0.5-1 Pressure drop (∆𝑃 (𝑃𝑎)) 2.5 0.8-2.9 2.6-3.8 Sensible effectiveness (𝜀𝑆 (%))   2.1-3 Latent effectiveness (𝜀𝐿 (%))   3.2-5  Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 20  2.4.  RESULTS AND DISCUSSION 2.4.1. Deposition Fraction and Particle Fouling Rate  Figure 2.4(a) shows the deposition fraction of ISO A3 dust particles onto the uncoated membrane surfaces of core A. Deposition curves are plotted as a function of optical particle diameter at three test air velocities.  Particle deposition fractions for the tested cores are found to be a strong function of air velocity and a weaker function of particle size. For small particles (<1μm), deposition fractions range from 0.05 to about 0.15. Primarily Brownian motion, and to a lesser extent, thermophoresis and gravitational settling are the mechanisms governing the deposition of particles in this size range [102]. Lower mean air velocities inside the membrane channels (corresponding to lower working flow rates) with a relatively large depth (L/Dh ~100) increase the particle residence time. This leads to a significant increase in the deposition fraction of small particles, which have higher diffusion velocities (Figure 2.4(a)). For large particles (>1μm), the deposition fraction in geometries similar to the enthalpy cores is primarily dominated by inertial impaction on the leading edges and gravitational settling inside narrow channels [103]. Depending on airflow characteristics and the operation conditions of exchangers, thermophoresis, and interception could also be important particle deposition mechanisms [103], [104]. Inertial deposition increases with increasing air velocity and particle size, as effective Stokes number increases. Gravitational settling also increases with particle size while it decreases with air velocity. As shown in Figure 2.4(a), the total deposition fraction of cores decreases with increased air velocity. Therefore, it can be concluded that gravitational settling is the dominant deposition mechanism for super-micron particles inside the enthalpy core, for the conditions studied.   (a) Deposition on the uncoated membrane side, at three mean air velocities  (b) comparison between deposition fractions on the coated and uncoated sides at 0.5 m/s Figure 2.4. Deposition fraction of ISO A3 medium dust particles in ERV core samples  Figure 2.4(b) compares the deposition on core B (loading on coated side, circles) with core A (loading on the uncoated side, squares) at a similar mean face air velocity of 0.5 m/s (corresponding Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 21  to 136 m3/h). The results are very similar for the two loading conditions. The error bars in Figure 2.4 and Figure 2.5 represent 95% confidence interval of 9 deposition fraction measurements at each data point.  Figure 2.5. Comparing measured deposition fractions before and after first dust insertion (~150 grams) at 0.5 m/s  Figure 2.5 shows a typical comparison between measured deposition fractions before and after the first dust loading step of enthalpy core A. Both curves are obtained at 0.5 m/s mean air velocity. A complete loading test is comprised of four 2-hour steps of accelerated dust loading. It can be observed that fractional deposition of dust particles on the loaded membrane surfaces is significantly smaller than that on clean membrane surfaces (before dust loading). It can also be observed that the uncertainty levels of deposition fractions increase for the loaded membrane surfaces, especially for larger particles. This is believed to be caused by re-suspension of previously deposited particles on the membrane surfaces and the test apparatus (upstream of the test section). The adhesion and potential re-suspension of particles are complicated phenomena that depend on the fluid flow regime, the surface roughness, the morphology and properties of previously deposited particles, the presence of condensation, and the balance of the forces acting on a particle on a membrane surface [105]–[107]. 2.4.2. Clean Performance Test  Performance evaluation of the enthalpy exchangers is conducted according to the AHRI summer (cooling) test conditions [101] for a practical range of working airflow rates (from 30% to 100% of the rated airflow by manufacturer) under clean and loaded conditions. To assess the repeatability of performance measurements, a control enthalpy core was tested initially with clean cores and also two more times before and after the testing of fouled core samples. Table 2.4 summarizes the results of measurements for the control enthalpy core. The performance data reported here are the average of three measurements taken with each core at five working flowrates. For test points at each flow rate, data were taken after 30 minutes to ensure that steady-Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 22  state conditions were achieved. It is found that measurements of effectiveness and average air-friction pressure drop were repeatable to within the uncertainty range of each measurement. Table 2.4. Repeatability performance measurements of the control enthalpy core Average flowrate (m3/h) Test 1 Test 2 Test 3a 𝜀𝑆 (%) 𝜀𝐿  (%) ∆𝑃 (𝑃𝑎) 𝜀𝑆 (%) 𝜀𝐿  (%) ∆𝑃 (𝑃𝑎) 𝜀𝑆 (%) 𝜀𝐿  (%) ∆𝑃 (𝑃𝑎) 60±3.5 79.8 56.5 14.4 77.8 56.8 13.1 78.9±2.5 58.39±2.4 13.1±2.8 85±3.5 77.0 50.9 18.6 75.1 51.5 19.3 77.2±2.3 51.40±3.9 19.2±2.7 110±3.5 76.7 44.7 23.3 73.6 46.2 24.0 76.2±2.4 48.56±3.0 24.9±2.6 135±3.5 74.3 40.9 28.2 71.8 42.3 29.9 74.1±2.4 44.03±4.2 30.9±3.5 160±3.5 71.6 37.8 32.5 70.6 40.3 36.2 70.5±2.5 42.79±4.3 37.8±3.7 a Typical uncertainty of measurements is reported for Test 3  2.4.3.  Sensible and Latent Effectiveness Results of the sensible and latent effectiveness measurements before and after the dust loadings for the two enthalpy cores A and B are represented in Figure 2.6. Enthalpy cores A and B were loaded on the uncoated and coated membrane surfaces, respectively. From the results in Figure 2.6, it appears that both sensible and latent effectiveness increase slightly but consistently after fouling with dust particles. The enhancement of the effectiveness of loaded enthalpy cores, especially in sensible effectiveness, is potentially due to the enhanced air-side boundary layer heat and mass transfer coefficients on the fouled side of the cores. As the dust deposit layer grows inside narrow membrane channels, the effective channel diameter decreases and the air velocity increases inside the channels. This is believed to increase the heat and mass transfer coefficients owing to the boundary layer thinning and potentially additional flow recirculation and enhanced mixing on the fouled air-side caused by the dust layer (see Figure 2.7(d)). The dust deposit layer also acts as an additional insulation layer increasing heat (and mass) transfer resistances, but apparently, this effect is smaller in the present type of fouling. Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 23   a) Core A loaded on the uncoated membrane surfaces  b) Core B loaded on the coated membrane surfaces Figure 2.6. Impact of dust loading on the sensible and latent effectiveness of cross-flow ERV cores  2.4.4. Mass Transfer Resistance Analysis The small moisture transfer resistance of dust deposit layers observed for heavily dust-loaded membrane-based enthalpy cores can be explained using the so-called “resistance in series” model. Figure 2.7(c) shows an SEM image of the dust deposit on a membrane sample along with a schematic summarizing the resistances to vapor transport through the membrane (Figure 2.7(d)). Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 24   Figure 2.7. Dust loaded membrane and mass transfer resistances to water vapor transport through the membrane  If the dust layer was continuous and densely packed; the equivalent moisture transfer resistance of ~22 s/m would be significant. However, since there is a large area that is not covered in dust, the deposit layer is modeled as an additional porous layer with a parallel resistance of large voids (discontinuities). Although the dust deposit contributes significant resistance, the discontinuities provide a low resistance pathway which is negligible compared to other series resistances in the membrane. Therefore, one can expect minimal impact on total vapor transport across the membrane due to the formation of the dust layer. Further analysis of moisture transport resistance in membrane layers under clean and fouled conditions will be presented in Chapter 3. Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 25  2.4.5. Core Pressure Drop Figure 2.8 represents the effect of dust loading on the air-friction pressure drop across the two loaded enthalpy cores before and after the dust loading. These results indicate that dust fouling has a much more significant impact on the core pressure drop than on the heat and mass transfer effectiveness of the cores. Heavy dust loadings, equivalent to a few years of operation in highly polluted environments, could result in pressure drop increases as high as 50%. To maintain a prescribed ventilation flow rate through the core, added pressure drop would result in added fan energy consumption and diminished energy recovery potential. This is generally the case for large high-rise residential and commercial buildings with ducted VAV systems, where system fans are equipped with speed controls (e.g., variable-frequency drives (VFDs) [81]) to maintain a minimum level of airflow required for acceptable indoor air quality. However, caution must be exercised in the assessment of fan energy consequences for smaller residential ERV systems with dedicated fans. The fans used in most residential HVAC systems use permanent split capacitor (PSC) motors without airflow controls. An increase in pressure drop across an ERV exchanger core will likely result in a decreased airflow through these systems, thus small energy consequences [108]. The magnitude of potential fan energy impacts associated with added pressure drop in ERV exchanger cores should be investigated considering different factors including, airflow changes (i.e., the change in working point on the fan performance curve), the fan and motor efficiency curves, and installation position of the fan with respect to the ERV exchanger core.   (a) Core A-loaded on the uncoated side (b) Core B-loaded on the coated side Figure 2.8. Impact of dust loading on static pressure drop across cross-flow ERV cores  Figure 2.9 shows the evolution of pressure drop across the enthalpy cores during the dust loading test. Given the coarse size of dust particles, using a minimal level of filtration to protect enthalpy cores could significantly reduce the impact of dust loading on their pressure drop. However, determination of an appropriate filtration level to optimize energy recovery potential would require a model accounting for trade-offs between filtration energy use and fouling rate and transient performance changes of the ERV. Chapter 2 – Dust fouling of fixed-plate enthalpy exchangers 26   Figure 2.9. Evolution of the normalized core pressure drop during the loading test  2.5. CONCLUSIONS The first part of the fouling study, presented in this chapter, measured the impact of fouling by coarse and fine dust particles on full-size membrane-based enthalpy exchanger cores. The rate of dust fouling in exchanger cores was investigated through the measurement of fractional deposition of aerosols in the size range of 0.3–10μm. Depending on core geometry, membrane surface roughness, and flow conditions, 5% to 20% of particles in the size range of 0.3 to 10μm deposit onto the membrane surfaces. Lower airflow rates lead to increased deposition, which is postulated to be caused by increased effects of gravitational settling and Brownian diffusion at lower air velocities inside the exchanger core. It was found that coarse dust loading has minimal impact on the sensible and latent effectiveness of the tested enthalpy exchanger cores. This can be explained by the fact that a dry particulate deposit is much more porous than the microporous substrate layers of the membrane and includes large discontinuities providing a low resistance pathway. However, heavy dust loadings, in the absence of appropriate filtration upstream, may result in added pressure drop (∼50%) and a fan energy penalty. It is also believed that enthalpy core performance, in addition to membrane resistance, is complicated by boundary layer transport resistances on the fouled airside which will counter membrane performance degradation due to the increased heat and mass transfer coefficients in partially restricted flow passages. These results led to the hypothesis that ERV membranes would be affected more by ultrafine particles that are comparable to the size of pores in the membrane substrate. In the second part of this study, presented in the next chapter, we investigate the impact of fouling with aerosol nanoparticles on membrane media used in enthalpy exchangers.  27  Chapter 3 - MEMBRANE MEDIA FOULING BY AEROSOL NANOPARTICLES 1   3.  3.1. OVERVIEW In this chapter, experimental work is focused on the material-level examination of fouling with aerosol nanoparticles of different hygroscopic properties. The changes to physical properties of membrane transport media used in commercial enthalpy exchanger cores were characterized to develop an understanding of potential air-side particulate fouling mechanisms and the resulting performance degradation during the lifetime of the membrane. Samples of commercial membrane media were loaded with hygroscopic NaCl and non-hygroscopic spark-generated graphite (SGG) aerosol nanoparticles. The results of water vapor permeance measurements showed that deposition of SGG and NaCl particles under dry loading conditions (RH<20%) had minimal influence on the membrane. However, when membranes loaded with hygroscopic particles in dry conditions were subsequently exposed to an elevated humidity (RH>70%) and the associated surface condensation, the membrane permeance reduced by up to 16%. Scanning electron microscopy (SEM) was used to examine the morphology of the fouled membrane surface. Analysis of SEM images showed a significant reduction in the average pore diameter of degraded samples, proportional to the fouling degree. The reversibility of the fouled membrane permeance variation, along with the surface analyses, imply that re-crystallization of salt ions, entrained close to the pores of membrane substrate in aqueous form, is a potential explanation for the permeance changes observed. Based on the findings of the experimental investigations in Chapters 2 and 3, a number of general recommendations to control and minimize airborne particulate fouling and its potential adverse effects on performance of membrane-based ERVs is presented at the end of this chapter.                                                               1 A version of this chapter has been submitted for publication in a peer-reviewed journal in July 2018: “Fouling of composite water vapor transport membranes by aerosol nanoparticles.” Chapter 3 –Membrane media fouling by aerosol nanoparticles 28  3.2.  INTRODUCTION Fouling is considered to be one of the challenges in membrane-based separation. The foulant particles (i.e., organic or inorganic precipitates, colloids and particulates) block or restrict the permeate flux and increase the hydraulic resistance of the membranes over time. The fouling mechanisms, including concentration polarization, particulate deposition, solute adsorption, and membrane blocking are directed by the operating conditions, design variables and physical and chemical characteristics of permeate and the membrane [58]. These mechanisms have been studied extensively in microfiltration (MF), ultrafiltration (UF), nanofiltration (NF), reverse osmosis (RO) and evaporative systems, where the liquid is in direct contact with the membrane [109]–[113]. Liquid-side fouling studies of composite membranes have limited application to the potential gas-side particulate fouling problem in water vapor transport membranes. The limiting mechanisms for fouling of liquid systems are often crystallization or precipitation fouling reactions (scaling) [111], as well as organic fouling by natural organic matter (NOM) [114], while these mechanisms are absent in gas-side particulate fouling problems. Unlike the liquid-induced fouling, studies on gas-side particulate fouling have been limited to narrow applications in “dead-end” and cross-flow filtration, such as removing dust from high-temperature flue gases [106], post-combustion products purification [109], and industrial flue gas filtration [116]–[118]. The majority of these studies on gas-side particulate fouling have focused on microporous membranes. The pressure-driven permeation mechanism (i.e., viscous pore-flow model) in these porous membranes is different from the solution-diffusion permeation in water-vapor-transport composite membranes with dense skin layers. Substantial pressure gradients across microporous membranes used in these industrial processes may result in significant particle entrainment toward the membrane surface and potentially into the pores of the microporous structure. Moreover, flue gas filtration systems usually perform at high temperatures and very high concentration of particles, including condensable vapors (VOCs) and liquid particles that could complicate the fouling process [117]. Thermophoretic effects, due to large temperature gradients between operating gas streams and membrane surfaces [100], as well as extremely high concentrations of contaminant particles are expected to result in much larger fouling rates with a drastic flux decline in these systems. Except for reverse osmosis, the fouling of dense membranes has often been neglected since the feeds are comparatively very clean. For water vapor transport membranes used in clean applications such as membrane-based ERVs, breathable clothing membranes, and clean gas/water vapor separation processes (e.g., dehydration of natural gas), the concentration of airborne particles and pressure gradients are insignificant compared to flue gas filtration and dehydration. The gas-side fouling in these applications is usually assumed to be negligible. The inclusion of moderate to high-efficiency filters upstream of these systems is believed to remove the majority of larger particles that could potentially result in fouling of membranes. Charles et al. [96] showed that the air-side particulate fouling is very limited on hollow fiber membranes used in evaporative cooling systems. In a more recent study, however, we [119] showed that high concentration of tobacco smoke in building exhaust streams (e.g., the application of ERV systems for casino and gaming spaces) particles containing liquids and condensable VOCs could accelerate the particulate fouling process. Moisture flux declines as high as 60% in the composite membranes of these Chapter 3 –Membrane media fouling by aerosol nanoparticles 29  systems were observed (See Appendix B for a selection of the results of a tobacco smoke fouling case study). Additional fouling processes may come into play when aerosol particles are water soluble, contain liquids, or are chemically active. This is particularly important in cases where operating conditions lead to condensation of liquid water on membrane surfaces. Although high moisture transfer rate through composite membranes minimizes the occurrence of condensation in membrane-based ERV systems, condensation may still occur to some extent, especially when the exhaust air stream is humid during the winter [120][20]. In such cases, hygroscopic airborne particles could significantly contribute to the membrane fouling. In this chapter, we investigate the air-side particulate fouling of water vapor transport membranes with aerosols of different chemistry to develop an understanding of the underlying fouling mechanisms and resulting performance degradations. The asymmetric nature of current-generation membranes for water vapor transport applications is shown to result in different fouling behavior on the two sides of the membrane. We limit this investigation to fine particles (<700nm) which may still penetrate significantly through conventional filters. 3.3. THEORY AND HYPOTHESIS OF EXPERIMENTS 3.3.1. Fouling in Composite Membranes Air-side fouling in asymmetric composite membranes may occur on both coated and uncoated sides. Two different types of fouling can be considered on the uncoated side (Figure 3.1(a)); (1) external fouling as the result of deposition and accumulation of airborne particles on the membrane surface, and (2) internal fouling by particles in the substrate pores. An external particle deposit, often referred to as a ‘cake layer,’ can grow layer by layer on the membrane surface, leading to an additional hydraulic resistance. During internal fouling, foulant particles may be entrained into the pores in different forms. Entrainment due to the permeate fluxes perpendicular to the membrane surfaces is expected to be negligible in the water vapor transport membrane studied here. However, the presence of condensed liquids on membrane surfaces may facilitate transport of foulant materials into the pores. It is hypothesized that foulant material can move when it is water soluble, and reach the pores of the microporous substrate. In the case of salt particles, liquid water on the uncoated surfaces of the membrane could entrain the salt ions in aqueous form into the membrane substrate pores. Under dry conditions, these ions could recrystallize inside the pores resulting in complete pore blockage or pore narrowing. Chapter 3 –Membrane media fouling by aerosol nanoparticles 30   (a) Internal and external fouling in porous substrate (pore blockage) (b) External fouling of dense coating (surface blocking and particle blocking) Figure 3.1. Fouling mechanisms of asymmetric composite membranes  On the coated side, due to the dense nature of the selective coating layer, particles cannot reach the pores of the underlying substrate layer. Therefore, only external fouling mechanisms are expected for the coated side. Two types of fouling can be considered on the dense coating (Figure 3.1(b)); surface blocking and particle blocking. In surface blocking (also known as ‘surface blinding’) it is assumed that the blocked membrane area is not available for transport, resulting in a reduction of the active membrane area. The effective flux through the partly blocked membrane can be described as a fraction of the initial flux through the clean membrane:  𝑱 = 𝑱𝟎𝑨𝟎 − 𝑨𝒃𝒍𝒐𝒄𝒌𝒆𝒅𝑨𝟎 (3.1)  In the case of particle blocking, in addition to the active membrane area reduction, an increased diffusion pathway through the dense layer may also contribute to the flux decline through the membrane (Figure 3.1(b)) [58]. External fouling on these dense surfaces is closely related to the interactions between the foulant particles and membranes surfaces. Physiochemical properties of the dense layer surface, such as surface roughness, electrostatic charges, and hydrophilicity are major factors determining fouling Chapter 3 –Membrane media fouling by aerosol nanoparticles 31  behavior [121]. A smoother surface on the coated side is expected to experience less fouling. It has been shown that foulant particles are more likely to be entrained by rougher topologies than by smoother membrane surfaces [122][123], though membranes with nano-patterned surfaces have also been shown to improve antifouling properties [124], [125]. Surface charges can also promote fouling from foulant particles with counter-charges due to favorable electrostatic interactions [126]. Increasing hydrophilicity of membrane surfaces (e.g., coating with a thin hydrophilic film or grafting of polymer chains on the surface) is accepted to improve fouling resistivity of membranes [121], [126]. Hydrophilic surfaces do not have an affinity towards commonly hydrophobic foulants (e.g., proteins, emulsion and organic compounds), thus preventing adsorption and deposition of these materials onto membrane surfaces. If foulant particles are hydrophilic, however, surface hydrophilicity could degrade the fouling resistivity of the membrane [127]. Air-side fouling on the coated side of water vapor transport membranes by hygroscopic salt particles is one such case. The high affinity of typical hydrophilic coating layers in water vapor transport membranes for salt particles may result in significant particle deposition on the coated surfaces. Humid conditions and surface condensation may further increase compactness of deposit layers and may also increase surface blinding by forming dense salt patches on membrane coated surfaces. 3.3.2. Water Vapor Transport in Composite Membranes Mass transfer in membrane modules depends on the membrane resistance and the resistances of the adjacent gas-side boundary layers [91]. The phenomenon is also known as concentration polarization [45], [128]. These boundary layer resistances lower the effective water vapor concentration gradient across the membrane and thus lower moisture fluxes in the module. This is more important for more permeable and selective membranes, where the boundary layers can represent a significant portion of the total resistance to mass transport [91]. Likewise, the moisture transfer resistance within the microporous support layer of composite membranes further lowers the concentration gradient across the dense coating layer and introduces asymmetry to the permeation properties of the membrane. It will be shown later in chapters 5 and 6 that changes of intrinsic permeation properties of the dense selective layer with varying operating conditions (due to effects such as plasticization, swelling, clustering, and competitive sorption) as well as membrane orientation can further alter these concentration profiles. The variations of the coating layer properties are assumed to be negligible in this chapter as the test conditions for permeation measurements are constant for all samples. Figure 3.2 schematically shows moisture transfer resistances altering concentration profiles across an asymmetric composite membrane. Chapter 3 –Membrane media fouling by aerosol nanoparticles 32   Figure 3.2. Schematic representation of concentration profiles within the boundary layers and the composite membrane during water vapor transport  The water vapor flux through a membrane can be represented as the product of total mass transfer coefficient and the concentration difference over the membrane  𝑱 = 𝒌𝑻(𝑪𝑭(𝒃)− 𝑪𝑷(𝒃)) (3.2)  where, 𝒌𝑻 is the total mass transfer coefficient (m/s), 𝐶𝐹𝑏 and 𝐶𝑃𝑏 are the bulk concentrations of water vapor (mol/m3) on the feed and permeate sides of membrane, respectively. The total mass transfer coefficient can be described by a one-dimensional ‘resistances in series’ model [129] as  𝟏𝒌𝑻=𝟏𝒌𝑩𝑳𝑭 +𝟏𝒌𝒎+𝟏𝒌𝑩𝑳𝑷  (3.3)  Alternatively, in terms of resistances  𝑹𝑻 = 𝑹𝑩𝑳𝑭 + 𝑹𝒎𝑴 + 𝑹𝑩𝑳𝑷  (3.4)  where it is assumed that all resistances to water vapor transport are additive; 𝑅𝐵𝐿𝐹  and 𝑅𝐵𝐿𝑃  represent the mass transfer resistances (s/m) in the module feed and permeate side boundary layers, respectively, and 𝑹𝒎𝑴 represents the composite membrane mass transfer resistance as the sum of resistances in the coating and substrate layers Chapter 3 –Membrane media fouling by aerosol nanoparticles 33   𝑹𝒎𝑴 = 𝑹𝒄𝑴 + 𝑹𝒔𝒖𝒃𝑴  (3.5)  While the resistance of a membrane can be reasonably assumed to be independent of the fluid dynamics on the adjacent gas sides, boundary layer resistances are known to be a strong function of cross-flow velocity and a weaker function of fluid properties (temperature and RH) on the gas sides [130]. Thus measuring the overall mass transfer rate of membrane samples in a module can give reliable values for intrinsic membrane properties only when the boundary resistances are known. The moisture transfer resistance of the dense coating layer can be calculated as  𝑹𝒄𝑴 =𝜹𝒄℘𝒄𝑹?̅?𝒄 (3.6)  where ?̅?𝑐 is the average coating layer temperature between the supply side and the interface between the coating and substrate layers, 𝛿𝑐 is the thickness of the coating layer, and  ℘𝑐 is the moisture permeability of this layer defined by the solution-diffusion model [48] as  ℘𝒄 = ?̅?(𝑪𝑭(𝒄)− 𝑪𝑷(𝒄))𝒑𝒗𝑭(𝒄)− 𝒑𝒗𝑷(𝒄) (3.7)  where,  𝑝𝑣𝐹(𝑐) and 𝑝𝑣𝑃(𝑐) are the partial water vapor pressures on two sides of the coating layer and ?̅? is the concentration-averaged diffusion coefficient through this layer  ?̅? =𝟏(𝑪𝑭(𝒄)− 𝑪𝑷(𝒄))∫ 𝑫(𝑪)𝒅𝑪𝑪𝑭(𝒄)𝑪𝑷(𝒄) (3.8)  where, 𝐶𝐹(𝑐) and 𝐶𝑃(𝑐)are the concentrations of water inside the dense layer at its two surfaces on the feed side and interface of coating and substrate layers, respectively. Determination of these values require the knowledge of material sorption isotherms at different operating vapor pressures and temperatures. The moisture transfer resistance of the microporous substrate layer can be calculated as follows  𝑹𝒔𝒖𝒃𝑴 =𝝉𝜹𝑺𝒖𝒃𝜺𝑫𝒔𝒖𝒃 (3.9)  where, 𝛿𝑆𝑢𝑏 is the substrate thickness, and tortuosity factor, 𝜏, and surface porosity, 𝜀, are characteristic parameters describing the microporous structure of the substrate layer. 𝐷𝑠𝑢𝑏 represents the effective diffusion coefficient in the substrate layer calculated using the dusty-gas model (DGM). This model considers three different transport mechanisms through a porous media; Knudsen and ordinary diffusion in series and together in parallel with the viscous pore flow [131]. Chapter 3 –Membrane media fouling by aerosol nanoparticles 34   𝑫𝒔𝒖𝒃 = (𝟏𝑫𝑲𝒏+𝟏𝑫𝒗𝒂)−𝟏+𝒅𝒎𝟐?̅?𝟑𝟐𝝁 (3.10)  where, 𝑑𝑚 is the average pore diameter, ?̅? is the average pore pressure, 𝜇 is vapor dynamic viscosity, and 𝐷𝐾𝑛 and 𝐷𝑣𝑎 are Knudsen diffusivity and vapor diffusivity in air, respectively, given by  𝑫𝒗𝒂 =𝟑. 𝟐 × 𝟏𝟎−𝟒 ?̅?𝒔𝒖𝒃𝟏.𝟕𝟓?̅? (𝝂𝒗𝟏𝟑⁄ + 𝝂𝒂𝟏𝟑⁄ )𝟐√𝟏𝑴𝒗+𝟏𝑴𝒂 (3.11)   𝑫𝑲𝒏 =𝒅𝒎𝟑√𝟖𝑹?̅?𝒔𝒖𝒃𝝅𝑴𝒗 (3.12)  where, 𝑀𝑣 and 𝑀𝑎 are the molar weights of water vapor and air, 𝜈𝑣 and 𝜈𝑎 are the molar volumes of water vapor and air (with values of 12.7 and 20.1, respectively [131]), and ?̅?𝑠𝑢𝑏 is the average substrate temperature defined between the interface of substrate and coating layers and the permeate side. The moisture flux through the composite membrane may be evaluated from the resistance of each layer and concentration gradient across that layer as  𝑱 =∆𝑪𝒊𝑹𝒊𝑴  (3.13)  This equation requires knowledge of intermediate values of vapor pressure and temperature inside the membrane at the interface between the coating and substrate layers (as shown in Figure 3.2). The sorption and diffusion data for the dense coating material is also required for permeability calculation in this layer (Eqs. (3.6) and (3.7)).  Due to the coupling of moisture transfer properties of the coating and substrate layers (as presented in Eqs. (3.5) to (3.13)), the flux of moisture through the composite membrane (under certain operating conditions on the feed and substrate sides) must be determined iteratively. This iterative process estimates the values of temperature and vapor pressure at the interface until the moisture flux through the two layers are equal. 3.4. MATERIALS AND EXPERIMENTAL METHODS 3.4.1. Membrane Materials The properties of the membrane materials tested are summarized in Table 3.1. These materials are samples of the membrane media extracted from three different commercial HVAC enthalpy exchangers: two polymer-based composites and another porous cellulosic paper-based media. The polymer-based membranes are designated as MA and MB, and the paper membrane as PA. The uncoated substrate samples of membranes MA and MA are designated as SA and SB, respectively. Chapter 3 –Membrane media fouling by aerosol nanoparticles 35  The paper membrane is a macro-porous cellulosic matrix; impregnated with a chloride salt to improve its water vapor transport and selectivity for ERV applications. Although polymer-based membranes have much better water vapor permeance and selectivity relative to undesirable indoor gases, paper-based ERV units are the incumbent technology on the market. Therefore, a typical paper-based membrane media was included in this study for comparison purposes. Table 3.1. Properties of membrane material samples Membrane Material Description Thickness (µm) Initial Water Vapor Permeance (GPU) a Selectivity, α (H2O/CO2) MA A hydrophilic film coated on a hydrophobic PE-based substrate [43] distributed by dPoint Technologies Inc. under MX4TM. 105-115 9100 ± 600 143 ± 15 MB A hydrophilic polymer film Coated on a hydrophobic PP substrate b 32-40 13800 ± 900 225 ± 19 PA A commercially available paper-based membrane 170-220 2000± 150 3.55 ± 0.27 SA A hydrophobic PE-based substrate 104-110 19,500± 750 2.28±0.36  SB A hydrophobic PP substrate 31-34 36,600± 950 1.91±0.51 a The initial water vapor permeance of each membrane was determined by averaging the initial permeance of all the samples tested in this work. The range reported indicates the 95% confidence interval. b The MB membrane, provided by dPoint Technologies Inc., is under development and the composition of the membrane material is proprietary.  3.4.2. Test Apparatus A laboratory test apparatus (Figure 3.3) was developed for accelerated loading of membrane samples with aerosol nanoparticles. This apparatus includes two different airstream circuits passing through a test module holding membrane samples: (1) a particle-laden airstream flowing over one side of the membrane sample in a circuit that allows for control of the size and concentration of aerosol, as well as RH and flowrate; (2) a dry sweep, HEPA-filtered airstream flowing on the opposite side of the membrane sample that allows control of flowrate and temperature. This arrangement enables establishment of temperature and moisture gradients across a membrane sample (similar to real ERV operating conditions) while loading it with nanoparticles. Aerosol nanoparticles of two different types are used for these experiments: hygroscopic NaCl salt nanoparticles, and non-hygroscopic soot-like spark-generated graphite (SGG) nanoparticles. A constant output atomizer (TSI 3076), connected to a dried and HEPA-filtered compressed air source (40 psi), is used for generating salt aerosols. The atomizer output is passed through a drying column to remove all moisture from the aerosol stream. The SGG aerosols were produced by a PALAS GFG 1000 with Argon carrier gas and subsequent air dilution. The aerosol from either source is passed through a soft X-Ray aerosol neutralizer (TSI 3088) to achieve a Boltzmann charge distribution. An RH-controlled make-up airstream is blended with the neutralized aerosol stream to balance the flowrate in the system and to control the RH of the aerosol stream flowing though the membrane test module. Chapter 3 –Membrane media fouling by aerosol nanoparticles 36   Figure 3.3. Schematic of the experimental test apparatus used for aerosol nanoparticle loading and deposition measurements  The size-resolved aerosol concentrations are determined using a TSI 3936 scanning mobility particle sizer (SMPS). The normalized number size distributions of typical aerosol particles produced by the test apparatus are presented in Figure 3.4.  Figure 3.4. Normalized particle mobility size distribution of SGG and NaCl nanoparticles generated for membrane loading and deposition tests.  3.4.3. Membrane Module A test module with a counter-flow arrangement is used for holding 18×5 cm flat sheet membrane samples. An isometric view of the module is shown in Figure 3.5. This module is comprised of 00.20.40.60.8110 100 1000Normalized dN/dlogDpParticle Size (nm)NaClGraphiteChapter 3 –Membrane media fouling by aerosol nanoparticles 37  two half shells with machined flow field pathways. On each side there are seven channels in parallel, machined 1mm deep, 3mm wide, and are separated by 1.5mm lands. The flow enters through push-connect elbow adaptors on each side and then spreads out to the seven channels.  The two sides are placed on either side of a membrane sample and sealed by compression. The module has an active membrane area of 45.6 cm2 ([132]).  Figure 3.5. Membrane permeation module [132]  3.4.4. Membrane Sample Preparation The membrane samples tested are flat sheets of media extracted from commercial ERV exchanger cores. The surface of these membrane samples can become charged as a result of many different processes, including manufacturing processes and initial performance testing. This potential surface charges may cause particle repulsion or attraction [126], interfering with particle loading tests. A method similar to that employed by Romay et al. 1998 [133] and Montgomery et al. [134] is used to remove the surface charge of the polymer-membrane samples. The polymeric samples were submerged in isopropyl alcohol (IPA) for 15 minutes and then dried for 24 hr in room conditions. Submersion in IPA was shown to have minimal impact on the physical transport properties of membrane samples by comparing their performance before- and after-submersion. 3.4.5. Particle Deposition and Loading Test Procedures Membrane samples are placed inside the test module (Figure 3.5) and the flowrate on both sides of the module is maintained at a constant value of 2 SLPM (Reynolds~150). This flow rate was selected to match the flow characteristics between the test module and membrane channels of the ERV cores at 136 m3/h operating air flow rate. Two differential pressure gauges (Dwyer 2000 Magnehelic®) are installed between pressure taps on entrance and exit ports, on opposing sides of the test module, to measure and correct any possible pressure gradient between the two membrane sides. The pressure differences are maintained below 100 Pa to minimize the effect of pressure-driven flow through the membrane samples on particle loading. Membrane samples are loaded Chapter 3 –Membrane media fouling by aerosol nanoparticles 38  under two different conditions, as follows, to represent typical conditions experienced in real ERV operation.  Dry loading cycles: Membrane samples are loaded for 8 hours with RH<20%.  This RH is well below the deliquescence point anywhere in the system, to avoid structural changes of aerosol particles and deposits. During the loading process, the bottom side of the test module is immersed inside a chilled water bath (5ºC), circulated by an external water chiller/recirculator (Thermo Scientific SC100-A28), to maintain a temperature gradient between sweep and aerosol airstreams. This temperature gradient mimics real operating conditions in “heating mode” and thermophoresis enhances the particle deposition rate. Producing high concentrations of aerosol particles in the test apparatus (up to 100 mg/m3) in dry loading cycles enables one to perform loading experiments (~ 8hr) that are the equivalent to a few years of operating in the field (i.e., having the same accumulated mass concentration of incident particles). For example, in a highly polluted environment with PM1 aerosol concentration of 65 µg/m3, 8 hours of laboratory loading translates to about two years of field operation. Wet loading cycles: During wet loading cycles, dry-loaded samples are exposed to intermittent humid conditions (RH~75%), leading to surface condensation. Membrane samples undergo four cycles of a 2hr dry loading followed by 30 minutes of exposure to HEPA-filtered humid air at 75%RH. Between each two cycles, the membrane test module and the aerosol lines are completely dried by running hot, dry air through the system for about two hours.  Although this loading cycle is ad-hoc, it does produce RH variations that might be experienced in real environments where ERVs are used. Deposition fraction. For each experiment, the loading apparatus was run continuously and two upstream samplings were taken with a downstream sampling in between. Deposition fraction was then calculated by comparing up- and down-stream concentrations.  𝝍(𝑫𝒑) = 𝟏 −𝑪𝑫𝒐𝒘𝒏𝑪𝑼𝒑,𝒆 (3.14)  where 𝐷𝑝 is particle size, 𝐶𝐷𝑜𝑤𝑛 is the downstream concentration of particles, and 𝐶𝑈𝑝,𝑒 is the estimated upstream concentration of particles by averaging two consecutive samples of upstream separated by a downstream sample. 3.4.6. Weight Measurements The areal density of particle loading (g/m2) on membrane samples was evaluated from the difference between weight measurements of loaded and cleaned samples. 3×3cm cut-outs from the middle of loaded samples were used for weight measurements. This was done to eliminate higher mass deposits near inlet and outlet ports of the membrane module due to the impingement and flow recirculation effects. A gravimetric analysis following EPA recommended practice was used with a Sartorius CP2 microbalance. Cut-outs of membrane samples were weighed after being left in a temperature and humidity controlled room (20±2°C, 35±5%RH) for at least 24 hours. The particle load was removed from sample cut-outs by soaking them in distilled water for ~24hr, and Chapter 3 –Membrane media fouling by aerosol nanoparticles 39  the weight of cleaned sample was measured subsequently. To ensure thorough cleaning of loaded samples, the basis weight of clean membrane samples was also evaluated from several measurements of pristine sample cut-outs. 3.4.7. Water vapor Flux and Permeance A dynamic water vapor transport testing apparatus detailed in chapter four is used for measurement of water vapor permeance of membrane samples (see Figure 3.6).   Figure 3.6. schematic of water vapor permeation test apparatus  The overall flux of water vapor through membrane samples is determined using the following equation  𝑱 =𝑸𝟒𝒑𝑽,𝟒𝑽𝒎𝜸𝑹𝑻𝑨𝒎 (3.15)  where, Q4 is the flowrate of sweep stream, 𝑝𝑉,4 is partial vapor pressure in the sweep outlet, 𝐴𝑚 is membrane effective area, 𝑉𝑚 is molar gas volume at STP, and 𝛾 is the activity coefficient (𝛾 is assumed to be unity for the sweep N2 stream). To determine the membrane permeability, water vapor flux is divided by effective vapor pressure difference (obtained from logarithmic vapor pressure difference in the test module) [91].  ℘ =𝑱𝜹𝒍𝒏 (𝒑𝑽,𝟐/(𝒑𝑽,𝟏 − 𝒑𝑽,𝟒))𝒑𝑽,𝟐 − (𝒑𝑽,𝟏 − 𝒑𝑽,𝟒) (3.16)  where, ℘ is membrane permeability, and 𝛿 is overall membrane thickness. Permeability can be expressed by various units. Barrer is the most widely used in the membrane technology literature, defined as (1 𝐵𝑎𝑟𝑟𝑒𝑟 =  10−10𝑐𝑚3(𝑆𝑇𝑃).𝑐𝑚𝑐𝑚2.𝑐𝑚𝐻𝑔.𝑠). Permeance is alternatively used for reporting permeation properties of composite membranes (with multiple layers with different materials and properties), defined as  𝑮 =℘𝜹 (3.17) Chapter 3 –Membrane media fouling by aerosol nanoparticles 40  where, 𝐺 is the membrane permeance in gas permeation units (𝐺𝑃𝑈 = 10−6𝑐𝑚3(𝑆𝑇𝑃) 𝑐𝑚2 .𝑠.𝑐𝑚𝐻𝑔).  As was described in section 3.3.2, boundary layer resistances inside membrane modules must be taken into account for determining intrinsic material permeation properties. Water vapor permeation testing of the membrane samples was performed inside the same module used for nanoparticle loadings (Figure 3.5). The boundary layer resistances to water vapor transport inside this module are characterized in detail elsewhere [27]. The value for combined feed and permeate side boundary layer resistances at the test conditions of our experiments (35°C and 50%RH at the feed inlet) is obtained as 32±3s/m. 3.4.8. Pressurized Air Leak Rate and Gas Permeance The air flow rate through samples was evaluated as an indication of the defects level in the coating layer of polymeric membrane samples or of the porosity of the paper-based membranes and substrate samples. These measurements were conducted in a custom-built constant pressure/variable volume apparatus (Figure 3.7) by maintaining a 20700 Pa (3 psi) air pressure differential between the two surfaces of the sample inside the counter-flow test module. The rate of air flow passing perpendicularly through the active area of a membrane sample was then measured by means of a bubble flow meter (Sensidyne Gilibrator-2).  Figure 3.7. Schematic of a constant pressure/variable volume apparatus for gas permeation measurements  By measuring the permeate flow rate Q(m3/s), the gas permeance of a porous sample can be calculated as  𝑱𝒊 = (𝑸𝑨(𝑷𝑭 − 𝑷𝑷)) (𝑻𝟎𝑻) (𝑷𝑷𝑷𝟎) (3.18)  where A is the effective membrane area, and 𝑇0 and 𝑃0 are the standard temperature and pressure (STP), respectively. Chapter 3 –Membrane media fouling by aerosol nanoparticles 41  3.4.9. Determination of Pore Structure of Substrate The DGM provides a non-intrusive method to characterize the effective pore size and effective porosity of the microporous substrates  [135]. Carman [136] suggests that any porous medium can be characterized for gas permeation by two morphological parameters, B0 and K0. For single gas permeation, the permeance of a porous material can be expressed as [137]  𝑮 =𝟒𝟑𝑲𝟎𝒗𝑴 +𝑩𝟎𝝁(?̅?) (3.19)  where 𝐾0 and 𝐵0 are morphological parameters related to Knudsen diffusion and viscous flow, respectively, ?̅? is the average pressure in the substrate, and 𝑣𝑀 is the mean molecular velocity, defined as  𝒗𝑴𝒊 = √𝟖𝑹𝑻𝝅𝑴𝒊 (3.20)  where 𝑻 is the absolute temperature, 𝑹 is the universal gas constant, and  𝑀 (kg/mol) is the molecular weight of the permeate gas. A linear plot of experimental data for the permeance, 𝐺, versus average pressure, ?̅?, of a specific gas through a porous medium can be used to obtain  morphological parameters 𝐵0 and 𝐾0 from the slope and intercept, respectively. The average pore diameter, 𝑑𝑚, and effective porosity of the substrate, 𝜀𝑞2, can then be determined by the following equations [135]  𝒅𝒎 =𝟒𝑩𝟎𝑲𝟎 (3.21)   𝜺𝒒𝟐=𝑲𝟎𝟐𝟏. 𝟔𝑩𝟎(𝑹𝑻. 𝜹) (3.22)  As fouling occurs, the available pores of the substrate for water vapor transport may decrease. A fouling factor (FF) is defined to relate the effective porosity of a fouled substrate to its initial value.  𝑭𝑭 =(𝜺𝒒𝟐)𝒇𝒐𝒖𝒍𝒆𝒅(𝜺𝒒𝟐)𝟎 (3.23)  FF takes values in the range 0-1, where a unity FF correlates to no membrane fouling and a zero value of FF correlates to complete pore blockage (i.e., vapor flux equal to zero). It should be noted that the fouling factor as defined is a measure of pore blockage due to fouling and does not necessarily translate into a physical change in membrane porosity which is a volumetric parameter. Using a fouling factor facilitates comparing the extent of fouling under different conditions. Chapter 3 –Membrane media fouling by aerosol nanoparticles 42  3.4.10. Microscopic Analysis Scanning electron microscopy (SEM) was used for membrane surface analysis. Membrane samples were coated with a thin gold layer (2-5nm) using a low vacuum sputter coater (Edwards S150A) and imaged using a Hitachi Model S3000N variable pressure SEM. The SEM images of loaded membrane samples were examined to determine the impact of loading parameters (particle charge distributions, surface charges, and relative humidity) on the deposit morphology and the distribution of salt and SGG particles relative to the membrane substrate pores. The SEM images of wet loaded samples were also analyzed to determine the mean pore size and surface porosity. 3.5. RESULTS AND DISCUSSION 3.5.1. Particle Deposition on Membrane Surfaces Deposition fraction measurements were completed for each membrane sample at the beginning of dry loading cycles. Figure 3.8 shows typical deposition curves of NaCl and SGG particles loaded on the uncoated side of MA membrane samples. Since the TSI SMPS measures the particle size based on electrical mobility, it can resolve the deposition curves for particle sizes as small as 16 nm mobility equivalent diameter.  Figure 3.8. Deposition fraction of NaCl and SGG particles on the uncoated side of MA membrane  The trend of deposition fractions in Figure 3.8 are consistent with those of the sub-micron particle size range of deposition curves presented in the previous chapter for dust loading experiments. Deposition fractions of ultrafine particles (<1μm) range from 0.05 to about 0.6. Primarily Brownian motion, and to a lesser extent, thermophoresis and gravitational settling are the mechanisms governing the deposition of particles in this size range [102]. Given the geometry and the operating flow conditions of the membrane test module, for ultrafine particles (<100nm); Brownian diffusion results in a significant increase in deposition fractions from 0.1 (at 100nm) to 0.6 (at 16nm). Considering the pore size range of the membrane substrates (1nm to 1μm with average pore diameters of 38 and 121nm for SA and SB substrates, respectively), it would be possible for a particle to enter the pores. 00.20.40.60.8110 100 1000Deposition FractionMobility equivalent diameter (nm)NaClSootChapter 3 –Membrane media fouling by aerosol nanoparticles 43  SEM images of the dry-loaded membrane samples were examined to determine the deposit layer morphology and surface coverage. Typical surface SEM of polymeric membrane sample MB loaded with NaCl and SGG particles on coated and uncoated sides are shown in Figure 3.9(a-f).   a) clean coated side of MB b) clean uncoated side of MB   c) NaCl particles on coated side of MB d) NaCl particles on uncoated side of MB   e) SGG particles on coated side of MB f) SGG particles on uncoated side of MB Figure 3.9. Scanning electron micrographs of the surface of dry-loaded membrane samples  The surface scanning electron micrographs in Figure 3.9 show formation of a uniform, cake-like deposit from salt particles on both membrane surfaces, while the deposition of PALAS soot-like Chapter 3 –Membrane media fouling by aerosol nanoparticles 44  SGG particles show relatively less surface coverage with a less uniform deposit structure. It can be observed that the SGG particles form deposit layers with an open fractal structure which would presumably offer little resistance to water vapor transport, but the NaCl particles are non-porous cubic crystals. Salt nanoparticles deposit layer on the uncoated membrane surfaces (Figure 3.9(d)) seems to be more densely packed compared to the salt deposit on the smoother coated surfaces (Figure 3.9(c)). However, there is no noticeable difference observed in deposition pattern of SGG particles between the coated and uncoated sides. The effects of particle charge distribution, membrane surface charges, and temperature gradients between the membrane surface and bulk air on the rate of particle deposition and deposit layer morphology were investigated. The most important factor influencing the deposit morphology was found to be the aerosol charge distribution. Aerosol particles neutralized with a soft x-Ray neutralizer (TSI 3088) showed a tendency to form uniform, compact deposit layers leading to cake layer formation on membrane surfaces while non-neutralized particles deposit in the form of sparse dendrites rather than a uniform layer Figure 3.10).   a) Uniform, compact deposit formed from neutralized particles b) Sparse aggregates formed from non-neutralized particles Figure 3.10. Effect of particle charge on deposit formation patterns on membrane surfaces  Although the state of aerosol and surface charges influence the deposition fraction and the deposit morphology, it is shown through vapor permeance measurements in the following sections that they have little direct influence on the degradation of membrane performance. 3.5.2. Impact of Fouling on Composite Membranes Dry Loading Conditions Table 3.2 summarizes the results of performance measurements (water vapor permeance, and pressurized air crossover leak rate) of composite membrane samples before and after dry loading cycles.   Chapter 3 –Membrane media fouling by aerosol nanoparticles 45  Table 3.2. Pre- and Post-loading performance of dry-loaded composite membrane samples. Membrane sample (particle/loaded side) Loading area density (gm-2) Water vapor permeance (GPU) a Pressurized air leak rate (m3/s) b   Pristine Loaded Change (%) Pristine Loaded MA-1 (NaCl/Uncoated) 2.41 8,542 8,375 -1.96 <1.0E–07 <1.0E–07 MA-2 (NaCl/Uncoated) 0.81 9,158 9,542 4.19 <1.0E–07 <1.0E–07 MA-3 (NaCl/Uncoated) 1.27 9,035 8,925 -1.22 <1.0E–07 <1.0E–07 MB-1 (NaCl/Uncoated) 7.56 14,717 13,489 -8.34 <1.0E–07 <1.0E–07 MB-2 (NaCl/Uncoated) 3.31 14,128 13,470 -4.66 <1.0E–07 <1.0E–07 PA-1 (NaCl/-) 5.31 2,049 2,015 -1.66 1.14E–05 1.08E–05 PA-2 (NaCl/-) 1.87 2,001 1,977 -1.20 1.10E–05 1.05E–05 MA-4 (NaCl/Coated) 4.32 10,009 9,735 -2.74 <1.0E–07 <1.0E–07 MA-5 (NaCl/Coated) 1.61 9,362 9,392 0.32 <1.0E–07 <1.0E–07 MB-3 (NaCl/Coated) 0.94 15,529 15,415 -0.73 <1.0E–07 <1.0E–07 MB-4 (NaCl/Coated) 1.32 15,040 14,593 -2.97 <1.0E–07 <1.0E–07 MA-6 (SGG/Uncoated) 4.58 10,209 10,111 -0.96 <1.0E–07 <1.0E–07 MA-7 (SGG/Uncoated) 4.67 9,547 9,088 -4.81 <1.0E–07 <1.0E–07 MB-5 (SGG/Uncoated) 2.02 14,958 14,670 -1.93 <1.0E–07 <1.0E–07 PA-3 (SGG/-) 1.34 1,972 2,020 2.43 1.15E–05 1.14E–05 PA-4 (SGG/-) 5.11 2,045 1,993 -2.54 1.18E–05 1.12E–05 MA-8 (SGG/Coated) 3.38 9,473 9,297 -1.86 <1.0E–07 <1.0E–07 MA-9 (SGG/Coated) 5.13 9,606 9,236 -3.85 <1.0E–07 <1.0E–07 MB-6 (SGG/Coated) 0.33 13,913 14,148 1.69 <1.0E–07 <1.0E–07 a Uncertainty (95% CI (±)) in vapor permeance measurements range from 5 to 9%.  b Bold entries indicate paper-based samples with measurable air leakage rates.  The two polymer membrane materials have much higher permeance for water vapor compared to the paper-based membrane (bold entries in Table 3.2, for readability). Moreover, paper membranes have relatively high air leakage rates, while polymer membranes have essentially no air leakage under the test pressure of 6.9kPa (1 psig). This indicates that paper samples have pores in their structure that allow air to permeate through them under a pressure gradient, while composite membrane samples have a dense, defect-free coating layer that eliminates crossover of gases by viscous flow and Knudsen diffusion transport mechanisms [138]. This allows membrane-based enthalpy cores to achieve high latent effectiveness while preventing transfer of unwanted gases and contaminants. Moreover, it can be observed in Table 3.2 that particle fouling does not significantly impact the air leak rate through polymer membranes loaded in dry conditions, whilst a slight decrease in dry loaded PA samples is noticeable. Chapter 3 –Membrane media fouling by aerosol nanoparticles 46    (a) MA membrane (b) MB membrane Figure 3.11. Water vapor permeance comparison of dry loaded membrane samples versus their pristine value  Figure 3.11 compares the water vapor permeance of dry loaded membrane samples versus their pristine value. Dry loading particles onto a membrane seems to have minimal impact on the water vapor transport through all of membrane samples, with the exception of salt particles on the uncoated side of polymer membrane MB, for which a slight decline in permeance is observed. The diminution of water vapour transport with salt deposition could be due to the irreversible changes in the structure of salt aggregates (i.e. formed during a dry load on the uncoated surface of polymer membranes) during vapor permeation testing at moderate RH of 50%. These structural changes could lead to a more compact salt deposit (less porosity and higher resistance) and therefore higher resistance of the deposit cake layer (see Figure 3.12(a)-(c)). Montgomery et al. [139] have observed similar structural changes in salt deposit cake on air filter media at RH values well below the NaCl deliquescence point (75% RH).     Chapter 3 –Membrane media fouling by aerosol nanoparticles 47   (a) Dry Loaded, stored in desiccator cabinet (RH<32%), before WVT test  (b) Dry Loaded, in room condition(RH~50%)  for 2 days, before WVT test  (c) Dry Loaded, in room condition for 2 days, after WVT at 35C, and 50%RH Figure 3.12. Impact of relative humidity changes on dry salt deposit  Chapter 3 –Membrane media fouling by aerosol nanoparticles 48  Wet Loading Conditions Table 3.3 summarizes the results of pre- and post-loading performance measurements of composite membrane samples loaded under wet loading cycles. Table 3.3. Pre- and Post-loading performance of wet-loaded composite membrane samples. Membrane sample (particle/loaded side) Loading area density (gm-2) Water vapor permeance (GPU) a Pressurized air leak rate (m3/s) b   Pristine Loaded Change (%) Pristine Loaded MA-10 (NaCl/Uncoated) 6.579 9,677 8,351 -13.70 <1.0E–07 <1.0E–07 MA-11 (NaCl/Uncoated) 1.974 9,473 8,892 -6.13 <1.0E–07 <1.0E–07 MA-12 (NaCl/Uncoated) 5.482 8,706 7,623 -12.44 <1.0E–07 <1.0E–07 MA-13 (NaCl/Uncoated) 8.772 9,940 8,604 -13.44 <1.0E–07 <1.0E–07 MB-7 (NaCl/Uncoated) 9.521 14,609 12,568 -13.97 <1.0E–07 <1.0E–07 MB-8 (NaCl/Uncoated) 7.98 14,359 12,083 -15.85 <1.0E–07 <1.0E–07 MA-14 (NaCl/Coated) 1.025 9,915 10,181 2.68 <1.0E–07 <1.0E–07 MA-15 (NaCl/Coated) 2.12 9,274 9,094 -1.94 <1.0E–07 <1.0E–07 MA-16 (NaCl/Coated) 0.74 8,850 8,877 0.31 <1.0E–07 <1.0E–07 MB-9 (NaCl/Coated) 3.19 14,293 13,788 -3.53 <1.0E–07 <1.0E–07 MB-10 (NaCl/Coated) 5.6 15,163 14,222 -6.21 <1.0E–07 <1.0E–07 MA-17 (SGG/Uncoated) 6.36 9,918 9,681 -2.93 <1.0E–07 <1.0E–07 MA-18 (SGG/Uncoated) 2.851 8,904 9,189 3.20 <1.0E–07 <1.0E–07 MA-19 (SGG/Uncoated) 7.237 9,136 8,719 -4.56 <1.0E–07 <1.0E–07 MB-11 (SGG/Uncoated) 3.46 15,600 15,542 0.00 <1.0E–07 <1.0E–07 a Uncertainty (95% CI (±)) in vapor permeance measurements range from 5 to 9%.     a) MA membrane b) MB membrane Figure 3.13. Water vapor permeance comparison of wet loaded membrane samples versus their pristine value  Figure 3.13 shows a comparison between loaded and pristine water vapor permeance of samples loaded in wet conditions. There is a consistent diminution in permeance when the uncoated side Chapter 3 –Membrane media fouling by aerosol nanoparticles 49  of the membrane is exposed to salt particulate in wet conditions, but no equivalent diminution is observed when the membrane is exposed to SGG particulate. Figure 3.14 summarizes the normalized water vapor permeance of loaded polymer membrane samples versus their particle mass loading areal density. As also apparent in Figure 3.13, wet-loading salt particles on the uncoated membrane surface significantly reduced the water vapor permeance. The same effect of wet loadings cannot be observed for samples loaded on the coated membrane side under similar particle mass loadings. Membranes wet-loaded with hygroscopic salt particles on the ‘uncoated’ side show vapor permeance declines of up to 16%, well above the level of permeance reductions due to the added cake layer resistance observed for dry loaded samples, as well as for wet loaded samples on the ‘coated’ side.  Figure 3.14. Changes in water vapor permeance of composite membrane samples resulted from dry and wet particle loading cycles  3.5.3. Pore Narrowing in Microporous Substrate Figure 3.15(c) shows an example of deposit pattern from salt particles on the uncoated side of an MB membrane sample at the end of a wet-loading experiment. Unlike salt deposit from dry loading cycles (Figure 3.15(a)), individual large salt crystals (~10μm) can be observed on substrate surfaces as a result of condensation during wet loading cycles. When the water vapor condenses on the microporous substrate surfaces, previously deposited salt particles dissolve in the condensed water droplets (Figure 3.15(b)). Large salt crystals are formed as the result of evaporation of these salt solution droplets [140] in a subsequent drying cycle. These crystals may block the pores which are located beneath them and decrease the surface porosity of the substrate. More importantly, dissolved salt in condensed water can reach the substrate pores in aqueous form. Under dry conditions, these salt ions recrystallize onto the edges of surface pores (and even potentially further into the depth of the pores) resulting in pore narrowing or complete pore blockage as shown in Figure 3.15(c). Chapter 3 –Membrane media fouling by aerosol nanoparticles 50   Figure 3.15. Substrate pore narrowing during wet loading experiments; (a) dry deposit layer at elevated relative humidity, (b) condensed water droplets, (c) salt crystals formed after a wet loading cycle  During the drying process of salt solution droplets, dissolved particles move toward the periphery of the droplet, initiating the pinning of the three-phase contact line. This is the case because the repulsive interaction between the salt particles and air is lower than that between water and air Chapter 3 –Membrane media fouling by aerosol nanoparticles 51  [141]. For a microporous substrate, the three-phase contact line accounts for the outer periphery of the droplet as well as the periphery of the pores in which air pockets are trapped beneath the droplet. As liquid evaporates from the borders, the outward liquid flux compensates for the evaporated water, transferring the dissolved particles to the three-phase contact line. The particles accumulate on the contact line and form a deposit, which perpetuates the pinning of the contact line [142]. This phenomenon is known as the “Coffee-Ring Effect” [143]. By the end of evaporation, the salt deposits can be observed on the three-phase contact lines, including the borders of the substrate pores. As shown in insets of Figure 3.15 (c), the salt deposits decrease the pore entrance size compared with the clean substrate. This leads to a net reduction in the surface porosity of the microporous substrate and thus restricted gas transport through the membrane.  Considering the fairly large break-through pressure for the pore size range of studied substrates (>10psi), it is unlikely the liquid can substantially penetrate into the pores and entrain salt ions inside the microporous structure of the substrate layer. Rather, we believe that the pore narrowing is a surface effect. However, an interesting observation from SEM micrographs of fouled substrate surfaces, particularly the ones on cleaner spots with less salt residue, is that smaller pores are narrowed below the range of detection, while larger pores are narrowed to some extent. We speculate that capillary condensation, which occurs inside pores with radius smaller than 4 nm [144], bridges a path for salt ions to migrate into the pores. After evaporation of water, recrystallization of salt blinds these small pores and results in a complete blockage of permeate transport through these pores. 3.5.4. Impact of Fouling on Microporous Substrate In order to characterize the changes to the microporous structure of substrate in a fouled membrane, fouling tests of individual uncoated substrate samples of membranes MA and MB (i.e., substrate samples SA and SB, respectively) were conducted. Substrate Fouling under Wet loading conditions Table 3.4 summarizes the results of pre- and post-loading performance measurements of uncoated substrate samples loaded under wet loading cycles. Both water vapor permeance and pressurized air leak rates are substantially reduced in loaded substrate samples. This is the result of reduced surface porosity in these samples. Table 3.4. Pre- and Post-loading performance parameters of wet-loaded substrate samples. Substrate sample (particle) Loading area density (gm-2) Water vapor permeance (GPU) a Pressurized air leak rate (m3/s) b   Pristine Loaded Change (%) Pristine Loaded SA-1 (NaCl) 7.50 20,530 16,827 -18.04 1.58E-05 9.91E-06 SA-2 (NaCl) 9.75 19,089 15,361 -19.53 1.50E-05 9.18E-06 SA-3 (NaCl) 3.29 18,467 15,930 -13.74 1.50E-05 1.23E-05 SA-4 (NaCl) 1.32 19,034 17,227 -9.50 1.55E-05 1.38E-05 SA-5 (NaCl) 0.44 19,519 18,603 -4.69 1.65E-05 1.45E-05 SB-1 (NaCl) 1.60 35,746 32,379 -9.42 2.15E-05 1.72E-05 Chapter 3 –Membrane media fouling by aerosol nanoparticles 52  SB-2 (NaCl) 1.82 37,383 34,022 -8.99 2.16E-05 1.68E-05 SB-3 (NaCl) 7.13 35,535 27,056 -23.86 2.08E-05 1.35E-05 SB-4 (NaCl) 6.43 36,184 28,007 -22.60 2.11E-05 1.40E-05 SB-5 (NaCl) 2.98 38,404 33,681 -12.30 2.17E-05 1.57E-05 SB-6 (NaCl) 1.01 36,722 32,531 -11.41 2.13E-05 1.75E-05 SA-6 (SGGl) 5.94 20,243 19,004 -6.12 1.70E-05 1.06E-05 SA-7 (SGGl) 3.38 19,396 19,198 -1.02 1.63E-05 1.20E-05 SB-7 (SGGl) 1.89 36,005 35,260 -2.07 2.11E-05 1.69E-05 SB-8 (SGG) 0.61 36,735 36,626 -0.30 2.15E-05 1.79E-05 a Uncertainty (95% CI (±)) in vapor permeance measurements range from 5 to 9%.  Figure 3.16 compares the normalized water vapor permeance of wet-loaded substrate-only samples with that of composite membrane samples (wet-loaded on the uncoated side). Uncoated substrate samples show a consistently higher flux decline compared to composite membranes with similar levels of loading areal density. This further verifies that the observed flux decline in membrane samples is caused by increased resistance of the microporous substrate due to the described pore-narrowing process.  Figure 3.16. Comparison of the changes in water vapor permeance of composite membrane and substrate-only samples under wet loading cycles  Characterization of Substrate Pore Size and Porosity Morphological characterization of microporous substrates is required in order to quantify the extent of pore narrowing fouling impact under wet-loading conditions. The DGM method as described in section 3.4.9 was applied to gas permeation measurements of pure N2 (PRAXAIR Canada, Grade 4.8 High purity>99.998%) in SB substrate samples. Two other methods, including mercury intrusion Porosimetry (MIP) and SEM surface analysis were also employed to characterize average pore diameter and porosity of the substrate samples. ImageJ, a Java-based image processing program (the U.S. National Institutes of Health), was used to binarize SEM Chapter 3 –Membrane media fouling by aerosol nanoparticles 53  images that indicate pore and non-pore areas. The pore size and surface porosity are then estimated statistically [145]. A minimum of three different spots were investigated for each sample to improve the accuracy of analysis. The average values of pore size and porosity are reported. An additional track-etched PC nanofiltration membrane with 6μm thickness and a nominal pore radius of 25nm (Whatman® nuclepore, GE Healthcare, PA, USA) was also employed as a control sample to evaluate the three methods. This porous membrane was selected because of its symmetrical structure with well-characterized pore morphology (monodispersed cylindrical pores). Table 3.5 summarizes morphological parameters of clean SB and track-etched PC substrate samples. Table 3.5. Morphological parameters of SB and PC substrates evaluated using different methods  SB track-etched PC Method 𝒅 (𝒏𝒎) 𝜺(%) 𝒅 (𝒏𝒎) 𝜺(%) MIP 121 N/A N/A N/A DGM 156±8 13.75±0.92 51±6 4.1±0.4 SEM 132±4 10.4±1.1 52±4 [146] 3.8±0.2  The results of PC substrate pore measurements align reasonably well between the two methods. These values are also consistent with reported values in the literature by Zhu et al. [146]. However, it can be observed that there are significant discrepancies between the three methods for the SB substrate. The typical porous substrates for the industrial composite membranes do not have uniform pore size and porosity. Moreover, surface characterization techniques such as SEM may not provide an accurate description of the effective pore size and porosity because some pores on the surface may have dead-ends [146]. Table 3.6 summarizes the results of DGM analysis of wet-loaded SB substrate samples. It can be seen that there is a consistent reduction in surface porosity of the fouled samples, which is believed to be responsible for the flux reductions discussed in previous sections. Table 3.6. Morphological parameters of wet-loaded SB substrates evaluated using DGM method Substrate sample Loading area density (gm-2) Mean pore diameter 𝒅 (𝒏𝒎) Fouling Factor (𝑭𝑭)a Surface porosity (𝜺(%)) b Clean SB - 156±8 1.00 13.75±0.92 SB-1 1.60 158±9 0.89 12.38±0.83 SB-5 2.98 154±8 0.86 12.00±0.86 SB-4 6.43 146±10 0.81 11.10±1.06 SB-3 7.13 150±8 0.78 10.49±0.67 a Fouling factors were calculated as the ratio of effective porosity (𝜀 𝑞2⁄ ) of a loaded sample to its clean value with the assumption that fouling does not affect the tortuosity factor of the sample. b The surface porosity values were calculated assuming a tortuosity factor of q=2.  3.5.5. Fouling Mechanisms The fouling mechanism that emerges from the SEM micrographs and membrane permeance data of wet loaded samples is schematically shown in Figure 3.17. Deposition starts with the initial accumulation of dry particles on the surface of substrate. The subsequent deposition of particles (i.e., either formation of a uniform cake layer or sparse aggregates) would depend on the extent Chapter 3 –Membrane media fouling by aerosol nanoparticles 54  and nature of this initial deposition determined by the state of aerosol and surface charges.  Given relatively small flux normal to the membrane surfaces, significant internal deposition does not occur on the uncoated side, but formation of a compact deposit on the surface of membrane is quite possible. Surface condensation during a wet loading cycle results in partial or complete pore blockage from hygroscopic particles, whereas it has no measurable impact on non-hygroscopic particle deposits such as the graphite particles studied here. In the case of hygroscopic salt particles, narrowing of pore entrance at the surface, as well as pore constriction and blockage inside the substrate are plausible scenarios.  Figure 3.17. Summary of fouling mechanisms from aerosols in asymmetric composite membranes; (a) hygroscopic particles, (b) non-hygroscopic particles  3.6. FOULING CONTROL IN MEMBRANE-BASED ENTHALPY EXCHANGERS There are in general two type of strategies that are usually employed to minimize the impact of fouling; 1) first group includes preventive measures for minimization of fouling by adequate pre-filtration of supplied air streams, membrane treatment and surface modification, operative measures, etc. 2) the second group involves membrane remediation by cleaning methods for membrane flux recovery. Based on the findings of the experimental investigation presented in the last two chapters, a number of general recommendations to control and minimize airborne particulate fouling and its potential adverse effects on performance of membrane-based ERVs may be made as follows. Chapter 3 –Membrane media fouling by aerosol nanoparticles 55  3.6.1. Upstream Filtration The sensible and latent effectiveness of membrane ERVs is not substantially degraded by fouling from dry dust, non-hygroscopic particles, and hygroscopic particles in dry conditions.  If the ERV is installed downstream of the HVAC system supply air filters, the typical level of filtration required to protect HVAC equipment is enough to prevent air-side fouling of ERV exchangers from dust in the air stream. On the exhaust side, medium- to low-MERV filters would be adequate to arrest >90% of coarse particles and to address the added core pressure drop resulted from dust loading [147]. For humid air containing substantial concentrations of soluble particles, the ERV may be more sensitive to fouling and therefore require better protection by filters. 3.6.2. HVAC System Operation Control Strategy From the results of deposition fraction measurements, it can be concluded that the rate of aerosol fouling would be lower at higher working airflow rates of the enthalpy exchanger core. Where system operation requirements allow, enthalpy exchangers should be run at the highest rated flow rate to minimize rate of particle deposition on membrane surfaces. The size-resolved particle deposition fractions studied here can be used in indoor aerosol transport models of HVAC systems to predict particle fouling rates of ERV cores for various residential and commercial applications. The predicted fouling rates can then be used to estimate energy implications of core fouling, and filter changing and cleaning schedules for enthalpy cores [148]. It must however be considered that these estimations are usually associated with large uncertainty bounds due to the uncertainty of deposition fraction measurements and degree of fouling, as well as variable operating conditions. These large uncertainties reinforce the need for investigation of more reliable methods of monitoring fouling in future studies, such as on-site monitoring of pressure drop across the enthalpy cores or their latent effectiveness. 3.6.3. Orientation of Membrane Based on the findings with regard to the membrane orientation-dependent impact of hygroscopic particle fouling under wet conditions, it is recommended that for membranes with directionality, the coated (dense polymer) side of membranes face the air stream with higher concentrations of nanoparticles. This could be either indoor or outdoor air streams depending on the building application. Furthermore, ERV cores should be installed such that potential condensation occurs on the coated surface of membrane media. This would minimize the occurrence of fouling in the pores of the substrate side as observed under wet loading conditions. 3.6.4. Membrane Cleaning and Flux Recovery The results from this study suggest that membrane fouling of enthalpy exchangers can be important in cases where foulant material could be transported into the pores of the membrane substrate. Such situations would arise when a large fraction of atmospheric aerosols are hygroscopic and exposed to high humidity (e.g., marine environment) or the aerosols contain liquids (e.g. cooking oils or tobacco smoke). Polymeric membranes can withstand liquid water and washing, and since hygroscopic particles could potentially be removed with a simple water washing procedure, future Chapter 3 –Membrane media fouling by aerosol nanoparticles 56  work should investigate the effectiveness of various membrane cleaning strategies. These studies should address the trade-offs between filtration requirements and cleaning/replacement frequency. 3.7. CONCLUSIONS The second step of particulate fouling assessment in membrane-based ERVs, presented in this chapter, investigated the impact of fouling by ultrafine aerosol nanoparticles (~100nm) on the performance of composite water vapor transport membranes (i.e., current generation membrane media for ERVs). The mechanisms of fouling on both sides of these asymmetric membranes were studied through accelerated loading tests with aerosols of different chemistry and varying operating conditions. The following conclusions can be drawn: o Moderate membrane fouling by both hygroscopic and non-hygroscopic particles under dry loading conditions (i.e., no condensation occurs) was shown to have minimal impact on the performance of membrane samples. o High levels of dry loading particles on both ‘coated’ and ‘uncoated’ membrane sides, that can form a uniform, compact, thick cake layer (≥membrane thickness), result in a slight reduction in water vapor permeance (<5%) due to the added resistance of the cake layer. o The state of the aerosol and surface charges influence the deposition fraction and determine the deposit morphology. Aerosol particles neutralized with a soft x-Ray neutralizer (TSI 3088) showed a tendency to form a uniform, compact deposit layers leading to cake layer formation. In contrast, non-neutralized particles showed a tendency to form sparse aggregates on membrane surfaces. o The impact of fouling on membrane permeance was found to be significantly larger when membranes were loaded in wet conditions: membranes wet-loaded with hygroscopic particles on the ‘uncoated’ side showed vapor permeance declines of up to 16%, whilst membranes loaded with SGG particles or salt particles on the ‘coated’ side did not show a significant flux decline under similar wet loading conditions. o Characterization of the microporous structure of the membrane substrate layers showed that the observed permeance degradation (under wet loading conditions) is the result of pore size and effective surface porosity reduction. o These results suggest that the optimal protection by filters and the orientation of the membrane (coated side on exhaust or supply side) would depend on the nature of the indoor and outdoor aerosols. Air-side particulate fouling of composite membranes can be controlled and minimized by measures, such as: (1) exposing membrane coated side to the stream with more nanoparticles; (2) membrane module installations such that any potential condensation occurs on the coated side; (3) periodic membrane cleaning (e.g., washing with distilled water).   57  Chapter 4 - THE EFFECTS OF TEMPERATURE AND HUMIDITY ON THE PERMEATION PROPERTIES OF MEMBRANE MEDIA1  4.  4.1. OVERVIEW This chapter addresses the third objective of the study. Samples from the two types of dense polymers; glassy and rubbery, are investigated to determine their suitability for ERV applications. The first part of this chapter discusses the fabrication of composite membranes from a series of commercially available polymers. For the coating layer, materials are selected based on two criteria to meet the requirements of ERV application; high water vapor permeation rate (>10 kg/m2day) and a selectivity higher than 100 for water vapor over indoor air contaminants. CO2 is selected as a surrogate for gas-phase indoor air contaminants to evaluate the selectivity of membrane samples. The choice of materials is narrowed down to four high-performance polymers; PEBAX®1074, PERMAXTM 230 (PU-PEO), sulfonated poly(ether ether ketone) (SPEEK), and Cellulose Acetate (CA). The second part discusses the experimental test apparatus and methods developed for measurement of simultaneous water vapor and CO2 permeation rates. A systematic study investigates the effects of relative humidity and temperature on the permeation properties of composite membrane samples. Results show that rubbery membrane samples, with glass transition temperatures well below the temperature range of experiments (30°C to 50°C), have a higher water vapor permeability and a much higher CO2 permeability compared to glassy membrane samples. In all polymer samples, water vapor permeability increases with relative humidity (up to an order of magnitude) and decreases with temperature, while opposite behavior is observed for CO2 permeability. In general, the permeability results reported here suggest that ERV exchangers using high-performance polymer membranes can achieve acceptable overall effectiveness (i.e.,>50%) over a wide range of operating temperature and relative humidity while maintaining very low CO2 crossover rates (<1%).                                                             1 A version of this chapter has been published: “The effects of temperature and humidity on the permeation properties of membrane transport media used in energy recovery ventilators”, ASHRAE 2017 Annual Conference Proceedings, D-LB-17-C067. Copyright © 2017 ASHRAE, Atlanta, GA. All rights reserved. Reprinted with permission. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 58  4.2. INTRODUCTION In fixed-plate membrane-based energy exchangers, latent effectiveness corresponds to the moisture transport properties of the membrane media (i.e., moisture permeation properties of the dense coating and pore morphology of the microporous substrate in composite membranes). As was discussed earlier in Section 1.1.2, membranes suitable for these exchangers must be extremely moisture permeable to achieve acceptable total effectiveness (>50%) required by ASHRAE 90.1 [81]. This is due to the minimal differences in partial vapor pressure between the supply and exhaust air streams of buildings (typically in the range of 1000-4000 Pa). Also, ERV operation must prevent significant crossover of indoor air contaminants between the supply and exhaust air streams. Transfer of contaminants through energy exchangers can be due to different mechanisms: air leakage, carryover, and adsorption to desiccant media (i.e., in rotary-type exchangers), as well as permeation through membrane media [32]. When selecting membrane material for plate-type energy exchangers, besides a high water vapor permeability, high selectivity for water vapor over unwanted gases (e.g., CO2 and VOCs) and contaminants that may be present in the outgoing indoor air from buildings is another important factor [30], [31]. Polymeric membranes have broad ranges of permeability for water vapor and various other chemical species found indoors. Permeation properties of polymeric membranes depend on a range of factors, such as the nature of the polymer material (chain packing and flexibility, degree of crystallinity, etc.), state of the polymer material based on the glass transition temperature, Tg (i.e., rubbery vs. glassy), polymer-gas and -vapor interactions, and operating conditions [30], [83]. In most polymers, water vapor permeates at a much higher rate compared to permanent gases (due to its superior solubility) and VOCs (due to its smaller molecular size thus superior diffusivity) [83], [88], [91]. Therefore, a high degree of separation can be achieved with the appropriate material selection for the membrane media of plate-type energy exchangers. Such membrane materials will be able to achieve acceptable latent effectiveness without allowing a significant crossover of pollutants. Chemical structure and physical properties of the polymer under a specific operating condition determines the effective permeability of a membrane for water vapor [83]. There are several studies in the membrane technology literature reporting that permeation properties (i.e., solubility and diffusivity) of dense membranes, particularly for low-pressure vapor separation applications, depend on the operating conditions of the adjacent process streams, including temperature, pressure, and composition of both feed and sweep sides (also referred to as ‘supply’ and ‘exhaust’ sides in this study) [83]. Reasons include varying sorption properties, polymer swelling [149], its simultaneous softening (plasticization) as well as clustering effects of the penetrant molecules [27], [88], [93]. In the case of composite membranes, the substrate layer exerts an additional resistance to the moisture transfer through the membrane [150]. It can also alter the effective vapor pressure and temperature gradients across the dense coating layer, depending on the membrane orientation (i.e., substrate exposure to the feed side or the sweep side). This could potentially result in significantly different permeability values for the dense coating layers with strong temperature- and concentration-dependence in solubility and diffusivity properties [69], [151]. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 59  Moreover, the transport of other gaseous and vapor species through dense polymers may be strongly affected by membrane moisture uptake at various humidity levels, and by the temperature of the working airstreams [88], [89], [94], [95], [152]. Different phenomena, such as competitive sorption and membrane swelling by moisture may either decrease or increase the transport rate of slow-permeating species (i.e., contaminants in ERV membranes) in dense membranes [94], [153]. Little is known on the simultaneous permeation of water vapor and indoor contaminants through highly moisture-permeable polymers. ERVs are used in various climates and seasonal conditions spanning a wide range of operating temperatures and relative humidity. It is therefore essential to understand the effects of these parameters on the performance of membrane media (moisture permeability and selectivity) and the overall performance of energy exchanger cores. This chapter presents a systematic experimental study of the effects of relative humidity and temperature of working air streams on the transport of water vapor and CO2 (as a surrogate for gas-phase indoor air contaminants to assess membrane selectivity) through a number of polymeric materials suitable for use in ERVs. The results reported provide some guidelines for future material selections in ERVs used in different environments, as well as the required understanding of important factors for the core-level performance modeling presented in Chapter 6. 4.2.1. Contaminant Transfer in ERVs ASHRAE 84-2013 [32] requires the evaluation of contaminant transport within energy exchangers (at a single test condition at room temperature) using two performance metrics: exhaust air transfer ratio (EATR), and outside air correction factor (OACF). EATR is a measure of mechanical mechanisms of contaminant transfer within energy exchangers (i.e., bulk leakage flow due to air pressure differences and carry-over in rotary-type exchangers) and is determined by measuring concentration of a tracer gas at the inlets and outlets of the working air streams.  𝑬𝑨𝑻𝑹 =𝑪𝒔,𝒊𝒏 − 𝑪𝒔,𝒐𝒖𝒕𝑪𝒆,𝒊𝒏 − 𝑪𝒔,𝒊𝒏 (4.1)  where 𝐶𝒔,𝒊𝒏, 𝐶𝒔,𝒐𝒖𝒕, and 𝐶𝒆,𝒊𝒏 are the tracer gas concentrations at supply air inlet, supply air outlet, and exhaust air inlet, respectively. Likewise, OACF characterizes mechanical air leakage transfer from the supplied outdoor air to the leaving exhaust air, defined by the following equation:  𝑶𝑨𝑪𝑭 =  ?̇?𝒔,𝒊𝒏?̇?𝒔,𝒐𝒖𝒕 (4.2)  where ?̇?𝑠,𝑖𝑛 and ?̇?𝑠,𝑜𝑢𝑡 are the mass flow rates of dry supply air inlet and outlet, respectively. These tracer gas and OACF tests are useful for measuring the air leakage and defect levels of the membrane media and the exchanger core construction in plate-type energy exchangers. However, they may not sufficiently account for the contaminant transfer by permeation phenomena through the membrane media, especially sorption and diffusion through the dense selective layer of composite membranes at different operating conditions. In fact, ASHRAE 84-2013 requires selection of an inert tracer gas for the EATR measurements (commonly sulfur hexafluoride, SF6) Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 60  that will not be significantly transferred by the desiccant surface of energy recovery devices (i.e., rotary wheels).  SF6 has been traditionally used as the challenge tracer gas for these tests because it is non-reactive and non-toxic, sensitive gas analyzers measuring in ppb range are readily available, and it can easily be separated from other detectable background gases chromatographically. However, the large, non-condensable SF6 gas molecule, with a kinetic diameter of dk=5.5A˚, is expected to have a significantly lower permeability in polymeric systems compared to most indoor air contaminants [83]. Thus, not a good surrogate for other gas-phase indoor contaminants to investigate membrane selectivity. Indoor air gaseous contaminants include a wide variety of chemical compounds, emitted from different sources indoors or brought into the building with outdoor air. They range from inorganic permanent gases, such as carbon monoxide (CO), nitrogen dioxide (NO2), Carbon dioxide (CO2), ozone (O3), and radon, to carcinogenic or sensory-irritant volatile and semi-volatile organic compounds (VOCs and SVOCs) with short-term and long-term adverse health effects (e.g. Benzene and Formaldehyde) [154]. Recent studies by Zhang [31] and Huizing [30] have investigated the permeation of water vapor and various indoor air contaminants through some different commercial ERV membranes. Using single gas measurements and constant test conditions, they have shown that the relative transport of water vapor, gases, and contaminants varies significantly depending on the membrane-permeating species pair. Due to the complex nature of the mass transfer phenomena in polymer membranes, it is evident that selection of any specific contaminant as the challenge tracer gas for EATR tests might be insufficient to adequately quantify the transfer of all contaminants in plate-type membrane-based exchangers. We have selected CO2 as the tracer gas to evaluate EATR and material selectivity of membrane samples in this study. Although indoor CO2 concentration (typically <1100ppm) is generally not a health concern, it is a related parameter most widely used for IAQ assessment and a surrogate indicator for other pollutants that are difficult to measure. CO2 concentrations are consistently higher indoors than outdoors. It is relatively easy to measure and also its association with the adverse health impacts of inadequate ventilation is extensively reported in the literature [155]–[158]. Mental and physical capability decreases as a result of CO2 concentration rise. OSHA recommends a time-weighted average of 5000ppm as the maximum limit of occupational exposure for a workday (8 hr) [154]. CO2 concentrations below 400 ppm meet the highest indoor air quality, between 400-600 ppm and 600-1000 ppm are considered as medium and moderate quality, respectively. Concentrations above 1000 ppm indicate poorest air quality [159]. More importantly, due to the special chemical nature of the CO2 molecule, it is believed to be a good surrogate for assessing membrane selectivity for water vapor over indoor gas-phase contaminants. Gas transport through dense polymers obeys the solution-diffusion mechanism, where permeability is the product of material sorption and diffusion properties (℘ = 𝑆 × 𝐷) [48]. The solubility of gas molecules in the membrane depends primarily on gas condensability (characterized by the critical temperature) and the affinity between gas molecules and membrane matrix. Therefore, gas solubility can be increased by increasing the condensability of gas molecules and/or by increasing the interactions of gas molecules with the membrane matrix. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 61  Gas diffusion through the membrane is governed by the free volume characteristics of the membrane bulk as well as the size of gas molecules. Free volume refers to the void space between polymer chains and is among the most important structural variables influencing diffusivity in membranes. Incompact polymer chain packing and the random motion of polymer chain segments allow gas molecules to diffuse through the matrix more freely [160]. Gas diffusivity increases with the decrease of gas molecule size and with the increase in the number and size distribution of free volume elements. Gas diffusivity through the membrane increases inversely with the gas kinetic diameter. A list of physical and chemical properties of various indoor gases and contaminants are summarized in Table 4.1. CO2 has a much higher critical temperature than other permanent gases, corresponding to higher condensability and higher gas solubility in membranes. Moreover, although the CO2 molecule as a whole is non-polar, localized polar sites may generate specific interactions with some functional groups in the membrane matrix, leading to higher solubility. Table 4.1. The physical and chemical properties of indoor gas-phase contaminants Gas Critical Temperature TC(℃) a Kinetic diameter dk(A˚) [83]  CO2 31 3.30 N2 -147 3.64 O2 -119 3.46 CO -140 3.76 NO2 158 3.40 Ozone (O3) -12 3.83 SF6 b 46 5.50 Formaldehyde (HCHO) 240 4.00 Benzene (C6H6) 289 5.85 Toluene (C7H8) 319 5.85 a www.NIST.gov. b SF6 is not an indoor air contaminant and is included in this table for comparison purpose only.  Because of oblate ellipsoidal shape of CO2 molecule [45], it also possess a smaller kinetic diameter compared to other indoor gases and contaminants, thus a higher diffusivity in polymers. Therefore, combining a high critical temperature and a low kinetic diameter relative to other indoor contaminants, CO2 is expected to have a higher permeability in many polymers compared to most non-condensable light indoor gaseous contaminants. In fact, application of membrane gas separation technology has been extensively reported for removal of CO2 from light gases [161]. In comparison to VOCs, however, solubility and diffusivity of CO2 follow different trends. Even though indoor pollutant VOCs, such as Formaldehyde and Benzene have significantly larger kinetic diameters compared to CO2, they are significantly more condensable than CO2 that could render them to be more permeable in polymer membranes. Consideration of CO2 as a tracer gas for EATR tests in this study is merely for comparison of selectivity between different membranes and is not meant to represent all indoor air contaminants. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 62  4.2.2. Membrane Requirements for ERV Exchangers Based on the guidelines in Section 5.16.3 of ASHRAE standard 62.1-2016 [9], the acceptable levels of cross-leakage in energy recovery devices were recommended as a maximum of 10% crossover for Class 2 air streams with moderate contaminat concetration (e.g. rest rooms, swimming pools, dining rooms, and wharehouses) and a maximum of 5% crossover  for Class 3 air with significant contaminant concentration or offernsive odors or sensory-irritation intensity that is suitable for recirculation within the same space (e.g. kitchens, dry cleaners, beauty salons, laboratories, and pet shops). Given typical single pass cross-flow geometry of fixed-plate enthalpy exchangers, following limits of membrane permeation properties can be considered as a guide to meet the requirements of ASHRAE 90.1 and ASHRAE 62.1 standards for energy recovery devices [31] - Water vapor flux >10 kg/m2day - Water vapor/CO2 selectivity > 100 A summary of water vapor and CO2 permeability for various commercially available polymers, mostly obtained from single gas permeability experiments, is presented in Table 4.2. Selectivity is simply calculated as the ratio of the permeability for the two species. As seen in this table, most of highly selective polymers also possess a high water vapor permeability, unlike the general permeability/selectivity trade-offs present in binary mixtures of permanent gases, represented by a Robeson plot [162]. Figure 4.1 compares the moisture flux versus water vapor/CO2 selectivity for the polymers of Table 4.2. Water vapor flux is estimated based on a film thickness of 5µm with water vapor activity of 0.5 and 0 on feed and permeate sides of membrane, respectively. The moisture flux (i.e. directly proportional to water vapor permeability) varies over 4 orders of magnitude and the selectivity varies up to 7 orders of magnitude between the various polymers.             Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 63  Table 4.2. Permeability data for water vapor and CO2 in various film-forming polymeric materials Polymer Tg(ºC)a Permeability * 𝛂𝒊𝒅𝒆𝒂𝒍 ℘𝑯𝟐𝑶(𝒗) ℘𝑪𝑶𝟐 (℘𝑯𝟐𝑶(𝒗)℘𝑪𝑶𝟐) (Barrer)b Ref. (Barrer) Ref.  Rubbery Polydimethylsiloxane PDMS -123 40000 [91] 2850 d [163] 14 1000PEO40PBT60 PEO-PBT -46 85500 [91] 71 [164] 1204 Poly(ether-b-amide) PEBAX®1074 -55 48000 [93] 110 d [165] 455 Polyethylene Oxide-Polyurethane PEO-PU -45 34000 [44] 50.5 [44] 1069 Polyethylene PE -44 12 [91] 13 c [166] 1 Polypropylene PP -15 68 [91] 9.1 [167] 7 Natural rubber NR -72 2600 [91] 131 d [168] 20 Buthyl rubber IIR -65 90 e [169] 4.7 c [170] 19 Poly(1,2-butadiene) PB -85 4100 e [171] 138 [83] 30 Polyisoprene IR -73 3300 e [171] 110 [172] 30 Glassy Polymethylpentene TPX 168 21000 c [173] 100 [172] 210 Poly(vinyl alcohol) PVA 85 19 [91] 0.019 [172] 1000 Polyamide 6 (Nylon 6) PA-6 50 275 [91] 0.088 d [165] 3125 Poly(vinyl chloride) PVC 87 275 [91] 0.029 [83] 9483 Polyimide (Kapton) PI 350 640 [91] 2.0 d [174] 320 Polystyrene PS 100 970 [91] 12 c [163] 81 Polycarbonate PC 150 1400 [91] 6 d [175] 233 Polysulfone PSF 190 2000 [91] 5.6 d [176] 357 Polyethersulfone PES 225 2620 [91] 3.38 [177] 775 Poly(phenylene oxide) PPO 220 4060 [91] 61 [178] 67 Cellulose acetatef CA 80 6000 [91] 4.8 d [179] 1250 Sulfonated polyethersulofon SPES 120 15000 [91] 2.27 d [177] 6608 Ethyl cellulose EC 140 20000 [91] 110 c [163] 182 Sulfonated polyetheretherketong SPEEK 196-220 61000 [91] 8.12 c [180] 7512 Perfluorosulfonic Acid Copolymer Nafion 117 120-140 230000 [181], [182] 8.07 [183] 28501 Polyacrylonitrile PAN 120 200 [91] 0.0003 c [83] 666667 Poly[1-(trimethylsilyl)-1-propyne] PTMSP 200 9200 d [184] 20000 [172] 0.5 * All permeability data are at 30ºC; at a feed pressure of 1 atm for CO2 and extrapolated to 0 activity for water vapor (infinite dilution), unless otherwise is stated. a Tg data are obtained from references [88], [94], [189], [190], [150], [163], [166], [172], [185]–[188]. b 1Barrer = 10-10 cm3 (STP).cm.cm-2.s-1.cmHg-1 = 7.5×10-18 m3 (STP).m.m-2.s-1.Pa-1  c, d, e Permeability data are reported at 25 ºC, 35 ºC, and 39.5 ºC, respectively. f Degree of acetylation (DS=2.45) [191]. g Degree of sulfonation (DS=0.44) [180].  Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 64   Figure 4.1. Water vapor flux vs water vapor/CO2 selectivity in various commercially used polymeric films  An interesting trend that can be observed in Figure 4.1 is the difference between glassy and rubbery polymers. In general, glassy polymers seem to show better selectivity properties (i.e located in the upper half of the plot) for water vapor over CO2. The polymers located at the top right corner of Figure 4.1 are desirable for ERV application. They could potentially meet the requirements of ASHRAE standards 62.1 and 90.1 if used in the development of membrane media for an enthalpy exchanger core. As indicated by the dashed zone, there are only a few polymers that combine a high water vapor flux (>10 kg/m2day) and selectivity within the range of requirements for high performance ERV exchanger cores. Three of these high performance dense polymers (SPEEK, PEBAX®1074, and PEO-PU) and a cost-effective, widely available polymer (CA) with a moderate performance were selected for this study. The following sections describe the procedures for preparing composite membranes from these polymers on an identical microporous substrate to enable their comparison under the investigated range of operating conditions. 4.3. MATERIALS AND MEMBRANE FABRICATION 4.3.1. Materials and Chemicals Microporous Substrate Layer. Celgard® 2500, a 25µm microporous monolayer polypropylene (PP) film was used as the substrate layer for preparing composite membrane samples. This microporous film has a uniform pore structure with an average pore diameter of 0.13 µm and 55% porosity [192]. It provides good mechanical and handling properties while maintaining relatively low resistance to water vapor transport through the resultant composite membranes. Surface Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 65  micrographs of the Celgard® 2500 substrate are presented in Figure 4.2 showing its microporous morphology. The structural and compositional data for this material is also summarized in Table 4.3.  Figure 4.2. Scanning electron micrographs of Celgard® 2500 film at 5k and 20k (inset) magnifications  Table 4.3. Properties of Celgard® 2500 substrate used to make composite membranes Material composition Polypropylene Porosity (cm3/cm3) 0.55 Average pore diameter (μm) 0.13 Thickness (μm) 25±1 Basis Weight (g/m2) 10.9±0.1 Density (kg/m3) 435± 59 Air permeability (cm3/cm2/Pa/s) 2.39×10-5±1.5×10-6 Water vapor fluxb (kg/m2/day) 32.054±0.748 Water vapor permeanceb (GPU) 41000±2100 a errors values are standard deviations for three measurements five different samples. b test conditions at T=50°C, feed RH=50%, Sweep RH=0%.  Dense Selective Layer. The select properties of the four dense polymer materials are summarized in Table 4.4. Densities of the films were measured by a pycnometer technique using hexane as the displacement fluid to an accuracy of approximately ±0.003 g/cc.    Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 66  Table 4.4. Properties of membrane coating materials Coating polymer WCA (°) 𝑻𝒈(℃) 𝝆(𝒈𝒄𝒄) a State at experimental temperature range Coated thickness (µm) CA 65 (hydrophilic) 105 1.28±0.17 Glassy 0.823±0.13 b SPEEK 70.5 (hydrophilic) >140 1.32±0.17 Glassy 2.63±0.35 PEO-PU 63 (hydrophilic) -48 1.21±0.16 Rubbery 2.52±0.33 Pebax® 1074 76.3 (hydrophilic) -55 1.14±0.15 Rubbery 1.85±0.26 a Error values indicate standard deviation of three measurements of density for each polymer. b Due to the extremely low permeability of CO2 through CA its thickness was deliberately maintained to be lower than other membranes so that a detectable concentration of CO2 can be measured at the outlet of sweep stream.  1. Cellulose Acetate (CA): The polymer, obtained as un-plasticized powder from Tennessee Eastman Co., has a density of 1.327g/cc, and degree of substitution (DS) of 2.45. The degree of substitution (DS) refers to the average number of acetyl groups per repeat unit. For example, a fully substituted material has a DS of 3 [179]. To prepare CA coating solutions, 7 wt.% solutions were prepared by dissolving polymer powder in acetone as the casting solvent. This solution was then allowed to sit for 24hr to remove bubbles. 2. Sulfonated aromatic poly(ether ether ketone) (S-PEEK): the S-PEEK solution was made from a solution of 10%wt. S-PEEK with an 80%wt. acetone water mixture as the casting solvent. 3. Poly(ether-block-amide) PEBAX®1074: Poly(ether-block-amide) copolymer is a relatively recent line of thermoplastic elastomers introduced by Arkema Inc. The polymer consists of rigid polyamide (PA) and soft polyether (PE) blocks. Various grades of this copolymer have been developed under the trade name PEBAX®; PEBAX®1074 containing 55 wt.% of poly(ethylene oxide)(PEO) and 45 wt.% of polyamide 12 (PA 12 or Nylon12) [185] possesses the highest water vapor permeability amongst all grades in this family [193]. Medical grade PEBAX® MV 1074 SA 01, received in pellets form (2-3 mm in diameter) from Arkema Inc., presents a Tg of about -55°C, density of 1.09g/cc. 10 wt.% PEBAX solutions were prepared by dissolving polymer in a 70% ethanol water casting solvent. This solution was then heated in a water bath to 90°C and coated while still warm. 4. PEO-PU: A Polyether–polyurethane wet dispersion, commercially available as PERMAX™ 230, was purchased from Lubrizol Advanced Materials with a polymer concentration of 32.33 wt.% in water. Polycarbodiimide cross-linker solution was obtained from Stahl under the trade name Picassian XL-702, with a concentration of 39.84 wt.% in water.  PERMAX™ 230 is a thermoplastic polyurethane (TPU) copolymer of PEO (75 wt.%) and hard polyurethane blocks (25 wt.%) [24]. PU-PEO polymer solutions were prepared by blending PERMAX™ 230 and XL-702 cross-linker (in solids wt. ratio of 12:1 (i.e. 6.0 wt.% polycarbodiimide cross-linker)) and diluting in DI water to obtain a 25 wt.% solution. 4.3.2. Composite Membrane Preparation Composite membranes are prepared by casting polymer solutions using a dosing rod method [167] onto the Celgard® 2500 substrate and subsequent evaporation of the solvent. The rod size and polymer solution concentrations are selected to control a very thin coating layer thickness (<3µm). Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 67  The resultant membrane has an asymmetric composite structure (see Figure 4.3). There is at least one industrial manufacturer (dPoint Technologies) currently producing such composite membranes for enthalpy exchangers. Such composite membranes are shown to be advantageous over free-standing dense membranes by providing; 1) better handling and manufacturing properties, 2) dimensional stability to the coating layer where it undergoes significant swelling as a result of exposure to high relative humidity or liquid water (e.g. condensing and freezing conditions) [43].   Figure 4.3. Cross-sectional SEM micrographs of a commercial asymmetric composite membrane [27]  Pressurized air leakage testing of membrane samples were completed using the method described in section 3.4.8 of Chapter 3 in order to ensure a defect-free coating layer is obtained. 4.3.3. Coating Thickness The Celgard® 2500 substrate has a very uniform, relatively low basis weight (10.88 g/m2) with variations of less than 1% (±0.11 g/m2), much lower than the dense polymer coating areal weight (raging from 1 to 4 g/m2) indicating that coating layer thickness can be relatively accurately estimated by gravimetric method. To determine the final coating thickness of membranes, the coated samples used in measurements were weighed to determine total weight. From this, the weight of the uncoated Celgard® 2500 was determined by averaging ten mass measurements from samples of the same size. The mass of the uncoated membrane was subtracted from total membrane mass. From measured mass and density of the coating layer, its thickness was determined. As the membranes used for this round of testing were all hand cast there is expected to be some variability in the coating thickness. Measurement uncertainties in coating thicknesses were determined from averaging the coated weight from five 2”×2” samples of the coated membranes. Results of coating thickness measurements along with the estimated uncertainty values are summarized Table 4.4. To compensate for some of this uncertainty, where possible the same sample was used in testing that the mass measurement was taken from. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 68  4.4. MEASUREMENT OF MIXED GAS/WATER VAPOR PERMEATION  This section describes in detail a mixed gas permeation (MGP) test apparatus for evaluating permeation properties of composite membrane samples. The permeability to water vapor and CO2 are simultaneously measured for membrane samples at varying feed side relative humidity and test temperatures relevant to ERV applications.  We have employed a dynamic water vapor transport rate (WVTR) testing method in the design of the MGP test apparatus similar to that described in ASTM F2298 [194]. In this method, permeated penetrants through the membrane samples are continuously swept by a sweep gas on the downstream side of the membrane (see Figure 4.4). Permeability is then evaluated by measuring the concentrations of retenate and permeate streams constantly using a dew-point chilled mirror sensor for water content and an infrared sensor for CO2. This method represents test conditions more similar to the actual conditions ERV membrane samples experience in operation.  Intrinsic material permeability data are reported by subtracting the boundary layer resistances characterized for the specific permeation test cell (Figure 4.5) used for holding membrane samples. 4.4.1. Test Apparatus The MGP test apparatus (Figure 4.4) enables the permeation testing of membrane samples in temperature and relative humidity ranges of 25-70°C and 0-85%RH, respectively. The test apparatus creates two gas streams, referred to as the “Feed” and “Sweep” streams, which counter-flow on either side of a flat sheet membrane sample held in a special permeation testing module (Figure 4.5). The flow rates are controlled by mass flow controllers MFC-1 and MFC-2 (Alicat Scientific MCS). The outlets of the two streams are open to ambient to minimize pressure forcing crossover through the membrane samples. In addition, pressure difference between the two streams inlets (ΔP1) is monitored using a differential pressure gauge (Dwyer 2000 Magnehelic®). The Feed stream contains 10% CO2 with the balance of N2 (PRAXAIR Canada). This concentration, although much higher than ambient air levels, allowed repeatable (within ±10%) and accurate concentration measurements at the outlet of sweep stream for all membranes. Plasticization effects of CO2 can be neglected at this concentration and ambient pressure [195]. The RH of Feed stream is adjusted by splitting it up into two branches; one of which passes through a humidifier HUMR (dPoint Px1-32) and gets saturated before recombining with the other branch to create the desired humidity level. The RH is then controlled by adjusting the proportion of these two branches using two manual needle valves (Figure 4.4). The Sweep stream flowing on the opposite side of the membrane is N2 from a separate gas cylinder (PRAXAIR Canada, Grade 4.8 High purity>99.998%, H2O<3ppmv, CO2 (-)) that removes the water vapor and CO2 permeate through the membrane material. The membrane permeation module along with all the gas lines are placed inside a temperature controlled forced convection oven (MT Model OF-22GW) to conduct tests isothermally. The operating manual of the oven specifies a temperature uniformity of ±1°C with ±0.2°C stability inside the oven.  Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 69   Figure 4.4. Schematic presentation of the mixed gas permeation (MGP) test apparatus  The temperature and relative humidity of all inlets and outlets of the membrane cell (S1 to S4) are recorded using four polymeric relative humidity and temperature sensors (TE Sensor Solutions HTM2500LF). Polymeric sensors suffer from a time-dependent drift of the measurement signal. This is mainly caused by aging and contamination of the incorporated polymer. Alternatively, dew-point chilled mirror sensors offer much greater accuracy (e.g. ±0.15°C dew point temperature accuracy that is equivalent to a ±0.4%RH at 50°C) and stability for direct water content measurements compared to the polymeric RH sensors. But they are much more expensive and sophisticated to handle. In order to maximize accuracy, the volume flow rate is limited to a very small range (usually <1SLPM). Thus dew-point mirrors are most often applied in side streams.  In order to achieve good applicability and high accuracy, a single dew-point chilled mirror sensor (EdgeTech DewMaster S2SCPT) is also placed at outlet of sweep stream (permeate S4) providing a means of direct measurements of water vapor flux through the sample. Prior to each experimental run the polymeric sensors are leveled by the dew point mirror and are used to monitor mass balances during the experiments. Hereby the theoretical sensor accuracy improved from 3%RH (i.e. the nominal absolute accuracy) to 0.5%RH (i.e. the nominal reproducibility). All calibrations were performed at T=35°C, V̇=1 SLPM, and relative humidity range of 0-80%. Appendix C presents details of data reduction and uncertainty analysis of the permeability measurements. The flow rates of the feed and sweep streams leaving the membrane test module are measured with a soap bubble flowmeter FL (Gilibrator-2) at the outlet of each stream outside of the oven. This flowmeter has an accuracy of ±1% for all readings and can operate in conditions up to 35ºC (Gilibrator-2 Specifications, 2016). A CO2 sensor (VAISALA GMP222) is placed at the outlet of sweep stream to measure the concentration of CO2 permeate. This sensor has a measurement range of 0-2000ppm with a measurement accuracy of ±25ppm+2% of the reading (GMP220 Series Carbon Dioxide Transmitters for Industrial Applications, 2013). To reduce the uncertainty level of CO2 concentration measurements which is especially important to increase the accuracy of CO2 permeability calculations for low-permeating membrane samples, the CO2 sensor is calibrated with several calibration-gas bottles of know concentration from 50ppm to 2000ppm. This reduced the Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 70  uncertainty of CO2 reading down to ±25.7ppm (95%CI) calculated from Standard Error of Estimate (SEE) for linear regression (see calibration curve in Appendix C).  The commercially available LabVIEW 2013 software program was used to record signals from the sensors connected to an NI USB-6009 DAQ (National Instruments, Austin TX). 4.4.2. Permeation Test Cell Permeation testing of membrane samples was performed in a custom permeation cell. This test cell uses a plug-flow arrangement (similar to ASTM 739 permeation cell [196]) with the addition of diffuser plates positioned 2mm from the membrane surface attached to the central ports on either sides of the membrane to force radial flow along the membrane to the outer edge of the open area (see Figure 4.5). On the coated side of the membrane, humid feed stream is directed through the central port of the cell and forced outwards towards the edge of the cell. Likewise, on the uncoated side of the membrane, dry sweep nitrogen enters from the central port and leaves the cell from the outer edge, resulting in a co-flow configuration. This co-flow arrangement increases the boundary layer resistances inside the cell compared to a counter-flow arrangement. However, it was adopted since it guarantees a flat membrane sample during the test under equal feed and sweep flow rates. The membrane samples in this test cell have an active permeation area of 15.9 cm2.  Figure 4.5. Schematic representation of permeation test cell   4.4.3. Permeation Test Cell Boundary Layer Resistances As was discussed in Chapter 3, the apparent permeability of the membrane (Eq.(3.16)) has to be corrected for the boundary layer resistances. This is necessary to obtain accurate intrinsic material permeability for highly water vapor permeable membranes. Therefore, calibration of the test cell is needed to determine the resistance of the boundary layer. Ideally, this should be done for all the experimental operating conditions and flow rates. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 71   (a) water vapor  (b) CO2 Figure 4.6. Boundary Layer Resistance Calibration of the permeation test cell at 30⁰C and 50⁰C, 50% RH on the feed side, and 1SLPM flow rate on both sides.  A few different experimental methods have been reported for determining boundary layer resistances in a permeation test cell. They usually require multiple permeation experiments under a certain operating condition [37], [60], [91]. As explored by Metz et. al. [91], an estimate of the combined boundary layer resistances in a permeation cell can be determined from a plot of total mass transfer coefficient versus thickness for a number of films of same polymer material with varying thickness. In this method, the intercept of a plot of 1𝑘𝑇 versus film thickness, regressed by a linear fit, gives an estimate of the combined boundary layers resistances in the test module. Typical such plots for both water vapor and CO2 permeation in our test cell are presented in Figure Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 72  4.6. Multiple layers of 25µm Celgrad® 2500 substrate (stacked together to give varying thickness) were used for these tests. Shaded error bounds on these graphs represent standard error of estimate (95% CI) for linear regression. Intercept error of estimate (95%CI), as indicated in these figures, is considered as the error of estimated boundary layer resistance used in error propagation analysis of Appendix C.  Table 4.5 and Table 4.6 summarize the results of the boundary layer characterization experiments for both water vapor and CO2 inside the test cell. These calibrations were performed under two test temperatures of 30ºC and 50ºC both at 50% RH on the Feed inlet. Tested flow rates through the test module were varied between 0.5-4SLPM for each membrane thickness. Sherwood correlations of the following form are generally used for developing empirical models to describe boundary layer resistances of a system under various operating conditions [37], [164].  𝑺𝒉 = 𝒂𝟏𝑹𝒆𝒂𝟐𝑺𝒄𝒂𝟑 (𝒅𝒄𝑳)𝒂𝟒 (4.3)  where,  𝑅𝑒 = (𝜌𝑚𝑢𝑑𝑐𝜇𝑚⁄ ), is Reynolds number, 𝑆𝑐 = (𝜇𝑚𝜌𝑚𝐷𝑖𝑚⁄ ), is Schmidt number, 𝑑𝑐, is characteristic length, defined as the diameter of the cell inlet port (shown in Figure 4.5), 𝐿, is flow path length taken as the cell radius, 𝜌𝑚 and 𝜇𝑚, are the density and viscosity of the gas mixture, respectively, and 𝑎1 to 𝑎4 are coefficients particular to the geometry of the system, determined experimentally. Sherwood number, 𝑆ℎ, represents the ratio of the convective mass transfer to the rate of diffusive mass transport as  𝑺𝒉 =𝒌𝒅𝒄𝑫𝒊𝒎 (4.4)  where, 𝑘, is the boundary layer mass transfer coefficient, and 𝐷𝑖𝑚, is the  diffusivity of a penetrant gas i into a mixture of two or more other gases (Appendix D). Employing the equations of Appendix D for gas mixture properties in Eq.(4.3) would enable using Sherwood correlations for a range of operating conditions in the experiments. Results of empirical fits of Eq.(4.3) to the experimental data for both water vapor and CO2 at 30ºC (by minimization of the sum of the squared residuals) are presented in Table 4.5 and Table 4.6. The boundary layer data at 50ºC is also estimated using this model and compared with the corresponding experimental data at this temperature.  It can be observed that the predictions of the model are in quantitative agreement with the experimentally determined values of boundary layer resistance at 50ºC (errors<5.2%). Therefore, the Sherwood model can be used to predict the boundary layer resistances at various flow, temperatures, and feed and sweep relative humidity set points, so that estimated boundary layer resistances can be determined for specific testing conditions used for both feed and sweep streams.   Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 73  Table 4.5. Experimental and modeled water vapor boundary layer resistance inside permeation test cell Flowrate (SLPM) Water vapor BL resistance a (at 30ºC) Water vapor BL resistance a (at 50ºC) Experiment (±95% CI) b Model Experiment (±95% CI) b Model  Total Feed Sweep Total Feed Sweep 0.5 111.9 (9.9) 56.6 54.8 97.6 (12.8) 51.8 50.1 1 90.4 (9.0) 45.5 44.2 78.8 (11.8) 41.6 40.4 2 75.3 (9.5) 36.7 35.7 65.7 (9.1) 33.6 32.7 3 64.6 (8.0) 32.4 31.3 56.3 (9.4) 29.6 28.8 4 58.1 (7.3) 29.6 28.7 50.7 (6.9) 27.0 26.3 a Resistance values are reported in (s/m). b Error values in parentheses represent a 95% confidence interval of BL resistance obtained from regression intercept c Fit parameters of Eq.(4.3) for water vapor at 30ºC; a1=1.061, a2=0.311, a3=0.412, a4=0.382, SSR=2.8.  Table 4.6. Experimental and modeled CO2 boundary layer resistances inside permeation test cell Flowrate (SLPM) CO2 BL resistance a (at 30ºC) CO2 BL resistance a (at 50ºC) Experiment (±95% CI) b Model Experiment (±95% CI) b Model  Total Feed Sweep Total Feed Sweep 0.5 171.1 (17.5) 86.7 86.4 156.5 (14.3) 80.6 80.3 1 140.0 (16.3) 70.3 70.1 128.1 (12.1) 65.5 65.1 2 113.3 (15.3) 57.0 56.9 103.7 (12.1) 53.1 52.8 3 100.0 (11.8) 50.4 50.3 91.5 (10.6) 47.0 46.7 4 91.1 (9.6) 46.3 46.1 83.4 (9.9) 43.1 42.8 a Resistance values are reported in (s/m). b Error values in parentheses represent a 95% confidence interval of BL resistance obtained from regression intercept c Fit parameters of Eq.(4.3) for CO2 at 30ºC; a1=0.910, a2=0.302, a3=0.326, a4=0.410, SSR=2.4.  Varying fluid properties, due to the variations of moisture content in the gas mixtures on both sides of the membrane inside permeation cell, at a constant operating temperature and flowrate, has minimal influence on the moisture transfer resistances of the boundary layer (<3%) [27]. However, variations of gas mixture properties as a function of average relative humidity between the four inlet and outlets of the test cell are considered in the Sherwood models developed here. Temperature effects (Figure 4.7 (a)) are more significant than the effect of humidity content of feed stream (Figure 4.7 (b)) (e.g. up to 18% for water vapor between 30ºC to 50ºC), since temperature impacts the diffusivity of both penetrants in the carrier N2 gas, in addition to the fluid properties.  Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 74    Figure 4.7. Permeation cell total boundary layer resistance predicted from Sherwood correlation at different flow rates; (a) temperature effect (feed and sweep side activity values are 0.5 and 0, respectively, (b) feed water vapor activity effect with dry sweep (activity at 0).    Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 75  4.4.4. Data Analysis In a typical mixed water vapor/CO2 permeation test, the feed stream with known water vapor and CO2 concentrations is supplied to the inlet of the permeation cell (S1in Figure 4.4). The sweep gas (i.e. dry, high purity nitrogen) is supplied to the sweep inlet on the other side of permeation cell (S3). Assuming ideal gas law (since both streams are operating at near atmospheric pressure), the flux of permeant species (water vapor and CO2) through a membrane sample can be calculated from the measured partial pressures at the sweep outlet (S4) as  𝑱𝒊 =𝒑𝒊,𝟒𝑸𝑺𝑽𝒎𝑹𝑻𝑨 (4.5)  Or the partial pressure difference between inlet and outlet of feed stream (S1 and S2)  𝑱𝒊 =(𝒑𝒊,𝟏 − 𝒑𝒊,𝟐)𝑸𝑭𝑽𝒎𝑹𝑻𝑨 (4.6)  Where, 𝑝𝑖 is the partial pressure of penetrant 𝑖 at each sampling port, 𝑸𝑭 and 𝑸𝑺 are the Feed and Sweep flow rates, 𝑉𝑚 is the molar gas volume, R is the gas constant, T is absolute test temperature, and 𝐴 is the membrane effective area. The apparent permeability coefficient is consequently determined based on the solution-diffusion mechanism, as the steady-state penetrant flux normalized by the pressure driving force  ℘𝒊𝒂𝒑𝒑𝒂𝒓𝒆𝒏𝒕 =𝑱𝒊 𝜹𝒎∆𝒑𝒊,𝑳𝑴𝑫 (4.7)  where, ∆𝒑𝒊,𝑳𝑴𝑫 is the logarithmic mean vapor pressure difference for the co-flow arrangement   ∆𝒑𝒊,𝑳𝑴𝑫 =(𝒑𝒊,𝟐 − 𝒑𝒊,𝟒) − (𝒑𝒊,𝟏 − 𝒑𝒊,𝟑)𝒍𝒏((𝒑𝒊,𝟐 − 𝒑𝒊,𝟒)(𝒑𝒊,𝟏 − 𝒑𝒊,𝟑)) (4.8)  As was discussed earlier, the apparent permeability of the membrane has to be corrected for the boundary layer resistances. This requires the knowledge of effective concentration (or partial pressure) difference between membrane surfaces while the bulk gas mixture values are being measured in the experiments. The total mass transfer resistance can be calculated as  𝑹𝑻 =∆𝑪𝒊,𝑳𝑴𝑫𝑱𝒊 (4.9)  where the logarithmic mean concentration difference, ∆𝑪𝒊,𝑳𝑴𝑫, can be calculated from the ideal gas law as  ∆𝑪𝒊,𝑳𝑴𝑫 =∆𝒑𝒊,𝑳𝑴𝑫𝑹𝑻 (4.10) Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 76   The membrane resistance is then obtained by subtracting boundary layers’ resistances from the overall mass transfer resistance  𝑹𝒎𝑴 = 𝑹𝑻 − 𝑹𝑩𝑳 (4.11)  It is now possible to estimate the effective concentration difference between membrane surfaces as  ∆𝑪𝒊,𝒎 = 𝑱𝒊𝑹𝒄𝑴 (4.12)  Thus the actual permeance of composite membrane as  [℘𝒊𝜹𝒎]𝒂𝒄𝒕𝒖𝒂𝒍=𝑱𝒊 𝑽𝒎∆𝑪𝒊,𝒎𝑹𝑻 (4.13)  Likewise, the membrane coating resistance is obtained by subtracting substrate resistance from the membrane resistance  𝑹𝒄𝑴 = 𝑹𝒎𝑴 − 𝑹𝒔𝒖𝒃𝑴  (4.14)  And thus the actual permeability coefficient of the dense coating layer can be written as  ℘𝒄,𝒊 =𝜹𝒄𝑽𝒎𝑹𝑻𝑹𝒄𝑴 (4.15)  where, 𝛿𝑐 is the thickness of dense coating layer and its permeability coefficient, ℘𝒄,𝒊, is the intrinsic material property dependent on operating conditions. The selectivity of a membrane for water vapor over CO2 is consequently defined as the ratio of their permeability values.  𝜶𝑯𝟐𝑶𝑪𝑶𝟐=℘𝑯𝟐𝑶℘𝑪𝑶𝟐 (4.16)  The crossover rate of CO2 is also calculated for equal flow rates on both sides of membrane as  𝝌𝑪𝑶𝟐 =𝑪𝑪𝑶𝟐,𝟒𝑪𝑪𝑶𝟐,𝟏× 𝟏𝟎𝟎% (4.17)  CO2 crossover values provide an indication of the portion of EATR in an enthalpy exchanger due to the contaminant transport through membrane media.   Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 77  4.5.  RESULTS AND DISCUSSION 4.5.1. Water Vapor Permeability The water vapor permeability data at various relative humidity and temperatures for membrane samples PEBAX®1074, SPEEK, PU-PEO, and CA are shown in Figure 4.8 (a)-(d), respectively. Each data point represents the average of measurements for three different samples of the same membrane material. Error bars represent the standard deviation of these three measurements, indicating a repeatability of less than 10% for moisture permeability measurements (i.e., much lower compared to the measured variations at different RH levels). Details of error propagation analysis in both moisture and CO2 permeability measurements to determine calculated bias error is presented in Appendix C.     Figure 4.8. Water vapor permeability of a) PEBAX®1074, b) SPEEK, c) PU-PEO, d) CA at 30°C and 50°C  It can be observed that water vapor permeability in all of investigated membranes increases at higher RH values of the feed stream, for each temperature considered. This is in agreement with the reported data in many other works in the literature [88], [89], [197]–[199]. The increasing trend of water vapor permeability, as discussed in these studies, could be due to the plasticizing effect of water vapor on the polymer matrix and the increased sorption of water vapor at higher RH values. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 78  The most substantial increase in water vapor permeability occurs for SPEEK (up to an order of magnitude at 80%RH at 50°C), while PEBAX®1074, PU-PEO, and CA show progressively lower variations at the same RH value. High water vapor permeability at high RH is very beneficial for energy recovery, especially for cooling in humid climates, where the latent heat load constitutes a significant fraction of the total cooling load of the HVAC system. The water vapor permeability in all polymers investigated decreases with increasing temperature except for polymer PU-PEO which is independent of test temperature to within the experimental uncertainty. The water vapor permeability of glassy membrane samples (CA and SPEEK) shows a strong dependence on the test temperature, whereas the effect of temperature on the permeability of rubbery samples (PEBAX and PU-PEO) is limited. This can be explained by considering the occurrence of two opposing effects: at higher temperatures, water vapor solubility decreases due to the negative enthalpy of water sorption in polymer matrix, whereas the water vapor diffusivity increases as a result of positive activation energy for diffusion [197] and [88].  For glassy polymers where permeability is controlled by diffusion rather than by solubility, the relative decrease in solubility of water vapor is more pronounced than the relative increase in diffusivity, as often observed for diffusion-controlled polymers [197].   (a) Membrane-on-Feed (b) Membrane-on-Sweep Figure 4.9. Membrane permeability measurement configurations   It is also important to note that the orientation of membrane affects the water vapor permeability measurements for asymmetric composite membranes. Two different measurement configurations according to Figure 4.9 were investigated.  For all of the studied polymers, the measured flux of water vapor and thus its permeability was consistently higher for the case where the coated side of the composite membrane was exposed to Feed stream (i.e., Membrane-on-Feed configuration (Figure 4.9(a))). Average values of all water vapor flux measurements for the two configurations at test conditions of 30°C and 50% Feed relative humidity are summarized in Table 4.7 for the studied membrane samples. The orientation effects on permeability are usually attributed to phenomena, such as pressure loss or capillary condensation within the microporous substrate of composite membranes [85]. Orientation effect will diminish if the difference between the Feed and Sweep sides relative humidity becomes smaller. Koester et al. [85] have reported differences as large as 30% between the permeability values obtained from the two configurations for a composite membrane with a dense coating layer similar to the PU-PEO polymer in this study. Zhang [200] recently published Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 79  simulation results which disclosed the impact of a porous substrate on concentration inhomogeneities within the dense coating layer. These concentration changes are expected to affect the intrinsic moisture permeation properties of the dense coating layer. Chapter 5 will present a detailed analysis of such concentration-dependent permeation properties for PU-PEO copolymer films. Table 4.7. Effect of membrane orientation on water vapor flux through different membranes Membrane sample Water vapor flux (kg/m2/day)  Membrane-on-Feed a Membrane-on-Sweep a PEBAX®1074 28.78±0.79 27.52±0.77 PU-PEO 9.81±0.69 8.96±0.44 SPEEK 10.78±0.73 9.89±0.56 CA 6.78±0.51 6.23±0.41 a Uncertainty bounds indicate standard deviation of all measurements.  4.5.2. CO2 Permeability Results of the CO2 permeation measurements as a function of relative humidity for membrane samples at two test temperatures of 30°C and 50°C are summarized in Table 4.8. The CO2 permeability of SPEEK polymer is close to the detection limit of the analytical method which makes it difficult to conclude a general trend for this particular membrane. The extremely low CO2 permeability of SPEEK membrane, combined with its relatively high water vapor permeability, makes this membrane an attractive candidate for ERV applications.  Table 4.8. CO2 permeability (crossover) (Barrer (%)) values in different membranes RH (%) PEBAX®1074 SPEEK PU-PEO CA  30°C 50°C 30°C 50°C 30°C 50°C 30°C 50°C 20 110.5 (0.47) 181.0 (0.73) 6.0 (<0.03) 7.6 (<0.03) 50.1 (0.15) 101.9 (0.31) 11.1 (0.04) 12.7 (0.04) 30 104.8 (0.44) 174.2 (0.72) 5.9 (<0.03) 7.6 (<0.03) 50.8 (0.15) 102.7 (0.30) 11.1 (0.04) 12.8 (0.04) 40 104.1 (0.44) 174.9 (0.71) 5.9 (<0.03) 7.5 (<0.03) 47.4 (0.15) 103.4 (0.30) 11.1 (0.04) 12.8 (0.04) 50 102.9 (0.43) 174.6 (0.71) 5.9 (<0.03) 7.6 (<0.03) 48.2 (0.15) 101.1 (0.30) 10.0 (0.03) 12.0 (0.04) 60 101.8 (0.42) 171.0 (0.71) 5.9 (<0.03) 7.6 (<0.03) 47.0 (0.15) 95.3 (0.29) 10.0 (0.03) 11.3 (0.04) 70 100.0 (0.41) 167.9 (0.70) 5.9 (<0.03) 7.7 (<0.03) 48.1 (0.14) 96.3 (0.29) 8.6 (0.03) 11.3 (0.04) 80 98.0 (0.41) 169.7 (0.69) 5.9 (<0.03) 7.7 (<0.03) 44.8 (0.14) 93.3 (0.28) 8.5 (0.03) 11.3 (0.04) * Uncertainty (95% CI (±)) in permeability measurements range from 7 to 11% and 0.015%, for permeability and crossover, respectively.  Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 80  The CO2 permeability of the rest of the polymers inspected is found to moderately decrease with increasing relative humidity. The same behavior is also observed in other studies of rubbery polymers: PEBAX1074 [89], PDMS [201], as well as glassy polymers: Matrimid [94], polyimide6FDA–6FpDA [199]. The CO2 permeability in CA membrane is the most affected on average, with a decrease of about 27% and 11% relative to the dry value at 80%RH for 30ºC and 50ºC, respectively. The decrease in CO2 permeability with RH is hypothesized to be due to the competitive sorption between water vapor and CO2; as the water vapor activity increases, its sorption coefficient increases and restricts the sorption of CO2 resulting in a net lower permeability [197]. This hypothesis is also supported by the fact that CO2 permeability decreases less at 50°C compared to 30°C, potentially due to a lower water vapor sorption at higher temperatures. In contrast with the water vapor permeability, the CO2 permeability increases with increasing test temperature. This may be a consequence of the higher increase in the diffusion coefficient of CO2 than the decrease in its solubility, in response to temperature increases [198]. It is also noticeable that for the rubbery membrane samples, CO2 permeability is much higher than those obtained for the glassy polymers. This is attributed to the general behavior of rubbery polymers, showing much larger diffusivity for non-condensable gases due to their high chain flexibility. Moreover, both rubbery PEBAX and PU-PEO polymers studied here are block copolymers consisting of soft, rubbery, and hydrophilic PEO blocks. The ether linkage present in the soft PEO blocks makes these polymers selective for CO2 [197]. As a result, PEBAX and PU-PEO are less selective for water vapor over CO2, thus less attractive for the ERV application. However, in applications with lower levels of indoor contaminants such as class 1 and class 2 air set by ASHRAE standard 62.1 [9], these polymers are still viable candidates due to their much higher water vapor permeability. 4.5.3. Membrane Selectivity Figure 4.10 shows the mixed H2O/CO2 selectivity of the membrane samples as a function of relative humidity in the feed stream at two test temperatures.   Figure 4.10. Water vapor/CO2 selectivity for four tested membranes: (a) 30°C and (b) 50°C  Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 81  In general, most dense polymer membranes show significantly higher permeability for water vapor compared to CO2, leading to a high selectivity. This is attributed to the high solubility (high critical temperature) and high diffusivity (small molecular size) of water vapor molecules [91]. Among the polymers investigated, the H2O/CO2 selectivity is higher for the glassy samples (black symbols in Figure 4.10) due to the much lower permeability of CO2 through the rigid polymer chains of these membranes. As can be observed in Figure 4.10, the selectivity of all of the membranes increases with RH because the water vapor permeability increases significantly with RH, while the CO2 permeability slightly decreases or remains constant. SPEEK polymer shows the most substantial increase in selectivity with RH (up to about an order of magnitude at 80%RH at 50ºC) which is in line with its water vapor permeability behavior. In general, increasing the temperature from 30ºC to 50ºC reduces the H2O/CO2 selectivity, owing to the increased CO2 permeability at higher temperatures. For the SPEEK polymer, however, this trend is reversed for RH values over 70% due to the dominance of the water vapor permeability increase. 4.5.4. Membrane Material Selection for ERVs Presented results in previous sections suggest that permeation properties of polymeric membranes are strongly material-dependent. Important factor include, the state of polymer (i.e. whether it is below or above its glass transition temperature), the kinetic diameter and polarity of the permeating molecule (gas/vapor), the relative humidity that is dictating the degree to which water absorbs into the membrane structure (which modifies the transport of the second gas CO2), and to a lesser extent temperature that influences mainly the diffusivity. The low absolute pressure difference across the membranes in ERV exchanger cores make their construction requirements less stringent. In addition to membrane material permeation, contaminant transfer and crossover through an ERV exchanger inside a ventilation system might be influenced by exchanger core leakages and manufacturing defects as well as flow passage geometry, and flow rates and boundary layer effects. However, these material-level testing provide guidelines in material selection, as well as input for realistic building energy models to estimate energy saving benefits from a membrane-based ERV installation. Depending on the membrane material, the permeability and selectivity vary up to an order of magnitude among studied polymers (see Figure 4.11). In general, rubbery membranes show higher water vapor permeability but lower selectivity compared to glassy membranes over a wide range of operating conditions (see Figure 4.11). It should, however, be noted that the crossover rates of CO2 in both types of polymeric samples are sufficiently low for practical applications in HVAC design. All of the samples possess H2O/CO2 selectivity values over 100 which is significantly higher than the typical selectivity of paper-based media used in ERVs that ranges from 2 to 6. Such high selectivity levels of polymeric membranes could result in CO2 crossover rates of less than 0.5% in ERV exchanger core. Caution must be taken in generalizing this conclusion to other indoor contaminants, especially in applications where indoor contaminants include volatile organic compounds (VOCs) with either sources of high emission rates or very low acceptable threshold concentrations. Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 82   Figure 4.11. Comparison of the selective performance of rubbery vs. glassy membranes at 30°C (hollow symbols) and 50°C (filled symbols)   Chapter 4 –The effects of temperature and humidity on the permeation properties of membrane media 83  4.6. CONCLUSIONS The effects of relative humidity and temperature on the permeation properties of a series of standard polymer membranes, suitable for ERV applications, has been investigated. The intrinsic water vapor permeability and selectivity for water vapor relative to CO2 were measured for four different polymer samples via binary water vapor/CO2 permeation measurements. Although the results suggest that membrane permeation properties are strongly material-dependent, some general conclusions regarding the ERV application may be made:  The combination of very high water vapor permeability with high selectivity for water vapor over gaseous contaminants such as CO2 shows the vast potential of polymeric membranes for ERV applications (achieving acceptable latent performance while maintaining very low crossover rates (corresponding to EATR <1%)).  The permeation behavior of polymer membranes greatly depends on whether the polymer is below or above its glass transition temperature. In general, rubbery polymers show higher water vapor permeability rates, but less selectivity for water vapor over CO2. Glassy polymer membranes, on the other hand, show negligible crossover rates for CO2 (<0.03%) over a wide range of operating conditions.  Depending on the membrane material, the operating temperature, and the relative humidity, the permeability and selectivity of membranes can vary up to about an order of magnitude. This variability would lead to significant changes in the actual performance of an ERV and the whole HVAC system, impacting building energy efficiency.   In general, increasing the water vapor permeability of a membrane leads to an increase in the latent effectiveness of ERV exchanger cores and higher energy saving potentials for high humidity conditions. However, the extent of increase in latent effectiveness of an ERV core is influenced by multiple factors (e.g., flow passage geometry and operating flow rates) beyond just the membrane properties. It is therefore essential to have predictive models that can link membrane characteristics to ERV core performance.  These modeling tools will be developed in the next two chapters.  Further work should investigate the effects of operating conditions in a similar range on the permeation of other indoor contaminant species, in particular, toxic VOCs with low threshold concentrations such as formaldehyde, benzene, and toluene.     84  Chapter 5 – MEASUREMENTS OF MOISTURE SORPTION ISOTHERMS AND DIFFUSION COEFFICIENTS IN DENSE POLYMERS1  5.  5.1. OVERVIEW This chapter reports on the experimental and analytical methods for evaluation of moisture permeation properties in dense film samples prepared from two poly(ethylene oxide)-based block copolymers, commercially available as PEBAX®1074 and PERMAX™230. The ultimate goal of this study is to extract sorption- and diffusion-concentration correlations (at different temperatures) suitable for modeling of the steady-state water vapor permeation through composite membranes consisting microporous support layers coated with these dense selective copolymers. The PERMAX™230 copolymer (also referred to as PU-b-PEO) is the dense, selective coating layer used in the asymmetric composite membranes studied in Chapter 6. The diffusion, solubility, and permeation behavior of water in the two copolymers were studied using transient gravimetric sorption and steady-state permeability measurements at various temperatures (5-55ºC), water vapor activities (0-0.9), and dry film thicknesses. Deviations from Fickian behavior were observed in the reduced sorption and desorption curves for both copolymers: (1) the sorption and desorption behavior at early times is sigmoidal, representative of slow interfacial concentration changes; and (2) the initial slope of sorption and desorption curves increases with film thickness, representing a slower relaxation process of polymer chains accompanying diffusion. Despite the non-Fickian behaviors, equilibrium diffusion coefficients can be determined from the early stages of desorption curves, or the early stages of sorption curves of thick films. For both copolymers these coefficients increased with temperature and decreased with concentration. These coefficients, combined with equilibrium sorption isotherms, can be used to estimate steady-state permeability. The predictions are validated using steady-state water vapor permeability measurements of free-standing dense films. Details of the non-Fickian water vapor transport through PERMAX™ 230 based polymers and PEBAX® 1074 have not previously been reported in the literature.                                                              1 A version of this chapter has been submitted for publication in a peer-reviewed journal in August 2018: “Non-Fickian water transport in poly(ethylene oxide)-based block copolymer membranes.” Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 85  5.2. INTRODUCTION Water-vapor-permeable membranes have practical importance in many applications, including breathable clothing [202], natural gas dehydration [203], flue gas dehydration [197], compressed air drying [204], food packaging [205], protective coatings [206], and biological processes [207]. Block copolymers, owing to their highly customizable structure and high permeability, have been used in such water-vapor-permeable membranes [208]. Their water permeation properties have been studied in the context of their use in food packaging [209], fuel cells [210], [211], air batteries [212], biomedical implants [213], drug delivery [214], and CO2 separation [215], [216]. Their structure-property relationships have been studied in [216], [217], [218]. General reviews are provided by [219], [220]. In this chapter, we investigate the moisture permeation properties of two highly permeable PEO-based block copolymers, commercially available as PEBAX® 1074 and PERMAXTM 230. These copolymers are believed to be suitable for the ERV application, offering high water vapor sorption and permeability due to the containment of large number of hydrophilic PEO blocks in their structure. They also have relativity low transport of gases (i.e., good selectivity) due to the low solubility of permeant gases in the amorphous PEO segments [27]. Transient sorption/desorption experiments are commonly employed to simultaneously determine sorption and diffusion coefficients of solvents in polymers [221].  The sorption coefficient is readily evaluated from the equilibrium mass uptake of a sorption experiment, while the diffusion coefficient is usually determined from regressing sorption curves (mass uptake/loss versus time) to a solution of Fick’s 2nd law. The one-dimensional diffusion of small penetrants in isotropic, thin polymeric films, under isothermal conditions (Figure 5.1) can be mathematically described by the following form of Fick’s 2nd law  𝝏𝑪𝝏𝒕=𝝏𝝏𝒙(𝑫𝝏𝑪𝝏𝒙)                            − 𝒍 < 𝒙 < 𝒍 (5.1)  where 𝑡 is time, and 𝐶 is the penetrant concentration.  Figure 5.1. An infinite film with the thickness 2l  Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 86  For ideal Fickian diffusion case, in Eq.(5.1) D may depend on concentration but not explicitly on time. The simplest form of solution to this equation (when D is constant) is given by Crank and others [221] and predicts a linear relationship between weight increase and √t/l for the initial parts of sorption curves. From the slope of these curves, Fickian diffusivity can be calculated. In polymer-solvent systems, however, the diffusion coefficient generally depends strongly on the concentration, especially over a large concentration range. In such cases, the differential equation in Eq.(5.1) becomes nonlinear. There are numerous approaches reported for evaluation of concentration dependency of diffusion in polymers [222], [223], [224]. The diffusion behavior of many solvent-polymer systems cannot be adequately described with a concentration-dependent form of Fick’s law with constant boundary conditions. In general, solvent diffusion in rubbery polymers is well described as Fickian, but in glassy polymers, with extensive swelling of the polymer by penetrant, significant deviations from Fickian diffusion is observed. There are several studies in the literature reporting deviations from Fickian diffusion for such polymer systems [225]–[233], as well as structured copolymer-solvent systems [234]–[236]. Non-Fickian behaviors are characterized by sorption and desorption curves that are not symmetric, sorption curves for different thicknesses that do not collapse to a single curve with √t/2l, and sorption curves that display an inflection point when plotted against either time or √t [222], [237]. In such cases, there is not a unique diffusion-concentration correlation governing the transient transport through the material (i.e. the transport is non-Fickian). In the present work, we use dynamic sorption measurements to determine the water vapor sorption equilibrium and water transport kinetics for two PEO-based copolymers, commercially available as PERMAXTM230 and PEBAX®1074. We will show that the rate of sorption in these elastomeric block copolymers is dependent on water vapor concentration and temperature, as well as the thickness of the film. The non-Fickian water sorption kinetics through these films is described using a modified sorption model combining variable surface concentration (VSC) and diffusion-relaxation models. Furthermore, two different methods are demonstrated for determination of diffusion coefficients at equilibrium state from the early time data of sorption experiments with such non-Fickian behavior. 5.3. THEORETICAL BACKGROUND 5.3.1. Equilibrium Sorption The equilibrium sorption coefficients at various steps of water vapor activity increase/decrease can be calculated using the following equation.  𝑪 =𝑽𝒎(𝑴𝒇 − 𝑴𝒅𝒓𝒚)𝑴𝒘𝝆𝒑𝑴𝒅𝒓𝒚 (5.2)  where 𝐶 is the water equilibrium concentration in the polymer in (𝑚3 𝐻2𝑂(𝑣) (𝑆𝑇𝑃)𝑚3−𝑝𝑜𝑙𝑦𝑚𝑒𝑟), 𝑀𝑓 and 𝑀𝑑𝑟𝑦 are the final equilibrium mass of sample in each step and dry sample mass, respectively.  𝑀𝑤 is the molecular weight of water, 𝑉𝑚 is the molar gas volume at STP (0°C and 1atm), and 𝜌𝑝 is the polymer density. Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 87  The solubility coefficient, S, in a polymer matrix is defined as  𝑺 =𝑪𝒑 (5.3)  Where, p is the water vapor partial pressure (corresponding to the sorption coefficient, 𝐶) in the gas phase adjacent to the polymer. 5.3.2. Fickian Diffusion In a typical sorption/desorption experiment, a thin film sample (of sufficiently large area so that there is negligible diffusion from edges), initially conditioned to be at a uniform penetrant concentration, is suddenly exposed to an environment of the penetrant vapor maintained at constant temperature and pressure (activity) and the sample weight gain or loss is measured vs. time. These initial and boundary conditions are represented by 𝑪 = 𝑪𝟎 −𝒍 < 𝒙 < 𝒍 𝒕 = 𝟎  𝑪 = 𝑪𝟏 𝒙 = ±𝒍 𝒕 ≥ 𝟎 (5.4) 𝝏𝑪𝝏𝒙= 𝟎 𝒙 = 𝟎 𝒕 ≥ 𝟎   Following the analysis of Crank [221], if it is assumed that the constant activity of the vapor leads to an instantaneous constant surface concentration at both faces of the film (i.e., the rate-limiting step for water absorption is diffusion), diffusion coefficient is constant, and polymer film does not swell, a solution to Eq.(5.1) under boundary conditions in Eq.(5.4) (integrated with respect to film thickness) has one of two standard forms (i) For small values of time:  𝑴∗ =𝑴𝒕 − 𝑴𝟎𝑴f − 𝑴𝟎= 𝟐(𝑫𝒕𝒍𝟐)𝟏𝟐{𝝅−𝟏𝟐 + 𝟐 ∑(−𝟏)𝒏𝒊𝒆𝒓𝒇𝒄 {𝒏𝒍√𝑫𝒕}∞𝒏=𝟏} (5.5)  (ii) For larger values of time:  𝑴∗ =𝑴𝒕 − 𝑴𝟎𝑴f − 𝑴𝟎= 𝟏 −𝟖𝝅𝟐∑𝟏(𝟐𝒏 + 𝟏)𝟐∞𝒏=𝟎𝒆𝒙𝒑(−(𝟐𝒏 + 𝟏)𝟐𝝅𝟐𝑫𝒕4𝒍𝟐) (5.6)  where, 𝑀∗, the fractional moisture uptake or loss, is defined as the ratio of the instantaneous moisture content of the polymer film (𝑀𝑡 − 𝑀0) to the the difference between the final equilibrium and initial moisture contents of the film (𝑀f − 𝑀0). Crank [221], and more recently Balik [238], have reviewed several methods of obtaining diffusion coefficients from sorption data based on these two equations. Two of the more common methods are: Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 88  (1) Initial-slope: the initial slope (𝑆𝐼) of a plot of 𝑀∗ versus 𝑡12 at sufficiently short times can be approximated by the first term of Eq.(5.5) as  𝑺𝑰 = 𝟐(𝑫𝒍𝟐𝝅)𝟏𝟐 (5.7)  (2) Sorption half-time: the time at which the value of fractional moisture sorption is 0.5 (𝒕𝟏/𝟐) can be determined using a two-term approximation of Eq.(5.6)  𝒕𝟏/𝟐 =𝟎. 𝟎𝟒𝟗𝟑𝟗(2𝑙)2𝑫 (5.8)  When sorption becomes important, it induces plasticizing of the polymeric material, and the variation of diffusion coefficients with penetrant concentration can no more be neglected. In fact, in such cases (i.e., solvent-polymer systems with strong concentration dependency) the methods mentioned above provide some average value of the diffusion coefficient within the range of the vapor concentration of the corresponding experiment. The strong concentration-dependence of the diffusion coefficient has to be taken into account by conducting multiple sorption experiments in the desired range of concentration [222], [223]. A modified method of differential sorption is presented in section E. 4 of Appendix E for evaluation of diffusion-concentration correlations. Moreover, the sorption of solvent vapors results in high degrees of swelling in polymers, especially at higher vapor activities [239]. This means that the assumed frame of reference of constant polymer dimensions in the solutions above, as diffusion proceeds, is no longer valid. This swelling effect is addressed by transforming the frame of reference through which diffusion occurs to a frame of reference fixed with respect to the membrane film mass [221]. A diffusion coefficient of vapor, 𝐷𝑉𝑚, in this frame of reference (i.e., obtained from the sorption experiment) is related to the Mutual diffusion coefficient 𝐷𝑉 (i.e., a measure of polymer intrinsic diffusion coefficient for the solvent) by  𝑫𝑽 =𝑫𝑽𝒎(𝟏 − 𝝓𝑽)𝝀 (5.9)  Where, 𝜙𝑉 is the volume fraction of penetrant water in the swollen polymer, and 𝜆 (thickness correction factor) is a power<2. Blume 1991 [240] suggests a value of 5/3 for 𝜆 for isotropic swelling of the sample. 5.3.3. Permeability According to the solution-diffusion model [45], Solubility coefficients are used in combination with average diffusion coefficients to calculate permeability coefficients.  ℘ = ?̅?(𝑪𝟎 − 𝑪𝒍)𝒑𝟎 − 𝒑𝒍 (5.10)  Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 89  where, 0 and 𝑙 subscripts refer to the membrane feed and permeate sides, and average diffusion coefficient, ?̅?, is calculated by integration of diffusion-concentration correlations over the concentration gradient across the membrane  ?̅? =𝟏(𝑪𝟎 − 𝑪𝒍)∫ 𝑫(𝑪)𝒅𝑪𝑪𝟎𝑪𝒍 (5.11)  5.4.  EXPERIMENTAL METHODS AND MATERIALS 5.4.1. Materials A Polyether–polyurethane wet dispersion, commercially available as PERMAX™ 230, was purchased from Lubrizol Advanced Materials with a polymer concentration of 32.33 wt.% in water. Polycarbodiimide cross-linker solution was obtained from Stahl under the trade name Picassian XL-702, with a concentration of 39.84 wt.% in water. Pebax® MV 1074 SA 01 was purchased from ARKEMA in the form of melt-processed polymer pellets (2-3 mm in diameter). Both materials are phase separated, linear segmented block copolymers containing the same polyether (PEO) as the “soft” block. Pebax®1074 is a copolymer of PEO (55 wt.%) and nylon 12 (PA12) (45 wt.%) as the “hard” block [16], whereas PERMAX™ 230 is a thermoplastic polyurethane (TPU) copolymer of PEO (75 wt.%) and hard polyurethane blocks (25 wt.%) [24]. The hard nylon and polyurethane blocks provide mechanical strength while the soft PEO blocks are responsible for most of the water transport. 5.4.2. Film Preparation  Sorption measurements were performed using dense isotropic films of copolymers, prepared using two methods: solvent-cast and melt- pressed. PU-PEO polymer solutions were prepared by blending PERMAX™ 230 and XL-702 cross-linker (in solids wt. ratio of 12:1 (i.e., 6.0 wt.% polycarbodiimide cross-linker)) and diluting in DI water to obtain a 25 wt.% solution. The PU-PEO solution was then cast onto a series of glass petri dishes with controlled wet thickness for obtaining homogeneous films of various dry thickness (in the range from 30 to 400μm). Samples were dried in a vacuum oven at 50ºC for one week to remove any residual solvent within the thick films. After drying, the PU-PEO films were removed from the petri dishes by floating off in DI water. They were subsequently washed with DI water for another 24h and then dried in a vacuum oven for 12h at 50°C to eliminate residual crystallite PEO in the film samples before the sorption experiments. This extra conditioning step was taken as some authors attribute some sorption anomalies in PEO-based block copolymers to the presence of residual crystallite PEO (uncross-linked material) within the copolymer structure [24], [8]. Pebax®1074 film samples were prepared using a melt-pressed process. Polymer pellets were melted onto a quartz glass plate preheated at 170⁰C. Another quartz glass plate preheated at the same temperature, fitted with a flat film die (round stainless steel shims of thickness ranging from 25 to 300μm), was used to sandwich the melt polymer to form a uniform film of desired thickness. Samples were subsequently cooled down in a vacuum oven at room temperature. Pebax®1074 Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 90  films were also floated off in DI water followed by a 24h wash with DI water and then dried in vacuum oven for 12h at 50°C.  Following the drying and conditioning process, all film samples were stored in a desiccator at room temperature until further use.  Film samples were cut into small circular pieces of approximately 7mm diameter (using a die) weighing from 2.04mg to 11.31mg depending on the film thickness. The thickness of sample films was measured using a Mitutoyo digital micrometer (Model H-2780 with 1.27μm resolution). Dry film samples prepared for gravimetric experiments had thicknesses of 39±4, 70±3, 90±6, 174±9, and 245±9 μm (for PU-PEO) and 48±4, 95±6, and 212±10 μm (for PEBAX® 1074). Thickness values are the average of five measurements over a two-week period (with three repetitions for each measurement), and the error values indicate a 95% CI of these measurements. 5.4.3. Gravimetric Sorption Balance The sorption-desorption kinetics and the equilibrium solubility of water vapor in film samples were measured using a Q5000SA moisture sorption analyzer (TA Instruments). The sorption apparatus is schematically shown in Figure 5.2. It employs a microanalytical thermo-balance maintained inside a temperature-controlled enclosure that allows for the detection of mass changes with a precision of 100 ng. The sample and reference pans are symmetrically positioned in a precisely-controlled humidity chamber with Peltier elements temperature control providing stability of ±0.1°C over the temperature range 5-85°C. The humidity control chamber maintains the sample and reference in the same environment.  Figure 5.2. Schematic drawing of the gravimetric moisture analyzer  A pair of mass flow controller, a humidifier, and gas transmission and mixing lines deliver symmetric control of relative humidity to both chambers. RH sensors are located adjacent to the sample and reference pans and continuously record the RH inside the chambers. However, fast Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 91  adjustment of RH inside the chamber is achieved by adjusting proportions of the mass flow controls.  This means that the sample chamber does not reach its relative humidity set point instantaneously. Sample chamber and gas transmission and mixing lines have a combined volume of approximately 30.2ml meaning that it takes about 6.7 seconds for the entire chamber to flush out dry purge nitrogen at a total experimental flow rate of 200 ml/min and stabilize the test condition at a desired humidity set point. This corresponds to a time constant of approximately 0.9 s-1 (approximately satisfying boundary condition in Eq.(5.4))  for the equilibration of the sample chamber to less than 0.1% of constant relative humidity. This time constant was accounted for in analyzing the kinetic sorption data using the procedure described in section E. 3 of Appendix E.  Figure 5.3. Measurement routine for determination of equilibrium sorption and diffusion coefficients as a function of water vapor activity.   Two different methods were adopted to conduct sorption/desorption measurements in the activity range of 0-0.9. (See Figure 5.3) In the first method, referred to as ‘integral sorption,’ at each step starting from a dry film the activity is raised from zero to the desired activity set point followed by full desorption back to zero activity. In the second method, referred to as ‘differential sorption,’ the activity is first incrementally raised from 0 to 0.9 in small steps of 0.05 followed by small desorption steps of 0.05 from 0.9 down to 0 activity. In order to remove any residual water in the film samples, they were dried by purging the sample chamber with dry nitrogen (PRAXAIR Canada, Grade 4.8 High purity>99.998%, H2O<3ppmv) at 60⁰C prior to starting the experiments using differential sorption method or prior to the start of each step during the experiments using the integral sorption method. The film weight was monitored until variations were below 0.01% for at least 15 minutes to ensure that films were sufficiently dried. To avoid condensation inside the sample chamber, experiments at temperatures below 15⁰C were conducted up to a maximum activity level of 0.8. The termination criteria for each step of sorption or desorption experiments in both methods is mass variations of less than 0.01% for at least 15 minutes. It has been observed that the longest experiment time for the thickest film at the highest humidity step was in the order of 2×104 seconds. Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 92  5.4.4. Water Vapor Permeation Steady-state water vapor permeability through PU-PEO films of various thickness was measured inside the counter-flow permeation cell and the constant-volume/variable-pressure (dynamic) permeation testing apparatus that was described in Chapter 4.    Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 93  5.5. RESULTS AND DISCUSSIONS 5.5.1. Equilibrium Sorption Isotherms Figure 5.4 and Figure 5.5 summarize the results of equilibrium sorption measurements using the differential sorption method for three representative dry film thicknesses and various test temperatures.  (a) PU-PEO  (b) PEBAX® 1074 Figure 5.4. Equilibrium sorption (open symbols) and desorption (filled symbols) isotherms at varying water vapor activity and dry film thickness at a constant test temperature (25⁰C).   In both copolymer films, the sorption isotherms are almost linear with respect to water vapor activity up to values of about 0.5. Beyond this level, the sorption curves at all temperatures (see Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 94  Figure 5.5) are convex with respect to the activity axis, indicating a dramatically increased moisture uptake by polymer films at higher activities, presumably due to significant swelling of the polymer matrix. This type of sorption isotherm is often found for the sorption of organic vapor in rubbery polymers like PDMS [43] and water vapor in several other polymers [44].  (a) PU-PEO  (b) PEBAX® 1074 Figure 5.5. Equilibrium sorption (open symbols) and desorption (filled symbols) isotherms at varying water vapor activity and test temperature for a constant film thickness: PU-PEO (245µm) and PEBAX® 1074 (95µm).  In Figure 5.4, a comparison is also made between the experimental data derived from the differential sorption method with a fit to the Flory-Huggins equation (Eq. (F.9) in Appendix F) to the data that was determined using the other integral sorption method. As can be observed, sorption Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 95  and desorption data in both copolymer films is independent of dry film thickness and collapse onto a single curve. This is in qualitative agreement with previous studies where the phase equilibrium in polymer films is independent of film thickness [241]. Therefore, in the investigation of the diffusion coefficients in these copolymers presented in the next sections, any impact from the equilibrium sorption values on the diffusivity of moisture through films with different dry thickness is not expected.   Furthermore, neither of these copolymers show any signs of the sorption behavior of glassy polymers, such as a point of inflection or dual-mode sorption. It can also be seen in Figure 5.5 that material sorption capacity decreases with increasing temperature, especially at higher water vapor activities (a>0.6). The data from Potreck et al. [45] (included in Figure 5.5 (b)) for the same PEBAX® 1074 copolymer (prepared using a wet casting method) is also in quantitative agreement with the results of this work. The sorption data for both copolymer films at various temperatures and film thicknesses are summarized in tables E.1 to E.3 of Appendix E. 5.5.2. Sorption and Desorption Kinetics A typical set of normalized sorption and desorption curves for a PU- PEO film (245µm) and a PEBAX® 1074 film (95µm) as a function of temperature (at a constant activity step of 0.55-0.6) are summarized in Figure 5.6 (a) and (b) (only a limited number of temperatures are shown for the sake of clarity). As expected, moisture uptake or loss rates increase with temperature, indicating an increasing diffusivity of water in the film samples with temperature. Similar trends were also observed for other film thicknesses of both copolymers. This increase in the diffusivity with temperature is due to the increased molecular mobility at higher temperatures [242].   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 96    (a) PU-PEO  (b) PEBAX® 1074 Figure 5.6. Sorption (solid lines) and desorption (dashed lines) curves for a typical activity step (0.55-0.6) at varying test temperature for a constant film thickness: PEO-PU (245µm) and PEBAX® 1074 (95µm).  Another noticeable trend in these figures is that desorption curves always lie above the sorption curves of the corresponding sorption step in both copolymers. This indicates that the mutual diffusion coefficient of the system is a decreasing function of the water concentration in the polymer. This trend is, however, reversed for very low water vapor activities, as shown in Figure 5.7 for a PU-PEO film at a typical temperature of 35ºC. This suggests that rather than a monotonically decreasing trend, D versus C has a maximum at a certain concentration (activity). Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 97  This maximum typically occurs between activity ranges of 0.05 to 0.2 for temperatures above 25⁰C in both copolymers (See figures in section E. 5 of Appendix E).  Figure 5.7. Sorption (solid lines) and desorption (dashed lines) curves for a typical test temperature (35⁰C) at varying activity steps for a constant film thickness: PU-PEO (245µm).  Reduced sorption and desorption plots (i.e., fractional uptake or loss curves plotted versus Fickian variable, √t/l) of three representative experiments for each copolymer are shown for various film thickness and water vapor activity steps in Figure 5.8. Results for the PU-PEO films (a-c) were obtained using the differential sorption method while the results for the PEBAX®1074 films (d-e) were obtained using the integral sorption method.   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 98         PU-PEO PEBAX® 1074 Figure 5.8. Reduced sorption (solid lines) and desorption (dashed lines) curves at varying water vapor activity and dry film thickness for PEO-PU (a-c) and PEBAX® 1074 (d-f). As indicated in the legend of the figures, thicker lines represent thicker film samples.  Although the equilibrium sorption values were shown to be independent of the film thickness, both sorption and desorption cases show a strong thickness dependency. It could be observed that for both copolymers, neither the sorption nor the desorption results collapse onto a single curve as Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 99  would be the case if the diffusion was Fickian and independent of film thickness. Rather, the initial slope of the curves increases with film thickness, particularly for reduced sorption curves at higher activity steps. The same behavior was observed for the rest of the experiments in the entire range of activity studied.  Another common feature in all of the reduced sorption and desorption curves in Figure 5.8, inconsistent with the characteristics of a Fickian process, is the presence of a small-time retardation effect. Curves of this kind are often referred to as sigmoidal sorption curves showing a point of inflection between the short times of sorption or desorption curves and the linear intermediate time part of the curves. Sigmoidal sorption curves may arise because surface equilibrium conditions are not established instantaneously (in contrast to the assumption underlying Eqs. (5.5) and (5.6)), either due to a non-ideal experimental condition or time-dependent changes of material interface properties in response to a sudden activity change (or both, which is the case in our experiments).  These short- and long-time anomalies interfere with the determination of diffusion coefficients from sorption/desorption measurements if one uses methods presented in section 5.3.2 based on the assumption of ideal Fickian behavior. Figure 5.9 summarizes the diffusion coefficients extracted for PEBAX films of various thickness using the half-time method (Eq. (5.7)). Solid lines with filled symbols show values extracted from differential sorption tests while dashed lines with open symbols show values from the integral sorption tests. Knowing the fact that D is a decreasing function of concentration for the majority of the studied activity range, it is reasonable to observe dashed lines lie above solid lines, especially for higher activities (leading to higher water concentrations in the film). This is because open symbols represent a mean value of diffusivity (with larger contributions from lower activities) in a range of activity from zero to the test activity while closed symbols only represent an average over a small step in the vicinity of the test activity.  Figure 5.9. Impact of film thickness on the diffusion coefficient evaluated using half-time method for PEBAX® 1074 at constant temperature 25⁰C. The data from Potreck et al. (2009) is at different temperatures of 20⁰C and 30⁰C, but close to the test conditions of this work.   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 100  A trend of increasing diffusion coefficient with film thickness is evident for both methods. As was explained above, this thickness-dependency of the diffusion coefficient extracted from the half-time method stems from the fact that retardation of sorption process due to the surface relaxation process (short-time sigmoidal effects) can interfere with the determination of the half-time. Since the surface relaxation process can be assumed to be independent of film thickness, it will alter the evaluated half-time of thinner films much more significantly. The diffusion data from Potreck et al. [45] on the same grade of PEBAX 1074 is also included in Figure 5.9. They used a method similar to the integral sorption method in this work, but with much coarser steps of activity to evaluate the diffusion coefficients. Although the thickness of the studied film is not explicitly mentioned in their paper, based on the wet film thickness (0.47-mm casting knife) and the concentration of polymer solution (7 wt.%) used for film preparation in their work, it is estimated that their dry film thickness was about 25µm. They also used a half-time method with the assumption of Fickian mechanism for determination of the diffusion coefficients. This explains why their reported diffusivity values lie well below our measurements. 5.5.3. Non-Fickian Diffusion Reduced sorption and desorption curves in Figure 5.8 indicate a time-dependent relaxation process accompanying the diffusion of water vapor through these copolymers at two different time scales. Sigmoidal sorption represents a slow interfacial moisture uptake at short times (<100 seconds), followed by a pseudo-Fickian behavior for intermediate times (up to a quasi-equilibrium concentration), and a slower stress-relaxation for the bulk film as the polymer chains rearrange to accommodate more water until the film equilibrates [229], [231], [243]. Such structural relaxation anomalies are often reported for the diffusion of organic vapors in amorphous homopolymers at experimental temperatures slightly below the polymer Tg) [225], [228], [233]. In glassy polymers, solvent plasticizes the polymer matrix (lowered Tg), causing an increase of the segmental motions of the stiff polymer backbone and a slow structural relaxation, which occurs at about the same rate or slower than the diffusion process [244]. The block copolymers studied here consist of alternating series of crystallizable soft PEO and hard segments; nylon 12 (PA12) (Tm= 156°C) in PEBAX®1074 and polyurethane (PU) (Tm= 235°C) in PU-PEO. These segments can exist in several phases within the copolymer matrix; continuous amorphous soft PEO, crystalline soft PEO, crystalline hard segments, non-crystallized glassy hard segments, intermediate phases of mixed hard and non-crystalline soft segments, and cross-linked hard segments [216], [245], [27]. Dissolution of water and subsequent diffusion in these block copolymers primarily occurs through the amorphous soft PEO phase. The hard nylon and polyurethane segments are able to highly crystallize and act as physical cross-links, providing mechanical strength of the polymer matrix. Water interactions with different phases of such semi-crystalline block copolymers present a complex system with multiple mechanisms potentially responsible for the observed non-Fickian behaviors. Although the soft water-vapor-transporting PEO segments of both copolymers are well above (~100°C) their glass transition temperatures (-55°C for PEBAX®1074 [216] and -45°C for PU-PEO [27]) in our experimental temperature range (25-55°C), plasticization effect is still a possibility for intermediate phases of copolymer segments, as well as non-crystalline glassy hard Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 101  segments. These regions may absorb water at a temperature below their glass transition [234] and result in a slow response to the changes in water concentration. This is particularly important for PEBAX®1074 containing PA12 with a Tg of 41°C [246]. Another possibility is the melt of crystalline PEO segments that are above their Tg, but below their melt temperature (35-50°C) in the experimental conditions. These segments could become disrupted as water content increases in the polymer [208], [27]. Chain immobilization and geometric impedance effects due to the presence of impermeable crystalline domains in these block copolymers could also interfere with the transport of water molecules in the continuous amorphous PEO phase. This has been noted by others for similar vapor-copolymer systems [235]. Cross-linked hard segments can constrain the swell in these copolymer. This involves a tension between swollen and unswollen segments because the latter tend to resist further swelling. In the early stages of sorption, the surface may fail to reach the equilibrium concentration of permeant for some time; however, the rate of sorption builds up slowly to give a sigmoidal curve. In later stages of sorption process, such stresses are either relaxed or dissipated by further swelling and rearrangement of the polymer segments. Huizing [27] has reported slower kinetics of water sorption in similar PU-PEO films with increased cross-linking ratio. 5.5.4. Diffusion-Relaxation Model Various mathematical models have been applied to fit the experimental sorption data in penetrant-polymer systems with non-Fickian behavior.  A combination of two-stage and sigmoidal absorption, the latter being a special case of the former, proposed by [243], seems to describe the sorption and desorption experiments presented here. One of the earliest treatments of initial sigmoidal sorption was reported by Crank and Park [225] who proposed and solved a time-dependent boundary condition (Eq. (5.12)) similar to that proposed later by Long and Richman [228].  𝑪(𝒕) = 𝑪𝟏{𝟏 − 𝒆𝒙𝒑(−𝜷𝒕)}        𝒙 = ±𝒍           𝒕 ≥ 𝟎 (5.12)  where 𝜷  is the surface relaxation rate, and 𝑪𝟏 is the equilibrium surface concentration. This boundary condition can represent a surface that responds to a change in environment concentration rapidly but not instantaneously [221]. With this boundary condition, the solution for Eq.(5.1) is  𝑪𝒕 − 𝑪𝟎𝑪𝟏 − 𝑪𝟎= 𝟏 − 𝒆𝒙𝒑(−𝜷𝒕)𝒄𝒐𝒔𝒙 (𝜷𝑫⁄ )𝟏𝟐𝒄𝒐𝒔𝒍 (𝜷𝑫⁄ )𝟏𝟐−𝟏𝟔𝜷𝒍𝟐𝝅∑(−𝟏)𝒏𝒆𝒙𝒑(−𝑫(𝟐𝒏 + 𝟏)𝟐𝝅𝟐𝒕𝟒𝒍𝟐)(𝟐𝒏 + 𝟏)[𝟒𝜷𝒍𝟐 − 𝑫𝝅𝟐(𝟐𝒏 + 𝟏)𝟐]∞𝒏=𝟎𝒄𝒐𝒔(𝟐𝒏 + 𝟏)𝝅𝒙𝟐𝒍 (5.13)  Moreover, the sorption time curves take the form Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 102   𝑴𝑭∗ =𝑴𝒕 − 𝑴𝟎𝑴∞ − 𝑴𝟎= 𝟏 − 𝒆𝒙𝒑(−𝜷𝒕) (𝑫𝜷𝒍𝟐⁄)𝟏𝟐𝒕𝒂𝒏(𝜷𝒍𝟐𝑫⁄ )𝟏𝟐−𝟖𝝅𝟐∑𝒆𝒙𝒑(−(𝟐𝒏 + 𝟏)𝟐𝝅𝟐𝑫𝒕𝟒𝒍𝟐)(𝟐𝒏 + 𝟏)𝟐 [𝟏 −(𝟐𝒏 + 𝟏)𝟐𝝅𝟐𝑫𝟒𝜷𝒍𝟐]∞𝒏=𝟎 (5.14)  The two-stage sorption is usually described by a model first proposed by Berens and Hopfenberg [247] as  𝑴(𝒕) =  𝑴𝒅(𝒕) +  𝑴𝒓(𝒕) (5.15)  where the sorption is superimposed by two distinct sorption regimes: a fast Fickian diffusion regime (𝑴𝒅) and a slower relaxation regime (𝑴𝒓) with the assumption that these fast and slow processes are independent of each other. This is usually a valid assumption since the diffusion-controlled regime is often far faster than the long-term relaxational regime [244]. Therefore, the sorption process can be considered as a sum of phenomenological independent contributions from Fickian diffusion and polymer relaxation:  𝑴(𝒕)𝑴∞=  ∅𝑴𝑭∗ (𝒕) + (𝟏 − ∅)(𝟏 − 𝒆𝒙𝒑(−𝒌𝒕)) (5.16)  where ∅ =𝑴𝒅∞𝑴∞ is defined as the ratio of the infinite sorbed mass of Fickian part to the infinite equilibrium sorption mass, and 𝒌 is the bulk relaxation constant at long times.  Figure 5.10 (a-c) shows the progressively modified model of sorption from purely Fickian to a complete combined sigmoidal and two-stage model for a typical sorption step for three different thicknesses of PU-PEO films at 25ºC. A classic Fickian model (Eq.(5.4)), was applied to the data for the entire duration of sorption step with a diffusion coefficient evaluated using the half-time method (Figure 5.10 (a)). The Fickian model produced very unsatisfactory fits; the values are accordingly unreliable. In contrast, the combined model (Figure 5.10 (c)) provides a much higher accuracy fit to the sorption data. The appearance of a second stage of sorption (the difference between fitted lines and sorption data in Figure 5.10 (b)) becomes less apparent with increasing the film thickness. This is due to the much slower diffusion in thicker films allowing for conformation of the polymer chains with stresses. Regressed model parameters for all sorption experiments are summarized in tables E4 and E5 of Appendix E. Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 103   (a) Comparison of experimental sorption data with Fickian diffusion model (Diffusion coefficients evaluated using the half-time method from sorption curves)  (b) Correction for short-time sigmoidal sorption anomaly   (c) Combined Sigmoidal and dual-stage sorption model Figure 5.10. Comparison between experimental sorption data and different sorption models for PU-PEO at various film thickness and constant temperature 25⁰C   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 104  The values of β and k (in Table E4 of Appendix E) average about 0.018 s-1 and 0.002 s-1, respectively, for all film thicknesses. Therefore, it can be reasonably assumed that the relaxation processes occurring upon the sorption of water are independent of the film dimensions [244]. The surface relaxation obeys the same behavior as the material as a whole but with a different relaxation time 1/β, which is considerably less than the bulk relaxation time (1/k). This is logical as the surface layer saturates with moisture in a much shorter time than the whole bulk and its relaxation is also faster. On the other hand, the diffusion-controlled sorption varies with the square of the film thickness. Therefore, the strong influence of sample thickness on the overlap in times of diffusion and relaxation in sorption kinetics is expected. The diffusional Deborah number often characterizes the ratio of the diffusion to relaxation rates during the transport process, firstly defined by Vrentas et al. [248] as  𝑫𝑬𝑩𝒃 =  𝝉𝑹𝝉𝑫=𝟏/𝒌𝒍𝟎𝟐𝑫⁄ (5.17)  where, 𝝉𝑫 =𝒍𝟎𝟐𝑫 is the characteristic diffusion time (𝒍𝟎 being the un-deformed dry film thickness, and D the Fickian mutual diffusion coefficient), and 𝝉𝑹 = 𝟏/𝒌 is the characteristic relaxation time of polymer chains in the bulk film. When the Deborah numbers are of O~1 (𝝉𝑹 ≈ 𝝉𝑫), the rates of relaxation and diffusion are comparable, and the two processes are superimposed, while for Deborah numbers of O«1, the relaxation rate is much faster and the two processes are well separated (as is the case for ideal Fickian diffusion in purely rubbery polymers). In the same manner, a surface Deborah number (𝑫𝑬𝑩𝒔) may be defined using the surface relaxation time (𝝉 = 𝟏/𝜷) in Eq.(5.17). The surface Deborah number compares the rate of interfacial dynamic changes (i.e., structural relaxation to reach equilibrium concentration at film interface) to the Fickian diffusion in the bulk film. Table E4 in Appendix E summarizes the bulk and surface Deborah numbers of different sorption and desorption experiments for PU-PEO films, calculated from the regressed diffusion coefficients and relaxation time constants using the Diffusion-Relaxation model. Average bulk Deborah numbers range from 2.26 for the 38µm film to 0.07 for the 245µm. The near-unit value of the Deborah number for the thin film indicates an overlap between diffusion and relaxation kinetics during the sorption process, while for thicker films the contributions of diffusion and relaxation are well-separated and bulk relaxation happens at a much faster timescale. This finding explains why the sorption process proceeds relatively more quickly for thicker films (i.e., reduced desorption curves of thicker films in Figure 5.8 lie above those of thinner films), which is characteristic of time-dependent diffusion in penetrant-polymer systems [249].  The average surface Deborah numbers range from 0.14 for the 38µm film to 0.012 for the 245µm, which implies that the relative time scale for the establishment of equilibrium condition at film interface of thicker film samples is far smaller than diffusion through bulk film compared to the Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 105  thinner film samples. Thus a much less relative impact of variable surface conditions on the diffusion process (and its overall time scale) is expected for thicker films.  5.5.5. Evaluation of Mutual Diffusion Coefficient at Equilibrium The ultimate goal of this study is to extract diffusion-concentration correlations suitable for modeling of the steady-state water vapor permeation through composite membranes consisting microporous support layers coated with the dense selective copolymers studied here. Therefore, evaluation of the diffusivity coefficient at equilibrium conditions is desired. Two methods are described in this section for evaluation of such diffusion coefficients. The asymmetry between absorption and desorption curves, particularly at higher water vapor activities (i.e., leading to larger degrees of swelling), is attributed to the polymer swelling process accompanying the water diffusion. In contrast, during desorption, particularly at early stages, the already swollen polymer matrix does not need to shrink before the water leaves the polymer. Crank and Park [225] noted that desorption could be faster than absorption because chain rearrangement and relaxation is not necessary for penetrant to leave the polymer. Moreover, Oparaji et al. [208] discuss that dissolution of crystalline PEO during the sorption process results in a non-Fickian behavior. They show that water desorption for their experiments is ten times faster than sorption for a similar gas-phase activity step, indicative of the absence of crystallite dissolution during desorption.  Therefore, the desorption curves obtained for limited activity steps (particularly at the early stage of desorption) are expected to provide a reasonable approximation of the equilibrium diffusion coefficient through a swollen polymer film. However, the time-dependent boundary condition (Eq. (5.12)) still holds for the desorption case as the polymer interface does not respond instantaneously to humidity changes in the gas phase. This is evident from the sigmoidal shape of desorption curves (Figure 5.8). Failing to consider this initial sigmoidal behavior could result in estimating diffusion coefficients that are too low. With this consideration, one can predict the diffusion coefficients of a fully swollen film at the final equilibrium state by applying the solution of Eq.(5.14) to the short times of a desorption curve. An approximation of Eq. (5.14)  with the first 16 terms of the sums was used in a least-squares regression of the first 200 seconds of desorption data. The β value was obtained from the corresponding sorption experiment, and the diffusion coefficient was the fit parameter.    A comparison between the diffusion coefficients extracted from the desorption curves (filled black symbols) with those of half-time method applied to the sorption curves assuming a Fickian mechanism (hollow blue symbols) is made in Figure 5.11. As can be observed, these diffusion coefficients appear to be thickness-independent.  Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 106   (a) PU-PEO film  (b) PEBAX® 1074   Figure 5.11. Impact of dry film thickness on diffusion coefficient at constant temperature 25⁰C.  As an alternative approach, the equilibrium diffusion coefficient may be calculated from the early time data of sorption for a sufficiently thick film (ideally a film of infinite thickness). This method is based on the idea that in a hypothetical film of infinite thickness, the sorption process approaches the ideal diffusion-controlled Fickian behavior [250]. The thicker the film, the slower the concentration changes at any point inside the film (as shown in Figure 5.12). Hence in a hypothetical film of infinite thickness, the polymer chains in any volume element can remain longer at equilibrium conformation during the sorption process, so that (beyond the initial sigmoidal anomaly) the conditions for steady-state diffusion hold as the sorption proceeds. Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 107  Following the discussions of Deborah numbers in the previous section, the fact that in thick films studied here (~200µm) relaxation happens at a much faster rate compared to the diffusion (i.e., a 𝑫𝑬𝑩𝒃 ≪ 𝟏) implies that sorption in these films resembles diffusion at the equilibrium state of the polymer. In fact, the tendency of the diffusion values to coincide with equilibrium diffusion coefficients (evaluated from desorption curves) for the thicker films can be observed in Figure 5.11. This suggests that, as the film thickness increases, the diffusion coefficient becomes less time-dependent and shifts toward purely a concentration dependence during the sorption process. The critical point in applying this method to the cases with considerable surface relaxation (initial sigmoidal anomaly) is that the sorption experiment has to have progressed sufficiently so that the surface condition is in equilibrium. The relative importance of surface relaxation phenomena in the sorption process may be realized from the concentration profiles shown in Figure 5.12. The concentration profiles (Eq. (5.13)) normalized by the equilibrium concentration are plotted at various time steps versus normalized film thickness for two cases of thin and thick films (Deborah numbers of O~1 and O<<1, respectively). During the early stage of the sorption process (~100 seconds), the fast relaxation rate at the surface of the film (β~0.018) results in a quick transformation into the equilibrium mode. In the case of a thick film (Figure 5.12 (b)), most of the film is at the initial concentration, and the surface relaxation process can be reasonably neglected compared to the diffusion. This results in concentration profiles resembling more closely a Fickian process, where the gradients of concentration become the dominant driving force generating mass fluxes. In contrast, in a thin film (Figure 5.12 (a)), at t=100 s the bulk of the film has already reached high concentrations comparable to the interface, and thus relaxation of the surface cannot be neglected. Neglecting relaxation of the surface would result in underestimation of the equilibrium diffusion coefficient from the initial sorption of thin films shown in Figure 5.13. The diffusion coefficients were therefore evaluated from a regression of Eq.(5.14) to the first 500 seconds of the sorption data (sufficiently longer than surface relaxation time ~100s) similar to the procedure described previously for the desorption curves.  Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 108   39μm film (DEBs=0.14, DEBb=2.54)  245μm film (DEBs=0.01, DEBb=0.104) Figure 5.12. Effect of film thickness on the concentration profile development at short-times of sorption at a typical activity step (0.55-0.6)   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 109   Figure 5.13. Effect of film thickness on the Integral equilibrium diffusion coefficients for PU-PEO films at constant temperature 25⁰C. Solid symbols represent values calculated from desorption curves while hollow symbols represent values from the sorption curves.   Figure 5.13 shows a comparison between the diffusion coefficients evaluated from desorption curves and those evaluated from the early time data of sorption curves at various film thickness. It can be seen that as the film thickness increases, the diffusion coefficient evaluated from the sorption curves approach the equilibrium diffusion coefficients of desorption curves. Therefore, the steady-state diffusivity values may also be determined from the measurements of a series of films of various thickness, extrapolated for a hypothetical film of infinite thickness.  Steady-state diffusion coefficients along with evaluated diffusion-concentration correlations (solid lines) using the procedures of section E. 4  in Appendix E are presented for PU-PEO copolymer in Figure 5.14. Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 110   Figure 5.14. Integral Diffusion coefficients and Diffusion-Concentration correlation for PEO-PU films at varying temperatures from 5⁰C to 55⁰C.  5.5.6. Steady-State Permeability To investigate the validity of the proposed method of evaluating equilibrium diffusion coefficients, we have conducted steady-state water vapor permeation testing of a few films of PU-PEO copolymer with varying thickness at different temperatures. Figure 5.15 compares the results of these measurements with the predictions of the solution-diffusion model (Eq.(5.10)) using equilibrium sorption values and D-C correlations obtained from sorption kinetic experiments.  Figure 5.15. Comparison of the measured steady-state permeability values with estimated values using Solution-Diffusion model for PU-PEO films of various thickness at different temperatures.   Chapter 5 – Measurements of moisture sorption isotherms and diffusion coefficients in dense polymers 111  As can be observed, there is quantitative agreement between the predictions of the solution-diffusion model and steady-state permeability measurements. Although it was shown in the previous section that diffusivity decreases with increasing water vapor activity (particularly above activity of 0.2) due to the polymer swelling and significant clustering, it can be seen in Figure 5.15 that overall permeability increases with activity. This indicates that the increase of solubility with activity outweighs the changes in diffusivity. Since the permeability is the product of solubility and integral diffusivity (P=SD), the overall effect is an increase in permeability with increased water vapor activity. Likewise, it can be observed that permeability slightly decreases with temperature, indicating that solubility decreases with temperature (Figure 5.5) more rapidly than diffusivity increases with temperature (Figure 5.14). It should also be mentioned that since clustering becomes less significant at higher temperatures, due to a lower moisture content in the polymer, the diffusivity is less influenced at higher activities and thus permeability increases with a steeper slope at higher temperatures and activities. 5.6.  CONCLUSIONS The kinetics of water vapor sorption and desorption in two highly water vapor permeable PEO-based block copolymers were investigated. It is demonstrated that the diffusion of water in these copolymers is non-Fickian at temperatures well above the glass transition temperature of the soft PEO phase in polymer samples. Practically, this means that the copolymer structure is in a non-equilibrium state that undergoes a time-dependent relaxation, superimposed on the Fickian diffusion, resulting in short-time sigmoidal and long-time two-stage sorption kinetics. A simple Fickian model does not adequately capture the dependence of water sorption kinetics on film thickness, temperature, and absorbed water concentration. Instead, a combined sigmoidal and two-stage sorption model can satisfactorily fit the sorption kinetics in these copolymers. In such cases, analytical solutions of the Fickian diffusion for both short- and long-times should be used with caution as they might result in significant errors (up to an order of magnitude) in determining diffusivity coefficients. It was shown that appropriate treatment of the short times of desorption curves for all film thickness and sorption curves for sufficiently thick films, corrected to account for variable surface conditions, leads to reliable estimates of equilibrium diffusion coefficients that are independent of the film thickness. Permeability values estimated using these diffusion coefficients in the solution-diffusion model show reasonable agreement with the experimental measurements of steady-state permeability for free-standing films. This information is critical when attempting to model the transport properties and performance of both free-standing films and composite membranes from kinetic sorption measurements of bulk material samples. The proposed method for inferring diffusion coefficients from the early time data of sorption curves is particularly useful in the case of swelling penetrants with very low diffusion coefficients (<10-14 cm2/s), such as large organic vapor molecules, where obtaining desorption data is experimentally odious owing to the very large sorption equilibrium time scales (~months to years). 112  Chapter 6 - IMPACT OF OPERATING CONDITIONS ON THE PERFORMANCE OF ENTHALPY EXCHANGERS1  6.  6.1. OVERVIEW This chapter combined with the previous Chapter 5 address the last two objectives of this study; developing predictive models capable of linking membrane properties to the system-level ERV exchanger core performance. A theoretical model is developed for current generation asymmetric composite membranes used in enthalpy exchangers. This model predicts the membrane permeability as a function of local values of air humidity and temperature, based on a limited number of kinetic water vapor sorption tests of the membrane material. The membrane model is coupled with a finite-difference model of the conjugate heat and mass transfer in full cross-flow enthalpy exchanger cores. The model predictions are validated against experimental data of a commercial-scale enthalpy exchanger. The model is used to predict the influence of outdoor air parameters (temperature, humidity) on an enthalpy exchanger and the predictions are compared against a baseline case that assumes constant membrane permeability. Such an assumption can result in deviations in effectiveness predictions by up to 15%. Depending on the mode of operation, outdoor air relative humidity can increase or decrease the effectiveness of enthalpy exchangers by up to 12%. In contrast, outdoor air temperature appears to have only a minimal influence on effectiveness parameters. This model is helpful in interpreting the membrane-level test results and provides a means for estimating the impacts of ERV installations on indoor air quality, fouling life-time, etc. The model is computationally fast enough to be incorporated in building energy simulation packages, and to allow the parametric study of specific ERV installations within buildings to determine the optimal application. This modeling tool, which is capable of capturing the full range of membrane media properties, is novel and has not been reported elsewhere in the literature.                                                               1 A version of this chapter has been published: ‘Heat and mass transfer modeling in enthalpy exchangers using asymmetric composite membranes,’ Journal of Membrane Science, 556 (2018) pp. 248-262. Copyright © 2018 Elsevier B.V. All rights reserved. Reprinted with permission. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 113  6.2. INTRODUCTION Core-level performance of membrane-based enthalpy exchangers, particularly latent effectiveness, can be significantly influenced by the permeation properties of the membrane media used [36], [251]. Thus one expects significant performance variations as a result of the operation in different climatic conditions. A full experimental evaluation of these variations would be practically impossible as a large number of experiments would be required to cover the range of operating conditions and installation configurations these systems might experience in the field, with each such experiment requiring hours to reach steady-state conditions [252]. A fundamental understanding of the influence of these variable parameters on the performance of enthalpy exchangers, therefore, requires modeling tools instead. These models should be computationally fast so that they can be incorporated in building energy simulation packages [253], [62]. Many studies report on heat and mass transfer modeling of flat-plate-type enthalpy exchangers using finite element methods [63], [65]–[67], [74], effectiveness-NTU shortcut methods [[59], [68], and CFD modeling tools [71]–[73], [254]. Most studies consider cross-flow and counter-flow configurations of the exchanger due to the simplicity of these geometries. In a recent study, Min et al. [255] compare the accuracy of numerical and effectiveness-NTU methods for evaluating the performance of membrane-type cross-flow enthalpy exchangers. They show that although NTU methods are easy to use and well-suited for fast estimation of performance parameters, they lack the capability of capturing various physical parameters of membrane media, which results in inaccurate estimations of latent and total effectivenesses. On the other hand, numerical methods are shown to not only provide more accurate estimations but also the detailed distributions of various quantities on membrane surfaces, including humidity and temperature, that is required for taking into account the variations of membrane permeation properties. In most previous studies the membrane is treated as a “black box” with a constant permeability, which is usually determined by a single permeation experiment or adjusted to best describe the experimental results [60], [63], [69], [72], [74], [256]–[258]. This simplifies the modeling, but it may fail to accurately predict the exchanger performance in conditions different from that of the basic experiment, especially for exchangers with asymmetric composite membranes. Zhang and Nui [64] included sorption isotherms of dense membranes into an NTU model of cross-flow cores and compared various materials with different sorption model constants. They have shown that materials with linear sorption isotherms render the best performance in the studied range of operating conditions. More recent studies [36], ([66], [67] extended the same modeling approach for coupled heat and mass transfer with the addition of constant diffusion coefficients, thermal conductivity, and experimental moisture sorption curves (there is no information reported on the test temperature for the sorption data in these studies).  Although these models improve upon previous black box models, they still do not account for membrane variable diffusion properties, temperature effects, synergistic substrate effects on the coating layer properties in a composite, and the asymmetric nature of current generation membranes.   Zhang et al. [259] models asymmetric porous membranes with finger-like macro-voids, however, the asymmetric membranes used in their study have a microporous structure for all of the layers with a pore-flow transport mechanism (different from the highly-selective solution-diffusion dense Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 114  membranes studied here). Zhang et al. [200] report a mesoscale Lattice-Boltzmann simulation approach to model moisture transport through composite membranes with a porous support layer and a dense skin layer. Although this method gives more detailed insights into the transport phenomena inside the membrane matrixes with inhomogeneity in the structures, their model approximates the dense coating layer as a plate with fixed solubility and diffusivity parameters. This approach would also be challenging to incorporate into building-scale simulation packages owing to its computational complexity. A recent study by Boardman and Glass [260] applied a data-driven modeling approach for cross-flow enthalpy exchangers. They conducted in situ measurements of latent effectiveness for an ERV installation over a full year of operation, showing variations ranged from 19% to 61% with relative humidity (averaged between indoor and outdoor conditions). They reported latent effectiveness increased with average relative humidity but decreased with average temperature, consistent with the predictions of this study. They also developed a membrane model based on material properties for the cellulosic paper-based membrane of their studied ERV, coupled with a simple finite difference heat and moisture transfer model, to predict the latent effectiveness of the ERV core.  Their membrane model takes into account the effects of humidity and temperature on permeability and provides reasonable agreement with field measurements. However, the membrane permeability correlations they presented are specific to microporous resin-impregnated paper-based membranes (optimized for the ERV in their field use), and cannot be applied to the asymmetric composite membranes of this study due to the different permeation mechanisms. Also, as will be shown later in this work, in asymmetric membranes permeability is a function of the relative humidity and temperatures of both sides of the membrane, and cannot be correlated with averaged air parameters. In this chapter, we report on a generalized membrane model that takes into account both substrate and coating contributions with respect to local conditions of the adjacent air streams. This membrane model is coupled with a computationally fast finite-difference scheme for modeling conjugate heat and mass transfer in cross-flow enthalpy exchanger cores.  Variable operating conditions, specifically the temperature and humidity of the air streams, are considered. Two different model calculations are presented and compared: (1) a constant permeability model based on the assumption of “ideal laminate” theory, and (2) an asymmetric composite membrane model capturing variable permeability of the membrane in the full range of operating conditions. 6.3. COUPLED HEAT AND MASS TRANSFER THROUGH MEMBRANE  6.3.1. Mass Transfer The ideal laminate theory (also referred to as the “series resistance model”) assumes that the composite membrane consists of two or more independent barrier layers stacked together in series. The equivalent membrane permeability is thus given by  ℘𝒎 =𝜹𝒎𝜹𝒄℘𝒄⁄ +𝜹𝒔𝒖𝒃℘𝒔𝒖𝒃⁄ (6.1)  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 115  where, ℘ and 𝛿 denote the permeability and thickness of various layers; and subscripts 𝑚, 𝑐, and 𝑠𝑢𝑏 refer to the membrane, coating, and substrate, respectively. Using the individual permeability values of membrane substrate and coating layers, at a test condition of 50°C and 50% relative humidity at the supply inlet (reported in Table 6.1), in Eq.(6.1) predicts a membrane permeability value of 3.82 × 10−10  𝑚𝑜𝑙.𝑚𝑚2𝑠𝑃𝑎. However, experiments show that for this membrane [27], the measured permeability of the composite membrane can significantly deviate from this prediction depending on the test conditions and membrane orientation. An alternative approach for modeling composite membrane is used in this chapter, where mass transfer through substrate and coating layers are coupled by defining an interface concentration on the phase boundary inside the membrane. The pore-flow and solution-diffusion models are combined using this interface concentration, resulting in a resistance-in-series model for fluxes through the dense and the substrate layers. The following assumptions are made in model development: (1) One-dimensional heat and mass transfer through the membrane (since the membrane is very thin (~100μm) the thermal and mass gradients are principally transversal) (2) Uniform thickness of both dense and substrate layers (3) Negligible intrusion of the dense coated layer into the pores of the substrate  (4) A defect-free homogeneous dense coating (5) Negligible restrictive influence of substrate on the diffusion through the dense coating layer. According to Zhu, et al. 2017 [261], this is a valid assumption for the membrane studied in our work with coating thicknesses of 1-5µm and an average substrate pore diameter of 38-100nm, resulting in a scaled selective layer thickness on the order of 100.  (6) The dense section of the microporous substrate has negligible moisture sorption compared to the coating layer. Therefore, moisture transfer through the substrate layer is only by pressure-driven pore diffusion in the vapor phase without a phase change.  (7) No capillary condensation occurs during the water vapor flow through the substrate layer. Figure 6.1 shows a schematic representation of the vapor pressure and moisture concentration profiles in the composite membrane model. Subscripts s, *, e, refer to supply, interface, and exhaust, and superscripts b, m, S, A, and T refer to bulk, membrane surface, sensible, adsorption, and total, respectively.  Under steady-state conditions, moisture and heat fluxes (transmitted from the bulk air supply to the bulk air exhaust) have constant values at any location through the composite membrane.  The values of water vapor pressure and temperature on the two membrane surfaces differ from the values of adjacent bulk air streams due to the heat and mass transfer resistances inside the air boundary layers (regions between membrane surface and dashed lines in Figure 6.1). Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 116   Figure 6.1. Schematic of heat and moisture transfer through the asymmetric composite membrane.  The so-called solution-diffusion model is typically used to describe the mass transport through dense polymeric membranes via a three-step mechanism: (1) sorption of penetrant to the membrane surface on the supply side, (2) diffusion through the membrane, and (3) desorption from membrane surface to the bulk flow on the exhaust side [48]. In this modeling framework, it is assumed that a thermodynamic solubility equilibrium exists between the dense polymer surface and the adjacent vapor phase outside the polymer film. Therefore, the surface concentrations inside the dense membrane layer and vapor pressures outside this layer at the supply side and interface with the substrate are connected by the solubility equilibrium conditions. 𝑇 ∗ and 𝑝𝑣 ∗ denote the temperature and vapor pressure inside the substrate at the phase interface between the dense coating and substrate layers. 𝐶 ∗ is the concentration inside the dense layer adjacent to the phase interface corresponding to this vapor pressure and temperature.  Penetrant flux through the coating layer in steady-state is therefore given by  𝑱 = ℘𝒄𝒑𝒗𝒔𝒎 − 𝒑𝒗 ∗𝜹𝒄 (6.2)  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 117  where, 𝑝𝑣𝑠𝑚 and 𝑝𝑣 ∗ are the partial vapor pressures on either side of the coating layer. In this model, membrane permeability, ℘, is the product of the material diffusivity and solubility  ℘ = 𝑺𝑫 (6.3)  The use of the permeability simplifies the solution-diffusion framework as it does not require knowledge of the penetrant concentration on membrane surfaces. However, as was shown by Mauviel et al. [262], it does not allow for a comparison of the membrane permeation properties in the case of variable permeability systems. The more fundamental form of solution-diffusion theory for transmembrane flux is given by  𝑱 = ?̅?(𝑪𝒔𝒎 − 𝑪 ∗)𝜹𝒄 (6.4)  where ?̅? is the average concentration-dependent diffusion coefficient (i.e., the case in most polymer membranes [221]) between the moisture concentrations at the two sides of the coating layer  ?̅? =𝟏(𝑪𝒔𝒎 − 𝑪 ∗)∫ 𝑫(𝑪)𝒅𝑪𝑪𝒔𝒎𝑪 ∗ (6.5)  According to the above equations, description of the moisture transfer through the membrane dense coating layer requires knowledge of the concentration-dependent diffusion coefficient and solubility coefficients of coating material in the desired range of operating temperature and concentrations. Appendix F describes the experimental work and modeling conducted to determine these permeation properties. Combining Eqs. (6.2), (6.4) and (6.5) results in  ℘𝒄 = ?̅?(𝑪𝒔𝒎 − 𝑪 ∗)𝒑𝒗𝒔𝒎 − 𝒑𝒗 ∗ (6.6)  The moisture transfer resistance of the membrane coating layer is then defined as  𝑹𝒄𝑴 =𝜹𝒄℘𝒄𝑹?̅?𝒄 (6.7)  where ?̅?𝒄 is the average coating temperature between the supply side and the phase interface. After leaving the thin dense coating layer, water enters the microporous substrate in the vapor phase with a vapor pressure, 𝑝𝑣∗, corresponding to the interface concentration 𝐶∗ as illustrated in Figure 6.1. There is no phase change when the vapor leaves the support layer entering the exhaust side. The driving force for the flux through the pores is the pressure difference between 𝑝𝑣∗ and the permeate pressure, 𝒑𝒗𝒆𝒎. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 118  The so-called dusty gas model (DGM), based on the kinetic theory of gases, is used for modeling the water vapor flux through the substrate layer [131]. This model includes mechanisms of ordinary diffusion and Knudsen diffusion as resistances in series, together in parallel with the resistance to viscous Poiseuille flow.  𝑱 =𝜺(𝒑𝒗 ∗ − 𝒑𝒗𝒆𝒎)𝝉𝜹𝑺𝒖𝒃∫ ([(𝑫𝑲𝒏𝑹?̅?𝒔𝒖𝒃)−𝟏+ (𝑫𝒗𝒂𝑹?̅?𝒔𝒖𝒃)−𝟏]−𝟏+𝒅𝒑𝒐𝒓𝒆𝟐 ?̅?𝒑𝒐𝒓𝒆𝟑𝟐𝝁𝑹?̅?𝒔𝒖𝒃)𝜳(𝒅𝒑𝒐𝒓𝒆). 𝒅𝒅𝒑𝒐𝒓𝒆∞𝟎∫ 𝜳(𝒅𝒑𝒐𝒓𝒆). 𝒅𝒅𝒑𝒐𝒓𝒆∞𝟎 (6.8)  where 𝜏 is the tortuosity, ?̅?𝑝𝑜𝑟𝑒 is the average pore pressure, ?̅?𝑠𝑢𝑏 is the average substrate temperature, 𝐷𝑣𝑎 is the water vapor diffusivity in the air given in [88], 𝝍(𝒅𝒑𝒐𝒓𝒆) is the pore size distribution (section 3 in Appendix F), 𝐷𝐾𝑛 is the Knudsen diffusivity  𝑫𝑲𝒏 =𝒅𝒑𝒐𝒓𝒆𝟑√𝟖𝑹?̅?𝒔𝒖𝒃𝝅𝑴𝒗 (6.9)  moreover, 𝜀 is the surface porosity (i.e., the ratio of total pore area to the total surface area)  𝜺 =𝑵𝟒∫ 𝝍(𝒅𝒑𝒐𝒓𝒆)𝝅𝒅𝒑𝒐𝒓𝒆𝟐 𝒅𝒅𝒑𝒐𝒓𝒆∞𝟎 (6.10)  Due to the negligible pressure difference across the membrane in enthalpy exchangers as well the dense layer blocking the viscous flow through pores, it is reasonable to assume negligible Poiseuille flow [131], and thus Eq.(6.8) reduces to  𝑱 =𝜺(𝒑𝒗 ∗ − 𝒑𝒗𝒆𝒎)𝝉𝜹𝑺𝒖𝒃∫ ([(𝑫𝑲𝒏𝑹?̅?𝒔𝒖𝒃)−𝟏+ (𝑫𝒗𝒂𝑹?̅?𝒔𝒖𝒃)−𝟏]−𝟏)𝜳(𝒅𝒑𝒐𝒓𝒆). 𝒅𝒅𝒑𝒐𝒓𝒆∞𝟎∫ 𝜳(𝒅𝒑𝒐𝒓𝒆). 𝒅𝒅𝒑𝒐𝒓𝒆∞𝟎 (6.11)  The moisture transfer resistance of the substrate layer is then given by  𝑹𝒔𝒖𝒃𝑴 =𝒑𝒗 ∗𝑹𝑻 ∗− 𝒑𝒗𝒆𝒎𝑹𝑻𝒆𝒎𝑱 (6.12)  The total moisture transfer resistance of the composite membrane according to the resistance-in-series model is  𝑹 𝑴 = 𝑹𝒄𝑴 + 𝑹𝒔𝒖𝒃𝑴  (6.13)  The composite membrane permeance is then given by  𝑮 =  ℘𝒎𝜹𝒎=𝑹 𝑴𝑹?̅?𝒎 (6.14) Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 119   where ?̅?𝑚 is the average membrane temperature between the supply and exhaust sides. 6.3.2. Heat Transfer The method reported by Min et al. [80] was used to account for the coupling of heat and moisture transfer through the composite membrane.  During the three-step solution-diffusion process, moisture sorption into the coating polymer, associated with condensation, releases heat (exothermic) while desorption on the interface is associated with evaporation and absorbs heat (endothermic) (as shown in Figure 6.1). The higher the moisture flux through the membrane the more it affects the membrane surface temperatures and thus transmembrane heat flux.  Conservation of energy on the supply side requires that the heat fluxes transmitted by convection and adsorption at the bulk air supply side membrane surface are conducted through the coating layer:  𝒒𝒔𝑺 + 𝒒𝒔𝑨 = −𝝀𝒄𝝏𝑻𝒄𝝏𝒛 (6.15)  On the exhaust side:  −𝝀𝒔𝒖𝒃𝝏𝑻𝒔𝒖𝒃𝝏𝒛= 𝒒𝒆𝑺 (6.16)  where 𝒒 𝑺 is the convective sensible heat flux from the bulk air to the membrane surface.   𝒒𝒔𝑺 = 𝒉𝒔(𝑻𝒔𝒃 − 𝑻𝒔𝒎) (6.17)   𝒒𝒆𝑺 = 𝒉𝒆(𝑻𝒆𝒎 − 𝑻𝒆𝒃) (6.18)  𝒉𝒔 and 𝒉𝒆 are the convective heat transfer coefficients on the supply and exhaust sides, respectively.  Likewise, at the coating layer interface with the substrate layer, conservation of energy requires that the net conduction through the coating layer equals the conduction heat flux through the substrate layer and the desorption heat flux at the interface:  −𝝀𝒄𝝏𝑻𝒄𝝏𝒛= −𝝀𝒔𝒖𝒃𝝏𝑻𝒔𝒖𝒃𝝏𝒛+ 𝒒∗𝑨 (6.19)  In Eqs. (6.15) and (6.19),  𝑞 𝐴 denotes the adsorptive or desorptive (latent) heat fluxes at membrane surfaces   𝒒𝒔𝑨 = 𝒒∗𝑨 = 𝑱𝒒𝒂𝒅 =  𝑱∆𝑯𝒗 (6.20)  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 120  where the heat of adsorption, 𝑞𝑎𝑑, is assumed to be equal to the latent heat of condensation or vaporization of water at STP, ∆𝑯𝒗 = 𝟐𝟓𝟎𝟏𝒌𝑱𝒌𝒈⁄ , independent of membrane adsorption capacity and surface temperature. This is a reasonable assumption for the operating range of enthalpy exchangers. Min et al. [79] have shown that for transmembrane moisture fluxes on the order of 10-3 𝑘𝑔𝑚2𝑠⁄  or lower (which is the case for the enthalpy exchangers studied here), this assumption introduces a negligible error (<0.2%) in the calculation of the heat of adsorption. Due to the very small enthalpy carried by moisture flux through the membrane, a linear temperature gradient across the membrane can be assumed. Thus the coating-substrate interface temperature, which is required for the mass transfer calculations, can be approximated from Eq. (6.19)  as  𝑻∗ = 𝟏(𝝀𝒄𝜹𝒄+𝝀𝒔𝒖𝒃𝜹𝒔𝒖𝒃)[(𝑻𝒔𝒎𝝀𝒄𝜹𝒄+𝑻𝒆𝒎𝝀𝒔𝒖𝒃𝜹𝒔𝒖𝒃) − 𝑱∆𝑯𝒗] (6.21)  where, 𝝀𝒄 and 𝝀𝒔𝒖𝒃 are the membrane coating and substrate layers thermal conductivity, respectively. The total heat flux between the two bulk air streams on the opposing sides of the composite membrane may be written as  𝒒𝑻 = 𝝀𝒎𝑻𝒔𝒎 − 𝑻𝒆𝒎𝜹𝒎 (6.22)  where 𝝀𝒎 is the composite membrane effective thermal conductivity defined according to the method of Min and coworkers [80], [79], [263].  𝝀𝒎 =𝜹𝒎𝜹𝒄(𝟏 + 𝜸𝒒)𝝀𝒄⁄ +𝜹𝒔𝒖𝒃𝝀𝒔𝒖𝒃⁄ (6.23)  and 𝜸𝒒 is the ratio of latent to sensible heat fluxes.  𝜸𝒒 =𝒒𝑨𝒒𝑺=𝑱∆𝑯𝑽𝒉𝒔(𝑻𝒔𝒃 − 𝑻𝒔𝒎) (6.24)  Thermal conductivity, particularly for the microporous substrate layer, may be affected by the moisture content and temperature of the material [257]. However, since the thermal resistance of the whole membrane contributes less than 5% of total heat transfer resistance in the enthalpy core, assuming constant thermal conductivities introduces a negligible error in model calculations. The total heat transfer resistance of the composite membrane is therefore given by  𝑹 𝑯 =𝜹𝒎𝝀𝒎 (6.25) Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 121   6.3.3. Membrane Material The properties of the composite membrane material used in this study are summarized in Table 6.1. This is a commercially available membrane, dPoint Technologies Inc. MX4TM, and currently used in enthalpy exchangers for building ventilation [43].  Table 6.1.  Properties of membrane material sample Membrane Layer Material Description Thickness (µm)b Average Water Vapor Permeability (𝒎𝒐𝒍.𝒎𝒎𝟐𝒔𝑷𝒂)a Water Vapor Diffusivity (𝒎𝟐𝒔) a Thermal conductivity (𝑾𝒎𝑲) coating PU-PEO copolymer 1-3+ 1.8×10-11 3.3×10-13 0.44 substrate A hydrophobic PE-based microporous substrate 100-120+ 6.2×10-10 1.13×10-10 0.159 a These values are measured under a test condition of T =50◦C and Feed, and permeate side inlet activity of 0.5 and 0, respectively. b The values were averages assumed for the model.  6.3.4. Moisture Permeability Calculation Procedures Given the temperature and humidity on supply and exhaust sides, the total resistance and permeability of the composite membrane are determined as follows using the equations derived above. (1) Approximate the interface temperature using Eq. (6.21) (2) Initialize the vapor pressure at the membrane interface with a value between the feed and permeate side vapor pressures. (3) Calculate coating diffusivity and sorption values at average coating temperature through Equations F (1) to F (10) in Appendix F (4) Calculate moisture flux through coating using Eq. (6.4) and equate to the substrate flux.  (5) Calculate the interface vapor pressure from Eq. (6.11)  (6) Repeat steps (2) to (5) until the value of interface vapor pressure is converged.  6.4. MATHEMATICAL ENTHALPY EXCHANGER CORE MODEL A mathematical model was developed to predict the performance of a typical cross-flow membrane-based enthalpy exchanger core. This model links the variable membrane permeation properties and local transfer coefficients to the core performance.   Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 122  6.4.1. Geometry Due to their ease of manufacturing and installation, cross-flow parallel-plates air-to-air channels is the most widely used configuration of membrane-based enthalpy exchanger cores. Therefore, this configuration was modeled in this study.  Taking advantage of the repetitive structure of a fixed-plate enthalpy exchanger (as shown in Figure 1.2 Chapter 1), the basic unit modeled by mathematical core model is a single layer for the supply (fresh) air and one for the exhaust (outgoing indoor) air (Figure 6.2). Due to symmetry, the computational domain includes a membrane plate and two half volumes of supply and exhaust sides (separated by corrugated spacers). The problem becomes two-dimensional; a full core is merely a stack of these units.  Figure 6.2. Schematic of a pair of core layers separated by a membrane plate  in cross-flow arrangement used in the mathematical model  A lumped value represents the temperature and humidity ratio for each channel cross-section. These parameters vary simultaneously along the flow directions (x for supply outdoor air and y for exhaust air) and the corresponding cross directions (y for supply outdoor air and x for exhaust air). In the present work, both the temperature and the humidity at the supply air inlet are greater than those at the exhaust air inlet during the cooling mode (summer conditions), while the opposite is true during the heating mode (winter conditions). 6.4.2. Assumptions The assumptions for formulating the enthalpy core model are as follows: (1) Steady-state heat and mass transfer (2) No phase change occurs for either air stream 𝒙𝒚𝒛Supply Outdoor Air Exhaust Indoor AirTriangular Channel GeometryChapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 123  (3) Negligible heat conduction and vapor diffusion occur in the stream-wise directions, relative to bulk convection (Peclet number>>1). (4) Since the membranes are rather thin (~ 100μm), heat and mass transfer through the membrane is considered one-dimensional (in the thickness direction). (5) Heat and moisture transfer in the two air streams are two-dimensional (x and y directions) (6) Membrane surfaces are in dynamic equilibrium at the temperature and vapor pressure of the adjacent air. 6.4.3. Governing Equations Mass Conservation: Supply side:  𝒗𝒔𝒂𝝏𝝎𝒔𝒃𝝏𝒙+ 𝟐𝒌𝒔(𝝎𝒔𝒃 − 𝝎𝒔𝒎) = 𝟎 (6.26)  Exhaust side:  𝒗𝒆𝒂𝝏𝝎𝒆𝒃𝝏𝒚+ 𝟐𝒌𝒆(𝝎𝒆𝒃 − 𝝎𝒆𝒎) = 𝟎 (6.27)  Energy Balance: Supply side:  𝝆𝒔𝒗𝒔𝒂𝑪𝒑𝒔𝝏𝑻𝒔𝒃𝝏𝒙+ 𝟐𝒉𝒔(𝑻𝒔𝒃 − 𝑻𝒔𝒎) + 𝑱𝑪𝒑𝒗?̅?𝒎 = 𝟎 (6.28)  Exhaust side:  𝝆𝒆𝒗𝒆𝒂𝑪𝒑𝒆𝝏𝑻𝒆𝒃𝝏𝒚+ 𝟐𝒉𝒆(𝑻𝒆𝒃 − 𝑻𝒆𝒎) − 𝑱𝑪𝒑𝒗?̅?𝒎 = 𝟎 (6.29)  where 𝜔 is humidity ratio in the air streams (𝑘𝑔−𝑤𝑣𝑘𝑔−𝑑𝑟𝑦 𝑎𝑖𝑟), 𝑇 is temperature, 𝒗 is the mean air velocity inside the flow channels (m/s), ρ is dry air density, 𝐶𝑝 is the specific heat (𝑘𝐽 𝑘𝑔𝐾⁄ ), 𝑘 and ℎ are the convective mass transfer coefficient (𝑚 𝑠⁄ ) and convective heat transfer coefficient (𝑊𝑚2𝐾⁄ ), respectively, and 𝑎 is the triangular channel height as depicted in Figure 6.2. Boundary and Interface Conditions The changes of enthalpy along the x and y directions in the two air streams on supply and exhaust sides (Eq. (6.26) to (6.29)) are coupled together by heat and mass transfer through the membrane plate, governed by the following equations.   Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 124  Membrane surface on the supply side:  𝒉𝒔(𝑻𝒔𝒃 − 𝑻𝒔𝒎) = 𝒒𝑻 =𝟏𝑹𝑻𝑯 (𝑻𝒔𝒃 − 𝑻𝒆𝒃) (6.30)   𝝆𝒔𝒌𝒔(𝝎𝒔𝒃 − 𝝎𝒔𝒎) = 𝑱 =𝟏𝑹𝑻𝑴 (𝑪𝒔𝒃 − 𝑪𝒆𝒃) (6.31)  Membrane surface on the exhaust side:  −𝒉𝒆(𝑻𝒆𝒃 − 𝑻𝒆𝒎) = 𝒒𝑻 =𝟏𝑹𝑻𝑯 (𝑻𝒔𝒃 − 𝑻𝒆𝒃) (6.32)   −𝝆𝒆𝒌𝒆(𝝎𝒆𝒃 − 𝝎𝒆𝒎) = 𝑱 =𝟏𝑹𝑻𝑴 (𝑪𝒔𝒃 − 𝑪𝒆𝒃) (6.33)  where, 𝐶𝑠𝑏 = 𝜌𝜔 is water vapor concentration in the bulk air (𝑘𝑔−𝑤𝑣𝑚3), and 𝑹𝑻𝑯 and 𝑹𝑻𝑴 are the total heat and mass transfer resistances, respectively.   𝑹𝑻𝑯 =𝟏𝒉𝒔+ 𝑹 𝑯 +𝟏𝒉𝒆 (6.34)   𝑹𝑻𝑴 =𝟏𝒌𝒔+ 𝑹 𝑴 +𝟏𝒌𝒆 (6.35)  The boundary conditions are defined as Supply side:  𝑻𝒔𝒃| 𝒙=𝟎 = 𝑻𝒐𝒖𝒕𝒅𝒐𝒐𝒓 ,        𝝎𝒔𝒃| 𝒙=𝟎 = 𝝎𝒐𝒖𝒕𝒅𝒐𝒐𝒓 (6.36)  Exhaust side:  𝑻𝒆𝒃| 𝒚=𝟎 = 𝑻𝒊𝒏𝒅𝒐𝒐𝒓 ,        𝝎𝒆𝒃| 𝒚=𝟎 = 𝝎𝒊𝒏𝒅𝒐𝒐𝒓 (6.37)  The dimensionless coordinates, temperature, and humidity ratio are defined as  𝒙∗ =𝒙𝑾 (6.38)   𝒚∗ =𝒚𝑾 (6.39)   𝜽 =𝑻 − 𝑻𝒆,𝒊𝒏𝒃𝑻𝒔,𝒊𝒏𝒃 − 𝑻𝒆,𝒊𝒏𝒃 (6.40) Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 125    𝜴 =𝝎 − 𝝎𝒆,𝒊𝒏𝒃𝝎𝒔,𝒊𝒏𝒃 − 𝝎𝒆,𝒊𝒏𝒃 (6.41) 6.4.4. Air-side Heat and Mass Transfer Coefficients Zhang et al. [25] showed that the hydrodynamic, thermal, and concentration entry regions account for a large fraction of the total duct length (up to 30%) in plate-type enthalpy exchangers. Therefore, the Nusselt correlations for both thermally and hydrodynamically developing flow for non-circular ducts by Muzychka and Yovanocic [264] are used.  𝑵𝒖√𝑨(𝒁∗) =[    (𝑪𝟒𝒇(𝑷𝒓)√𝒁∗)𝒎+ ({𝑪𝟐𝑪𝟑 (𝒇𝑹𝒆√𝑨𝒁∗)𝟏𝟑⁄}𝟓+ {𝑪𝟏 (𝒇𝑹𝒆√𝑨𝟖√𝝅𝝐𝜞)}𝟓)𝒎𝟓⁄]    𝟏𝒎⁄ (6.42)  where constants 𝐶1 to 𝐶4 are used to describe boundary conditions (uniform wall flux) and Nu type (local), blending parameter, 𝑚, is defined as a linear function of Pr, duct geometry is defined by the aspect ratio, 𝝐, and shape parameter, Γ (𝜖 =𝑎𝑏 and Γ = −0.3 for an isosceles triangle when 𝑎 <𝑏), and the dimensionless length, 𝑍∗, defined by  𝒁∗ =𝒁𝑳√𝑨⁄𝑹𝒆√𝑨𝑷𝒓 (6.43)  where 𝐿√𝐴 is the characteristic length scale defined as the square root of the channel cross-sectional area. The local heat transfer coefficients are then calculated from the definition of the Nusselt number as 𝑵𝒖√𝑨(𝒁∗) =𝒉(𝒁∗)𝑳√𝑨𝝀𝒂𝒊𝒓⁄ . It is understood that the boundary conditions on membrane surfaces are neither uniform wall temperature (UWT) nor uniform wall flux (UWF), which are common approximations in heat transfer problems. Rather, boundary conditions are formed by the coupling between the supply and exhaust air streams. For cross-flow plate-type enthalpy exchangers, Zhang et al. [25] have shown that the boundary conditions lie between those under UWT and UWF. Therefore, the assumption of UWT in Eq. (6.42) is expected to introduce an error of less than 9% in approximation of the Nusselt number. The Chilton-Colburn analogy is used to estimate the convective mass transfer coefficient from the heat transfer coefficient 𝒉(𝒁∗)𝒌(𝒁∗)𝑪𝑷= 𝑳𝒆𝟐𝟑⁄  (6.44)  where 𝐿𝑒 is the Lewis number, which is about 0.85 for ventilation air at temperatures between 0-40ºC [67]. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 126  Fin effects of the corrugated aluminum spacers used to separate membrane layers in the studied geometry, representing plate-fin triangular channels of finite fin conductance, has been shown to significantly influence the fully developed Nusselt and Sherwood numbers in membrane channels of enthalpy exchangers [75], [76]. In fact, much smaller efficiencies of aluminum fins for moisture transfer compared to the heat transfer makes the validity of the analogy presented in Eq. (6.44) questionable. To address such fin effects, we have used a correction factor for constants 𝐶1 and 𝐶3, that represent the boundary conditions of Eq. (6.42), defined as 𝜂𝑓𝑖𝑛 =𝑁𝑢Ω𝑇𝑳√𝑨𝑁𝑢√𝐴𝑇 𝑫𝒉⁄ , where 𝑁𝑢√𝐴𝑇  represents the fully-developed Nusselt number predicted by Eq. (6.42) and 𝑁𝑢Ω𝑇  is the fully-developed Nusselt number taken from the tabulated data in Zhang [76] for fins of different thermal conductivities; an isothermal fin (infinitely conductive) and an adiabatic fin (non-conductive) are assumed for obtaining heat and mass transfer coefficients, respectively. This correction method approximates variations of local Nu numbers to within 5% of the data in [76] for a channel aspect ratio of 0.5 and UWT boundary conditions with different fin conductance parameters. 6.4.5. Solution Procedures The forward finite difference scheme is used for discretization of the differential equations on both sides of the membrane. An iterative procedure used to solve the coupled equations is as follows: (1) Initialize the humidity and temperature fields on the two sides of the membrane plate at inlet indoor and outdoor air conditions. (2) Calculate membrane surface humidity and temperatures through Eq. (6.30) to (6.33). (3) Calculate membrane permeation and heat transfer properties given these surface conditions. (4) Calculate humidity and temperature profiles of the bulk air streams (Eq. (6.26) to (6.29)) on the two surfaces of the membrane plate given surface values calculated from the previous step. (5) Repeat steps (2) to (4) until the values of humidity and temperature fields for the bulk air streams are converged. Numerical tests were conducted to determine the impact of grid size on the accuracy of the presented results. It was determined that 70 grids in each direction be adequate for the simulations (resulting in less than 0.1% difference from the case with 100 grids). 6.4.6. Enthalpy Exchanger Performance When the temperature and humidity fields in the exchanger are calculated, the sensible and latent effectiveness are accordingly calculated using mean outlet values assuming equal flow rates for supply and exhaust sides(i.e., a reasonable assumption for most real applications [74]).  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 127   𝜺𝑺 =(𝑻𝒔,𝒊𝒏𝒃 − 𝑻𝒔,𝒐𝒖𝒕𝒃 ) + (𝑻𝒆,𝒐𝒖𝒕𝒃 − 𝑻𝒆,𝒊𝒏𝒃 )𝟐(𝑻𝒔,𝒊𝒏𝒃 − 𝑻𝒆,𝒊𝒏𝒃 ) (6.45)   𝜺𝑳 =(𝝎𝒔,𝒊𝒏𝒃 − 𝝎𝒔,𝒐𝒖𝒕𝒃 ) + (𝝎𝒆,𝒐𝒖𝒕𝒃 − 𝝎𝒆,𝒊𝒏𝒃 )𝟐(𝝎𝒔,𝒊𝒏𝒃 − 𝝎𝒆,𝒊𝒏𝒃 ) (6.46)  The total performance of the energy exchanger is consequently defined as  𝜺𝑻 =(𝒉𝒔,𝒊𝒏𝒃 − 𝒉𝒔,𝒐𝒖𝒕𝒃 ) + (𝒉𝒆,𝒐𝒖𝒕𝒃 − 𝒉𝒆,𝒊𝒏𝒃 )𝟐(𝒉𝒔,𝒊𝒏𝒃 − 𝒉𝒆,𝒊𝒏𝒃 ) (6.47)  where ℎ is the enthalpy of humid air. 6.5.  RESULTS AND DISCUSSION 6.5.1. Moisture Permeation through Composite Membrane Composite membrane permeance for water vapor at various supply and exhaust side activities (i.e., the ratio of vapor pressure to saturation vapor pressure) are plotted in Figure 6.3. It can be observed that the membrane permeance is independently a function of supply and exhaust activities.  Figure 6.3. Membrane permeance at various supply and exhaust side activities at T = 35°C.  The impact of membrane orientation on the permeation through asymmetric composite membranes can also be realized from the asymmetry of contours about the 1:1 line (dashed line) in Figure 6.3. Membrane permeance is consistently higher when the dense coating layer is exposed to the feed side with higher humidity content. This difference becomes more substantial at higher feed side activities, lower permeate-to-feed activity ratios, and higher temperatures.  It will be shown in Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 128  section 6.5.6 that the membrane orientation will result in different performance variations of an enthalpy exchanger in cooling and heating modes.  Figure 6.4 shows the impact of operating temperature on membrane permeance at various levels of supply activity. Higher operating temperatures, on average, result in a moderate decrease in permeability, which is caused by the decreased sorption capacity of dense polymer dominating its diffusivity increase. However, at very low temperatures, such as 5ºC in Figure 6.4, it can be seen that permeability decreases significantly, especially at very high activities. This is attributed to the high sorption capacity of material at very low temperatures resulting in significant clustering and so a drop in diffusivity dominating the increased sorption at very low temperatures [93].  a) Exhaust activity 𝜙𝑒 = 0.1  b) Exhaust activity 𝜙𝑒 = 0.5 Figure 6.4. Effect of temperature on water vapor permeance at various supply side activities  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 129  6.5.2. Validation of Enthalpy Core Model The model results were verified by comparing the calculated effectiveness of a commercial-size core (see for Table 6.2 specifications) with the experimental performance measurements of the core tested under AHRI summer and winter test conditions (as specified in Table 6.3) at various operating flow rates.  Table 6.2.  Geometrical specifications of the enthalpy exchanger core tested in this study. Footprint (Dc×Wc) (mm×mm) 552×552 Height (Hc) (mm) 200 Membrane MX4TM Flow spacer Corrugated  Aluminum sheet Number of layers 72 Pitch (a) (mm) 2.6±0.1 Base (b) (mm) 7.4±0.1 Apex angle (α) (degree) 54±2  Table 6.3. AHRI test conditions. Parameter Cooling mode (summer) Heating mode (winter) Outdoor Air Indoor Air Outdoor Air Indoor Air Dry-bulb Temperature (◦C) 35 24 1.7 21 Wet-bulb temperature (◦C) 26 17 0.5 14.5 Relative Humidity (%) 50 50 78 50  The results of two sets of measurements of sensible and latent effectiveness for each mode of operation along with the model predictions are presented in Table 6.4. A summary of these results is plotted in Figure 6.5. Discrete symbols represent measured data, and solid and dashed lines represent calculated sensible and latent effectiveness, respectively. Black symbols show calculated effectiveness values from the difference in measured air parameters on the supply side while hollow symbols show those from the exhaust side differences. The maximum deviations are 6% for sensible effectiveness in cooling mode and 10.2% for latent effectiveness in heating mode, indicating that the model satisfactorily predicts effectiveness. The results of both measurements and the model predictions presented in Figure 6.5 suggest that sensible and latent effectiveness are both affected by weather conditions and are consistently higher for the heating mode. Correspondingly, the total effectiveness is also higher for the heating condition. This is due to the higher permeability of the membrane at lower temperatures (as was shown in Figure 6.4) and stronger heat and mass transfer coupling in the cooling mode, the latter due to much larger moisture fluxes through the membrane. This behavior is partly attributed to the material properties of the particular PU-PEO polymer membrane tested in this study. As was discussed in Chapter 4, it can be significantly different for another membrane with different Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 130  permeation properties, such as stronger temperature-dependency or increasing diffusivity with the moisture content of membrane. Koester et al. [85] discuss such variations of water vapor permeance through different membranes suitable for use in enthalpy exchangers.  a) Cooling mode  a) Heating mode Figure 6.5. Variations of enthalpy exchanger performance with air flow rate. The experimental measurements are shown by symbols, and the corresponding model predictions are shown by the faired curves.       Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 131  Table 6.4.  Modeling and experimental results of validation test enthalpy exchanger core.  Mode Experimental Model (coated up) supply exhaust  Q(𝑚3ℎ𝑟) 𝜺𝑺 𝜺𝑳 𝜺𝑻 Q(𝑚3ℎ𝑟) 𝜺𝑺 𝜺𝑳 𝜺𝑻 Q(𝑚3ℎ𝑟) 𝜺𝑺 𝜺𝑳 𝜺𝑻 Heating 264 79.22 61.20 70.42 254 72.91 62.20 66.83 259  76.96 62.52 71.72 401 73.09 55.35 65.26 390 68.99 55.75 63.54 395 71.84 54.71 65.62 531 69.40 50.11 61.57 518 66.59 52.21 60.53 524 67.85 48.93 60.99 661 67.31 46.60 59.15 641 64.52 49.11 58.91 651 64.46 44.30 57.14 801 65.60 42.62 57.03 780 63.01 46.80 56.90 791 61.20 40.13 53.55 Cooling 279 74.55 57.14 62.85 283 70.23 54.02 59.55 281 76.76 59.87 65.66 417 70.80 51.18 57.35 424 67.89 47.87 54.32 420 71.80 52.06 58.82 561 68.63 45.95 53.71 567 65.45 43.48 49.96 564 67.68 46.02 53.44 695 64.73 42.09 49.63 712 64.22 40.66 47.85 704 64.19 41.30 49.13 826 64.22 39.13 47.44 839 62.45 38.09 45.68 833 61.36 37.72 45.82  6.5.3. Effect of Variable Membrane Permeability The impact of variable permeability on effectiveness is illustrated in Figure 6.6 (a) and (b), for cooling and heating modes with constant operating temperature and variable outdoor relative humidity. Two scenarios are considered in the plot 1) variable membrane permeability, 2) a constant membrane permeability estimated using ideal laminate theory from individual measurements of coating and substrate permeability at 50oC and 50%RH test conditions.    Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 132    a) Cooling mode  b) Heating mode Figure 6.6. Variations of  enthalpy exchanger performance with outdoor air relative humidity; comparison of constant permeability model and composite membrane model with variable permeability  Assuming a constant permeability can result in deviations in effectiveness predictions of up to 15%. These deviations would lead to significant errors in predicting potential energy savings from ERV installation in buildings. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 133   a) Cooling mode (Toutdoor = 35°C)  b) Heating mode (Toutdoor = 1.7°C) Figure 6.7. Variations of moisture flux through membrane surface; comparison of constant permeability model (dashed curves) and composite membrane model with variable permeability (solid curves) at 50% outdoor relative humidity.  Figure 6.7 shows the differences in moisture flux prediction over the membrane surface for a constant permeability model (dashed lines) and the composite model (solid lines) during cooling and heating modes. 6.5.4. Effect of Operating Humidity and Temperatures In a theoretical study by Min et al. [54], the coupled heat and moisture transfer in a plate-type membrane-based enthalpy exchanger was investigated over a wide range of weather conditions. They have shown that depending on the operating conditions, heat and moisture may transfer either Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 134  in the same direction, or opposite directions, or even partially the same and partially opposite directions over the membrane surface. They further discuss that when the heat and moisture transfer in opposite directions, the enthalpy effectiveness loses its significance since the concept of enthalpy effectiveness is valid only in cases where heat and moisture transfer have the same directions. Similar results are also reported by Simonson and Besant for performance variations of an enthalpy wheel [55]. Therefore, the range of variations of outdoor air relative humidity and temperature in our study is limited to those cases where the heat and moisture transfer in the same direction across the entire membrane surface; from the supply outdoor air to exhaust indoor air during the cooling mode, and vice versa during the heating mode. Figure 6.8 shows the variation of enthalpy exchanger effectiveness with outdoor relative humidity at three different temperatures for cooling mode operation. Figure 6.9 is an equivalent plot for heating mode operation. Outdoor air temperature has minimal influence on effectiveness. In both heating and cooling modes, at lower relative humidities, higher operating temperatures result in slightly lower sensible and latent effectiveness while at higher relative humidities this trend is reversed.  Figure 6.8. Variations of  enthalpy exchanger performance with outdoor air state in cooling mode (flowrate = 544 m3/hr)  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 135   Figure 6.9. Variations of  enthalpy exchanger performance with outdoor air state in heating mode (flowrate = 544 m3/hr)  Unlike temperature, outdoor relative humidity has a larger influence on both sensible and latent effectiveness in the cooling mode. The latent effectiveness increases from 45% to 50% as the relative humidity increases from 30% to 90%. Sensible effectiveness decreases slightly from 68.4% to 67.7% with similar variations of relative humidity. This is attributed to the heat and mass transfer coupling effect due to the relatively large moisture flux through the membrane in cooling mode. Total effectiveness is correspondingly varied in this operating humidity range. At lower values of relative humidity, its variations are dictated by the decrease in sensible effectiveness while it approaches the latent effectiveness at higher relative humidity. On the other hand, under similar variations of relative humidity in the heating mode, sensible effectiveness remains nearly unchanged while latent effectiveness slightly increases from 46.5% to 48.4% at an operating temperature of 1.7oC. As a result, total effectiveness monotonically increases from 57.5% to 60.6%. The variations in effectiveness with temperature and relative humidity discussed above can be explained by the variations of membrane moisture transfer resistance predicted by the asymmetric composite membrane permeability model. Figure 6.10 shows an example of these variations in moisture transfer resistance of the membrane for cooling and heating modes with 30% outdoor air relative humidity. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 136    Figure 6.10. Contours of local membrane moisture transfer resistance, 𝑹 𝑴 (𝒔 𝒎⁄ ); solid and dashed lines indicate cooling (Toutdoor = 35°C) and heating (Toutdoor = 1.7°C) modes, respectively. (RHoutdoor = 30%)  Figure 6.11 shows an averaged value of moisture transfer resistance over the membrane plate surface at each operating condition.  Figure 6.11. Variations of average membrane moisture transfer resistance with outdoor air state; hollow and black symbols indicate cooling and heating conditions, respectively.  For higher supply side (outdoor) relative humidity at a fixed exhaust (indoor) RH (which is the case for both cooling and heating conditions), the membrane has lower resistance to moisture transfer resulting in an increase in latent effectiveness in the cooling mode. For the heating mode, this trend is reversed at a very high relative humidity of the supply side (RH>70%) which explains the nearly constant latent effectiveness of the core for higher humidity in this mode (see Figure 6.9). This is believed to be due to the significant clustering of water molecules in the membrane coating at lower temperatures (i.e., resulting in higher solubility (see Chapter 5 and Appendix F) and thus moisture content inside the polymer) lowering overall membrane permeability. Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 137  6.5.5. Membrane Surface Temperature Profiles Temperature profiles of the bulk air for supply (solid lines) and exhaust (dashed lines) sides of the membrane are plotted for both cooling and heating conditions in Figure 6.12. Since the membrane thermal resistance has little contribution to the overall heat transfer resistance inside the exchanger, it can be seen that these non-dimensionalized profiles are quite similar for both heating and cooling conditions although they have reverse directions. The temperature profiles on the membrane surface (shown in Figure 6.13) are, however, quite different between the cooling and heating modes. In the cooling mode, they are skewed due to the much larger moisture transfer across the membrane resulting in a much stronger coupling between heat and mass transfer. This is the cause of decreasing sensible effectiveness with increasing outdoor relative humidity in the cooling mode.  a) Cooling mode (Toutdoor = 35oC)  b) Heating mode (Toutdoor = 1.7oC) Figure 6.12. Contours of dimensionless temperature in bulk air; solid and dashed lines indicate supply and exhaust sides, respectively.  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 138   a) Cooling mode (Toutdoor = 35oC)  b) Heating mode (Toutdoor = 1.7oC) Figure 6.13. Contours of dimensionless membrane surface temperature; solid and dashed lines indicate supply and exhaust sides, respectively.  6.5.6. Effect of Membrane Orientation Figure 6.14(b) compares the latent effectiveness calculated for two different scenarios: (a) coated side of membrane exposed to the supplied outdoor air referred to as ‘Membrane-on-supply’, (b) coated side of membrane exposed to the exhausted indoor air referred to as ‘Membrane-on-exhaust’ (as shown in Figure 6.14(a)). Indoor air conditions in these scenarios are fixed according to the AHRI test conditions (see Table 6.3).  Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 139   a) Membrane configuration; (I) Membrane-on-supply, (II) Membrane-on-exhaust  b) latent effectiveness Figure 6.14. Membrane orientation effect at various outdoor air relative humidities; outdoor air temperatures are 35°C and 1.7°C for cooling and heating modes, respectively.  In the cooling mode, exposure of the membrane to the exhaust air (i.e., Membrane-on-exhaust scenario) results in slightly lower latent effectiveness of the core while it increases the latent effectiveness in the heating mode. The sensible effectiveness in both cases is almost independent of membrane orientation (See Figure 6.15). Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 140   a) Cooling mode (Toutdoor = 35oC)  b) Heating mode (Toutdoor = 1.7oC) Figure 6.15. Membrane orientation effect at various outdoor air relative humidities and a constant operating flowrate (544 m3/hr).  6.6. CONCLUSIONS The impact of operating conditions (temperature and relative humidity) on the performance of cross-flow membrane-based enthalpy exchangers was studied through material testing and exchanger core modeling. A generalized model for coupled heat and moisture transfer through asymmetric composite membranes used in the state-of-the-art enthalpy exchangers was developed. The model takes into account permeation properties of the dense polymeric coating layer, extracted from a limited Chapter 6 – Impact of operating conditions on the performance of enthalpy exchangers 141  number of kinetic sorption experiments, and the microstructure of the substrate layer, to predict variable membrane permeability in a wide range of operating conditions. It was shown that membrane permeability is a strong function of the relative humidity of the air streams on both sides of the membrane and a weaker function of operating air temperatures and membrane orientation.  A finite-difference heat and mass transfer model was developed to predict the system-level enthalpy exchanger performance.  This model takes into account the variable membrane permeability as a function of local operating humidity and temperature values on the membrane surfaces. The model was validated against experimental measurements on a commercial enthalpy exchanger. Depending on the mode of operation, membrane permeability variance (Figure 6.3) was shown to influence predicted performance of the exchanger core by up to 15% compared to the case with constant permeability (Figure 6.6). It is understood that the uncertainty in the estimation of material permeation properties from measured values (i.e., moisture solubility and diffusivity), could influence the performance predictions of the core model, particularly its latent effectiveness. However, such errors, which would lead to a maximum error of 30% in overall moisture permeability (maximum deviations in Figure 5.15) are likely to have negligible effects given that a nearly three-fold variation in moisture permeability of studied membrane resulted in only a 15% variation in overall latent effectiveness. Other conclusions from this study are:  In general, both sensible and latent effectiveness (and thus the total effectiveness) are stronger functions of operating relative humidity and weaker functions of the operating temperature and core orientation.  In the cooling mode, both sensible and latent effectiveness depend strongly on the outdoor air relative humidity. Sensible effectiveness decreases with increasing outdoor relative humidity while latent effectiveness increases. At RH values lower than 50%, total effectiveness is more closely aligned with sensible effectiveness while at higher RH values it lies closer to the latent effectiveness.  In the heating mode, due to the very low moisture transfer in the enthalpy exchanger, sensible effectiveness remains nearly constant. Latent effectiveness slightly increases with outdoor relative humidity and has a higher value compared to the cooling mode for outdoor relative humidity below 60%.  Relative to the baseline case of exposure to the outside air of the membrane coated surface, exposure of the membrane substrate results in slightly lower latent effectiveness of the core in the cooling mode while it has a more pronounced, beneficial effect on the latent effectiveness in the heating mode.   Operating air temperature appears to have minimal impact on the core performance in both heating and cooling modes.    142  Chapter 7 – SUMMARY OF CONCLUSIONS, CONTRIBUTIONS, AND RECOMMENDATIONS FOR FUTURE WORK  7.  7.1. OVERVIEW This chapter presents a summary of the results and conclusions of this dissertation and highlights the contributions and limitations of the current study. Finally, it provides recommendations for applying the results of this study in operation and control of membrane-based ERVs, as well as recommendations for future work.  7.2. CONCLUSIONS AND CONTRIBUTIONS Energy recovery systems are becoming a more important part of building engineering. These systems may be used in a wide range of climates and building applications. ERVs using water-vapor-selective polymeric membranes have great potential for saving energy while maintaining minimal contaminant crossover rates between the exhaust and fresh air streams. Current-generation ERV membranes typically consist of a polymeric microporous layer as the support for a very thin perm-selective dense polymer film in an asymmetric laminate configuration. Results of long-term field studies are not available due to the recent implementation of this technology. However, there are preliminary indications that performance might vary significantly with operating conditions or degrade with the extended operation, possibly as the result of exposure to air pollution, or other environmental stresses. This dissertation contributes to a fundamental understanding of the effects of environmental factors, including airborne particulate matter, relative humidity, and temperature, on the permeation properties of the membrane media and the performance of full ERV exchanger cores. In the material-level study, permeation properties of current-generation ERV membranes were studied experimentally and through modeling. The experimental work provides guidelines for future material selection in ERVs used for different applications and different environments. The modeling tools developed can quantify the impact of material properties and operating conditions on the membrane heat and mass transport properties with significantly reduced time and cost of the investigation. Core-level experimental and modeling studies were also conducted to complement the material-level research. The heat and mass transfer core model developed in this study is helpful in interpreting the membrane-level test results and provides a means for better estimation of the impacts of ERV installations on energy savings, indoor air quality, and fouling in building ventilation systems.   Chapter 7 –Conclusions and contributions 143  7.2.1. Fouling by Coarse Aerosol Particles In Chapter 2, a test facility developed for assessment of air-side particulate fouling in full enthalpy exchanger cores was described. An experimental test procedure comprising accelerated dust loading tests, deposition fraction measurements, and pre- and post-fouling performance evaluation was presented. Core-level fouling experiments using Arizona Road test dust (with a dispersed aerosol in size range of 0.3–10 μm) were conducted for two residential-size enthalpy exchanger cores. It was shown that the compact construction of these cores make them susceptible to accumulation of dust particles; deposition fractions were measured ranging from 5-20% for low to high operating air flowrates. Without appropriate filter protection on both sides of an exchanger core, dust accumulation equivalent to that of a few years of exposure in a heavily polluted environment was found to result in added pressure drop across the exchanger cores and a fan energy penalty up to 50%. Surprisingly, such levels of accumulation of dust particles on membrane surfaces showed minimal impact on the sensible and latent effectiveness of the enthalpy cores. This is an important result that was first introduced in this Ph.D. study. With regard to sensible heat transfer, the main resistance is on the air side, and the membrane contributes to less than 5% of total heat transfer resistance. Dust deposits, having much higher conductivity than air, have minimal influence on this resistance. The fact that dust deposits do not affect the latent effectiveness is attributed to their highly porous structure which includes large discontinuities, offering minimal moisture transfer resistance. It is also postulated that the slight increase in sensible and latent effectiveness parameters of the cores is the consequence of increased air-side heat and mass transfer coefficients in partially restricted flow passages. 7.2.2. Fouling by Aerosol nanoparticles The results described in Chapter 2 led to the hypothesis that ERV membranes would be affected more by ultrafine particles that are comparable to the size of pores in the membrane substrate.  In the second step of the fouling study, presented in Chapter 3, the impact of fouling with aerosol nanoparticles (~100nm) on the performance of membrane transport media was investigated. The changes to physical properties of membrane transport media used in commercial enthalpy exchanger cores were characterized to develop an understanding of potential air-side particulate fouling mechanisms and the resulting performance degradation during the lifetime of the membrane. This chapter first described a new experimental apparatus developed for conducting accelerated material loading experiments under various operating conditions similar to those an enthalpy exchanger core might experience in the field. Samples of three different commercial membrane media were loaded with two types of aerosols; hygroscopic NaCl, and non-hygroscopic spark-generated graphite (SGG). Relative humidity and the orientation of asymmetric composite membranes were found to play a significant role in determining the water vapor permeance degradation of membrane samples. The only condition leading to a significant vapor permeance reduction was when membrane samples loaded with hygroscopic particles on the ‘uncoated’ side were exposed to an elevated humidity (RH>70%) and subsequent surface condensation. Under these conditions, the vapor permeance declined by up to 16%. Membranes loaded with SGG particles, or salt particles on the ‘coated’ side, did not show a significant flux decline under similar Chapter 7 –Conclusions and contributions 144  wet loading conditions. Characterization of the microporous structure of substrate layers in these membrane samples using SEM and utilization of the dusty gas model (DGM) verified that the observed permeance degradation is the result of pore size and effective surface porosity reduction (pore narrowing) in substrate layers, proportional to the fouling degree. It was also found that cleaning of fouled samples by a simple wash in distilled water can partially restore their permeance. Further permeance recovery, back to nearly the pre-exposure value, was achieved through the ultrasonic washing of fouled membrane samples in a distilled water bath. The reversibility of the fouled membrane permeance variation, along with the porosity analysis, implies that re-crystallization of salt ions, entrained close to the pores of membrane substrate in aqueous form, is a potential explanation for the mechanism causing pore narrowing of membrane substrate.  Based on the findings of the experimental investigations in Chapters 2 and 3, a number of general recommendations to control and minimize airborne particulate fouling and its adverse effects on performance of membrane-based ERVs, including filtration requirements, ERV installation guidelines, ventilation system operation control, and cleaning schedules were discussed. 7.2.3. CO2 Crossover The second goal of this study was to understand the effects of in-service operating conditions on the performance of membrane-based ERVs. This was achieved through a multi-stage investigation of the effects of relative humidity and temperature on the permeation properties of membrane media (i.e., moisture permeability and selectivity over indoor contaminants) and subsequently on the performance of enthalpy exchangers (i.e., sensible and latent effectiveness) in chapters 4 to 6.  In a first step, presented in Chapter 4, a systematic experimental study of the effects of relative humidity and temperature on the transport of water vapor and CO2 (as a surrogate for gas-phase indoor air pollutants to assess membrane selectivity) was conducted for current-generation composite membranes. A large number of standard commercial film-forming polymers were reviewed to determine their potential for use as the selective coating of membrane media in ERV exchanger cores. The choice of materials studied was narrowed to four highly water vapor permeable polymers of two major types; glassy (SPEEK and Cellulose Acetate) and rubbery (PEBAX®1074 and PERMAXTM 230). A new experimental apparatus and methods developed for determining intrinsic material properties during simultaneous permeation of water vapor and CO2 were introduced. Permeation behavior of the dense polymers was found to be strongly material-dependent, and influenced by the polymer state – glassy vs. rubbery (i.e., whether it is below or above its glass transition temperature). In general, rubbery polymer films showed higher water vapor permeability, but lower selectivity for water vapor over CO2 compared to the glassy samples over a wide range of operating conditions. Nevertheless, the CO2 permeability in both types of polymer membranes ranged from 6 to 200 Barrer which is up to 10,000 times lower than water vapor permeability through these samples. This is sufficiently low for most practical applications in HVAC design (typical selectivity of paper-based media used in the incumbent ERV exchanger cores ranges from 2 to 6). Chapter 7 –Conclusions and contributions 145  The combination of high water vapor permeability and extremely high selectivity levels in polymeric membranes make them interesting candidates for a wide range of ERV applications. Such selectivity levels of polymer membranes would result in CO2 crossover rates of less than 0.5% in ERV exchanger cores. It should be noted that in addition to the membrane material selectivity, contaminant crossover through an ERV exchanger core might also be influenced by exchanger core leakages and manufacturing defects. However, these material level testing could provide some guidelines for future material selections in different applications of membrane-based ERVs with varying levels of effectiveness and contaminant crossover requirements. 7.2.4. Material-level Studies of Water Diffusion and Sorption in Membranes For various polymeric membranes studied in this work, it was shown that water vapor permeability could vary up to about an order of magnitude depending on the operating temperature and the relative humidity on both feed and permeate sides of the membrane, as well as membrane orientation in asymmetric composite membranes. Such variable permeation properties of membranes lead to significant changes in the performance of an ERV exchanger core, particularly in latent effectiveness as the membrane contributes a large fraction of the overall moisture transfer resistance. A full experimental evaluation of these variations, even at a material-level, would be practically impossible as a large number of experiments would be required to cover the range of operating conditions and installation configurations these systems might experience in the field, with each such experiment requiring hours to reach steady-state conditions. A fundamental understanding of the influence of these variable parameters on the performance of enthalpy exchangers, therefore, requires modeling tools instead. Such predictive models require knowledge of the permeation properties of dense coating polymers and morphology of the microporous substrate layers. In Chapter 5, transient gravimetric sorption tests were investigated as a potential method to fully characterize moisture permeation properties (including concentration-dependent diffusion coefficients and sorption isotherms) of dense polymer films from a limited number of tests. This chapter focused on the two rubbery polymer samples previously studied in Chapter 4 (PEBAX® 1074 and PERMAXTM 230). The water vapor sorption equilibrium and water transport kinetics were studied in these polymers at various temperatures (5 to 55ºC), relative humidity (0-90%), and film thicknesses (38 - 240µm). Deviations from normal Fickian behavior were observed in the sorption/desorption curves for both copolymers. Nonetheless, it was shown that equilibrium diffusion coefficients could be determined from the early stages of desorption curves, or the early stages of sorption curves of sufficiently thick films. These methods were successfully validated against experimental data. Permeability values estimated using extracted diffusion coefficients and sorption isotherms in the solution-diffusion model showed reasonable agreement with the experimental measurements of steady-state permeability for free-standing films. This information is critical when attempting to model the transport properties and performance of both free-standing films and composite membranes from kinetic sorption measurements of bulk material samples. Chapter 7 –Conclusions and contributions 146  7.2.5. A Comprehensive Model of Water Vapor Permeability in Asymmetric Composite Membranes In the first part of Chapter 6, a generalized model for coupled heat and moisture transfer through current-generation asymmetric composite membranes used in enthalpy exchangers was developed. This model takes into account both substrate and coating contributions with respect to local conditions of the adjacent air streams and predicts variable membrane permeability in a wide range of operating conditions. A fundamental understanding of the interactions between membrane coating and substrate layers under various operating conditions and installation configurations was enabled using model predictions. It was shown that membrane permeability is a strong function of the relative humidity of the air streams on both sides of the membrane and a weaker function of operating air temperatures and membrane orientation. 7.2.6. A Full ERV Core Model Including Variable Membrane Properties In the last step of this work, a theoretical heat and mass transfer model was developed for fixed-plate enthalpy exchanger cores to interpret the significance of membrane-level variations in terms of core-level performance. The composite membrane permeability model was coupled with a finite-difference model of the conjugate heat and mass transfer in full cross-flow enthalpy exchanger cores. The model predictions were validated against experimental data of a commercial-scale enthalpy exchanger core. The model was then used to predict the influence of outdoor air parameters (temperature, humidity) on an enthalpy exchanger and the predictions were compared against a baseline case assuming constant membrane permeability. It was shown that such assumption could result in typical deviations in effectiveness predictions by up to 15%. Depending on the mode of operation, outdoor air relative humidity can increase or decrease the effectiveness of enthalpy exchangers by up to 12%. In contrast, outdoor air temperature appeared to have only a minimal influence on effectiveness parameters. This modeling tool, which is capable of capturing the full range of membrane media properties, is new and has not been reported elsewhere in the literature. 7.3. RECOMMENDATIONS FOR FUTURE WORK 7.3.1. Field Investigation of Fouling An important gap in the literature related to ERV systems is a shortage of available field data for comparison to accelerated laboratory test results. This study showed that the membrane performance was degraded as a result of direct exposure to hygroscopic particles and humid operating conditions. Further work is needed to determine whether the damage threshold is within the range of practical environmental exposures. Field investigation of fouling in membrane-based ERVs in various climates with airborne particles of different chemistry would be particularly useful to answer this question. Extra caution is required for field investigations of fouling problems as the time-scale for these studies can range from a few months to several years. ERV exchanger core performance in these time frames may also be influenced by other phenomena such as material degradation issues which could complicate field investigations of the fouling problem. Chapter 7 –Conclusions and contributions 147  Additional control enthalpy exchanger cores with high-efficiency filter protection may need to be considered in these studies.  7.3.2. Fouling Control and Mitigation Measures It was shown that membrane-based ERVs could in many conditions tolerate high levels of fouling with minimal change in their sensible and latent effectiveness parameters. This has important implications regarding filtration requirements for these systems. Common filtration on the supply air streams of ventilation systems is believed to be adequate for protecting ERV exchanger cores. However, additional filtration on the exhaust air stream may be required to ameliorate the added core pressure drop associated with dust loading, as well as potential fouling issues under humid conditions. Future studies should investigate trade-offs between energy savings from ERV installations and the added energy requirements of improved filtration systems. The size-resolved particle deposition fractions of enthalpy exchanger cores presented in Chapter 2 can be used to predict fouling rates of these cores for various residential and commercial applications. Combined with indoor aerosol transport models of HVAC systems, they can be used to estimate filter changing and cleaning schedules for enthalpy cores, energy implications of core fouling, and IAQ impacts associated with deposited particles. The case study of fouling by environmental tobacco smoke suggests that fouling could be detrimental to the performance of a membrane when exhaust airstreams include condensable VOCs and liquid-containing aerosol particles. Some preliminary experiments also reveal that heavy exposure to oils (e.g., cooking oils in kitchen exhausts) causes a marked decrease in water vapor transport. Polymeric membranes can withstand washing for performance recovery if fouling is reversible. Research is needed to investigate the effectiveness of filtration and different cleaning measures in controlling and reversing the extreme fouling in these cases. 7.3.3. Membrane Longevity and Degradation Mechanisms The results of membrane fouling investigations presented in chapter 3 showed a maximum flux decline of about 16% for very high levels of areal loading density (~10gm-2) of hygroscopic particles on uncoated membrane surfaces (equivalent to several years of operation in a highly polluted environment). The overall impact of such fouling levels on ERV exchanger core performance would be much lower due to the contribution of air-side mass transfer resistances that remain nearly unchanged. Preliminary results for two cores obtained from the field showed a 25% latent performance drop for an ERV core operating for nearly three years in a commercial building on Vancouver’s east side, while another similar core which was operating for the same amount of time in a residential building on Vancouver’s west side did not show a significant performance drop. Although particulate fouling could be partially responsible for such performance degradation, especially in commercial buildings with high levels of air pollutants, it cannot be entirely responsible for such a high level of decline in latent effectiveness. Further research is required to understand the sources of these performance degradations. Material degradation mechanisms resulted from daily, and seasonal humidity and temperature cycling, as well as degradations due to environmental stresses, oxidation mechanisms or other chemical reactions, are potential areas of investigation. Chapter 7 –Conclusions and contributions 148  7.3.4. Contaminant Transport in Membrane-based ERVs Although it was shown in this study that composite membranes using dense selective coating layers can minimize crossover rates of indoor gaseous contaminants such as CO2, caution must be taken in generalizing this conclusion to other indoor air contaminants. In particular, for applications where indoor contaminants include condensable vapors such as volatile organic compounds (VOCs) with high solubility in polymeric membranes. Zhang et al. [31] measured the permeability of water vapor and several VOCs through membranes made of different materials. They found selectivity values in the range of 100–400. While these selectivity levels are still adequate for most building applications, they may become important in cases with either indoor sources of high emission rates or very low acceptable threshold concentrations. More importantly, recent studies are indicating that permeation rates of VOCs through polymeric membranes, particularly glassy polymers, may be significantly influenced by the polymer moisture content. Further work should investigate the effects of relative humidity and temperature on the permeation of other indoor contaminant species, in particular, odors and VOCs with low threshold concentrations such as formaldehyde, benzene, and toluene. 7.3.5. Indoor Air Quality-Energy Trade-offs Contaminant crossover in ERVs, if significant, can be mitigated by increasing the ventilation flow to maintain specified indoor air quality requirements. However, this increases the energy requirements for air conditioning and reduces the net energy saving benefits of an ERV installation. Modeling tools developed in this work can be used for conducting IAQ-energy trade-offs to determine the circumstances where crossover can be significant. A detailed energy efficiency analysis would consider the trade-off based on the performance of the ERV exchanger, the crossover, the mechanical system, and outdoor climate conditions over the year; the financial trade-off is based on local utility costs.  7.3.6. Moisture Permeation through Asymmetric Composite Membranes The transient method proposed in Chapter 5 for evaluation of equilibrium diffusion coefficients in rubbery block copolymers may apply to other types of polymers (e.g., glassy ones) with strong non-Fickian sorption behavior. A future study should validate this hypothesis by comparing moisture diffusion properties of such measurements with those of steady-state permeation measurements. The proposed transient method for evaluating the moisture permeability of the dense layer in composite membranes is validated in the range of temperature and humidity studied in this dissertation. Core level performance is also validated for AHRAI 1060 summer and winter test conditions. More research is required to investigate the validity of this transient material testing and subsequent modeling approach for extended temperature and humidity conditions. In particular, situations where moisture can condense on membrane surfaces (e.g., sub-zero temperatures or extremely humid conditions) need further investigation. The composite membrane modeling framework introduced in chapter 6 could allow for deconvolution of the individual moisture transport resistances of coating and substrate layers in a Chapter 7 –Conclusions and contributions 149  composite membrane, thus enabling the optimization of its geometry under certain operating conditions. This model involves some simplifying assumptions, including the negligible restrictive influence of the substrate on the diffusion through the dense coating layer, and negligible moisture transport by the solution-diffusion mechanism through the substrate layer. A future study should validate these assumptions, particularly for extending the model application to new generation thin film composite membranes (TFC) with coating layers as thin as 100nm. 7.3.7. Heat and Moisture Transfer Modeling in ERV Cores The heat and moisture transfer model of enthalpy exchanger cores developed in this study employs a generalized model of composite membrane permeability, as well as general Nusselt correlations used for air-side heat and mass transfer resistance estimations in both thermally and hydrodynamically developing flow for non-circular ducts. Therefore, it allows for a parametric study of core geometry and material properties with the aim of optimizing core performance.  This model can also be incorporated into building energy simulation packages, providing a means for evaluation of the actual energy savings potential of such energy recovery devices in building ventilation systems. The current core model is set up for a cross-flow arrangement. This could be relatively easily converted to counter- and co-flow arrangements. 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