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On the development of a method for continuous fractionation of non-Brownian particles in a viscoplastic… Shanb Ghazani, Mohammad 2020

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On the Development of a Method forContinuous Fractionation ofnon-Brownian Particles in aViscoplastic FluidbyMohammad Shanb GhazaniA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Chemical and Biological Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)January 2020c© Mohammad Shanb Ghazani, 2020The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the dis-sertation entitled:On the development of a method for continuous fractionation ofnon-Brownian particles in a viscoplastic fluidsubmitted by Mohammad Shanb Ghazani in partial fulfillment of therequirements for the degree of Doctor of Philosophy in Chemical andBiological EngineeringExamining Committee:D. Mark Martinez, Chemical and Biological EngineeringSupervisorJames A. Olson, Mechanical EngineeringCo-supervisorIan Frigaard, Mechanical Engineering, MathematicsSupervisory Committee MemberHeather Trajano, Chemical and Biological EngineeringSupervisory Committee MemberScott Renneckar, ForestryUniversity ExaminerKevin Smith, Chemical and Biological EngineeringUniversity ExaminerAnders Rasmuson, Chalmers University of TechnologyExternal ExamineriiAbstractThis study focuses on the mechanical fractionation of non-Brownian parti-cles in layered yield stress fluids. We extend a novel principle outlined ina batchwise technique- which works based upon the difference in startingcriteria for motion in a weak gel- and create a continuous separation in anannular gap undergoing the spiral Poiseuille flow. Experimental equipmentis designed, constructed and operated to evaluate -continuously- the afore-mentioned fractionation idea. This work is presented in three different, yetcomplementary studies. In the first study, we performed a series of batch-wise tests, in a centrifuge, to develop criteria for motion of the individualclasses of particles of both monodisperse and bidisperse suspensions in lay-ered fluids, and to determine the stability of this multilayer fluid undergoingcentrifugation. We also examined the usefulness of this separation techniqueon three different suspensions related to the bio-product industry. In thesecond part, the design challenges of the continuous device were elaboratedand the essential design elements were addressed. Next, the fully developedflow field inside the fractionator was analyzed and shown that not all theoperating conditions result in stable operation. We found that there is asubset of all potential operating conditions in which this methodology willwork and this critically depends upon rheology and radii of the multilayerfluid. We summarized our findings into a number of qualitative ”rules ofthumb” to run the device. In the last part of the work, we extended thework to a continuous methodology and demonstrated particle fractionationusing both ideal and industrial particle suspensions. To benchmark ourcalibration curves, we examined and measured the critical force to initiatethe motion for (monodisperse) spherical and fibre-shape particle suspensionsand found that this critical force presents a similar trend to the batchwisetest but at a lower threshold. A similar finding was found in the second testwhere we examined the separation of MFC. We argue that this is an an-ticipated result as the two geometries are in different stress states. Despitethis, we were able to achieve a separation at the same trend as the batchwisemethodology.iiiLay SummaryThe focus of this study is the development of a methodology to mechanicallyseparate or sort particles into different size classes, however, the industrialmotivation is to continuously separate microfibre particles. In this work, weextend a batchwise principle and create a continuous separation method.This principle works by suspending different classes of particles in a gel tohold the particles and then subjecting these to a prescribed centrifugal forceto initiate motion in only one class of particles. From a series of batch-wise tests, we found that it is more efficient to use multiple fluids insteadof one fluid. Maintaining stable multilayer flow inside the device was themain scientific problem which we tried to address through an analytical andexperimental study. In the last part, we designed the continuous prototypeand successfully demonstrated a continuous separation with performancesimilar to that achieved in the batchwise tests.ivPrefaceThis thesis is an unpublished original work by Mohammad Shanb Ghazanihereafter referred to as the “author”. This research project was proposedby Dr. Mark Martinez and Dr. James Olson and the research presented inthis work was performed by the author. The author designed, constructedand operated the experimental equipment necessary to collect data in thecontinuous part of the work. The experimental procedures were designed bythe author and performed by or under supervision of the author.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Micro Fibrillated Cellulose (MFC) . . . . . . . . . . . . . . . 32.1.1 Production and Characterization . . . . . . . . . . . . 52.1.2 Fractionation . . . . . . . . . . . . . . . . . . . . . . . 92.1.3 State of MFC Suspension . . . . . . . . . . . . . . . . 112.2 Fractionation in Microfluidics . . . . . . . . . . . . . . . . . . 122.3 Particle Motion in Newtonian Fluids . . . . . . . . . . . . . 152.4 Yield Stress Fluids . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Particle Motion in Yield Stress Fluids . . . . . . . . . . . . . 172.6 Madani’s Fractionation Method . . . . . . . . . . . . . . . . 212.7 Industrially Available Centrifugal Separators . . . . . . . . . 222.8 Hydrodynamic Instabilities and Entry Length . . . . . . . . 252.9 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28vi2.10 Literature Summary and motivation . . . . . . . . . . . . . . 282.11 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Batchwise Separation . . . . . . . . . . . . . . . . . . . . . . . 323.1 Feasibility of MFC Fractionation . . . . . . . . . . . . . . . . 323.1.1 Material and Method . . . . . . . . . . . . . . . . . . 323.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Extending the Original Idea Using Multilayer Fluids . . . . 403.2.1 Establishing Stable Layered Fluids . . . . . . . . . . 433.2.2 Establishing a Separation in Layered Fluids . . . . . 453.3 Batchwise Fractionation in Multilayer Fluids . . . . . . . . . 473.3.1 Waste Stream Recovery . . . . . . . . . . . . . . . . . 493.3.2 Fractionation of NBSK-MFC . . . . . . . . . . . . . . 513.3.3 Carboxymethylated Cellulose . . . . . . . . . . . . . . 583.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604 Process and Mechanical Design of Continuous Device . . 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2 Essential Elements of the Design . . . . . . . . . . . . . . . . 644.3 Design Challenges . . . . . . . . . . . . . . . . . . . . . . . . 664.4 Key Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 664.5 Device Description . . . . . . . . . . . . . . . . . . . . . . . 704.6 Flow Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Fully Developed Flow in Continuous Device . . . . . . . . 725.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2 Fully Developed Problem: Spiral Poiseuille Flow in Annulus 735.3 Method of Solution . . . . . . . . . . . . . . . . . . . . . . . 775.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796 Fractionation in Continuous Device . . . . . . . . . . . . . . 806.1 Material and Method . . . . . . . . . . . . . . . . . . . . . . 806.2 Idealized Separation . . . . . . . . . . . . . . . . . . . . . . . 816.2.1 Mono-dispersed . . . . . . . . . . . . . . . . . . . . . 826.2.2 Bi-dispersed . . . . . . . . . . . . . . . . . . . . . . . 826.2.3 Nylon Fibres . . . . . . . . . . . . . . . . . . . . . . . 846.3 Continuous Fractionation of MFC . . . . . . . . . . . . . . . 856.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86vii7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.1 Limitations and Future Work . . . . . . . . . . . . . . . . . . 91Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93AppendicesA Design Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.1 Fluid Entrance . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.1.1 Splitter or Separator . . . . . . . . . . . . . . . . . . 109A.1.2 Separating Zone . . . . . . . . . . . . . . . . . . . . . 109A.1.3 Sealing . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.1.4 Driver . . . . . . . . . . . . . . . . . . . . . . . . . . . 111A.2 Device Description . . . . . . . . . . . . . . . . . . . . . . . 113B Method of Solution for BVP . . . . . . . . . . . . . . . . . . . 118C Device Characterization . . . . . . . . . . . . . . . . . . . . . . 119C.1 Material and Method . . . . . . . . . . . . . . . . . . . . . . 119C.2 Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . 119C.3 Dye test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122C.3.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . 122C.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 123C.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124D Operations Manual . . . . . . . . . . . . . . . . . . . . . . . . . 126D.1 Start-up and Sample Preparation . . . . . . . . . . . . . . . 126D.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . 127viiiList of Tables2.1 Comparison between active and passive separation methods . 154.1 Fluid and geometrical properties . . . . . . . . . . . . . . . . 696.1 Particles tested in the fractionator . . . . . . . . . . . . . . . 80ixList of Figures2.1 Units currently exist for fractionation purposes . . . . . . . . 42.2 Images of MFC . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Fibre components . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 SEM images of secondary layer of fibre . . . . . . . . . . . . . 72.5 SEM images of mechanically refined fibre . . . . . . . . . . . 82.6 Energy consumption of MFC production . . . . . . . . . . . . 92.7 MFC characterization with permeable fractionation . . . . . . 102.8 Particle sorting system using pinched flow . . . . . . . . . . . 132.9 Separation mechanism using gravity and hydrodynamic fo-cusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.10 Speed contours of two particles . . . . . . . . . . . . . . . . . 182.11 Speed colourmap and yield surfaces . . . . . . . . . . . . . . 192.12 Geometrical aspect ratio and orientation of a rectangular par-ticle in 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.13 A demonstration of the fractionation of a bidispersed suspen-sion of cylindrical particles . . . . . . . . . . . . . . . . . . . . 222.14 An illustration of the batchwise separation methodology ad-vanced by Madani . . . . . . . . . . . . . . . . . . . . . . . . 232.15 Proposed continuous device . . . . . . . . . . . . . . . . . . . 242.16 Sketch of an annular centrifugal contactor . . . . . . . . . . . 252.17 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 293.1 An example of the flowcurve data for 0.16% Carbopol solution. 343.2 MFC sedimentation graph . . . . . . . . . . . . . . . . . . . . 363.3 Bacthwise separation of BEKP-MFC . . . . . . . . . . . . . 373.4 Cumulative mass yield of BEKP-MFC . . . . . . . . . . . . . 383.5 A comparison between size and shape of original and frac-tionated BEKP-MFC . . . . . . . . . . . . . . . . . . . . . . . 393.6 Comparison between size distribution of reject and accept offractionated BEKP-MFC . . . . . . . . . . . . . . . . . . . . 403.7 Highlights of Madani’s concept for fractionation . . . . . . . 41x3.8 Extensions to Madani’s original separation concept . . . . . . 423.9 Schematic of two different possible configurations of layeredfluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.10 A demonstration of density unstable double layered fluid . . . 453.11 Experimental stability map . . . . . . . . . . . . . . . . . . . 463.12 A representative example of a separation in layered fluid andcritical force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.13 A demonstration of the separation of three different size spher-ical particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.14 Schematic of the process was used to fractionate nylon fibressequentially. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.15 Particle size distribution of nylon particles . . . . . . . . . . . 513.16 SEM images of waste stream . . . . . . . . . . . . . . . . . . 523.17 Illustration of typical fibre size distributions from the fibrequality analyzer (FQA) . . . . . . . . . . . . . . . . . . . . . 523.18 Schematic of the procedure used to separate sands and debris 533.19 Optical images of the waste pulp after fractionation. . . . . . 533.20 Characterization of NBSK-MFC . . . . . . . . . . . . . . . . 543.21 Batchwise fractionation results of NBSK-MFC . . . . . . . . 553.22 SEM images of NBSK-MFC before and after fractionation . . 563.23 Changes in the tensile strength of MFC reinforced compositehandsheets at different percentage . . . . . . . . . . . . . . . 573.24 Characterization of 1000 kWh/t refined fibres . . . . . . . . 583.25 Optical images of CMC . . . . . . . . . . . . . . . . . . . . . 593.26 A schematic of the procedure used to fractionate CMC particles 593.27 Particle size distribution of CMC . . . . . . . . . . . . . . . . 603.28 Optical images of CMC . . . . . . . . . . . . . . . . . . . . . 614.1 Split-flow lateral-transport thin (SPLITT) separation . . . . . 644.2 An overvirew of continuous device design . . . . . . . . . . . 654.3 Interface position at different flow-rate ratio . . . . . . . . . 684.4 Entrance length inside a pipe for Newtonian and yield stressfluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.5 A schematic of the flow loop . . . . . . . . . . . . . . . . . . . 705.1 A cross-section view of the fractionator . . . . . . . . . . . . . 735.2 Fully developed flow field and stability map . . . . . . . . . . 786.1 The ratio of the number of particles retained at the inner fluidto the total number of particles . . . . . . . . . . . . . . . . . 83xi6.2 Spherical particle fractionation in the continuous device . . . 846.3 Calibration curve of different size nylon fibres in the continu-ous device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.4 Particle size distribution and volume weighted mean diameterof BEKP-MFC fractionated in the continuous device. . . . . . 866.5 Fractionation results of BEKP-MFC suspension . . . . . . . . 87A.1 Entrance ammsembly of device . . . . . . . . . . . . . . . . . 110A.2 Bottom and top splitters . . . . . . . . . . . . . . . . . . . . . 110A.3 Seal, housing and shaft assembly of a typical Turcon seal . . 111A.4 Displacement and von Mises stress on the shaft under designcases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112A.5 Section view of the fractionator . . . . . . . . . . . . . . . . . 113A.6 Engineering drawing of the fractionator . . . . . . . . . . . . 114A.7 Fractionator, driver and support structure . . . . . . . . . . . 115A.8 A schematic of the experimental set-up loop . . . . . . . . . . 116A.9 Experimental setup in the lab . . . . . . . . . . . . . . . . . . 116A.10 Piping and instrumentation diagram (P & ID) of the experi-mental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 117C.1 Flowrates labelling within the device . . . . . . . . . . . . . . 120C.2 Pressure difference between inner fluid (Pi) and Accept (Pa) . 121C.3 Scetch of the experimental setup in a confocal microscopy . . 122C.4 Intensity concentration calibration for LIF test . . . . . . . . 123C.5 Flowrate and concentration ratio of accept and inner flowwith respect to the outer flow . . . . . . . . . . . . . . . . . . 125xiiNomenclatureAcronymsCNF Cellulose nanofibreMFC Micro fibrillated celluloseRCF Relative centrifugal forceSEM Scanning electron microscopeTEM Transmission electron microscopeGreek Symbolsχ Particle aspect ratioγ˙ Shear rate S−1κ Annulus radius ratioµ Dynamic viscosity Pa · sω Rotational speed rad/sρ Density kg/m3τ Deviatoric stress tensor Paτy Yield stress PaRoman SymbolsA Area m2B Bingham numberC ConcentrationCD Drag coefficientxiiiD Diameter mF Force NG Pressure drop per unit length Pa/mg Gravity m2/sK Consistencyl Particle width mm Mass kgN Crowding numbern Power-law indexQ Volumetric flowrate m3/sR Radius mr Radial position mRe Reynolds numberu Velocity PaV Volume m3w Fibre coarseness kg/mSubscripts⊥ Perpendicularθ Tangential directiona Acceptcp Carbopolm Masso Originalr Radial directionxivv Volumetetricw Length-weightedz Axial directionxvAcknowledgementsMany individuals have contributed to this research and their assistance isgratefully acknowledged. I would like to express my sincere gratitude to mysupervisors Dr. Mark Martinez and Dr. James Olson for all their supportand patience during the course of this project. I am immensely gratefulto you both. In addition I would like to thank Ronald Lai at Akzonobeland Dr. Braz Demuner at Suzano, Brazil, who provided us with MFC. Mysincere thanks to all of the undergraduate, research engineers and visitingscientists who worked with me on this project.Eka Chemicals and the National Sciences and Engineering ResearchCouncil of Canada (NSERC) are thanked for their financial support.The staff and students at the Pulp and Paper Centre (PPC) have beensupportive throughout this project. Special thanks to George Soong for hishelp and devotion to myself and the students at PPC. I would also like tothank my friends and research colleagues Dr. Masoud Daneshi, Dr. EhsanZaman, Dr. Ali Vakil, Dr. Farzad Foroughi and Dr. Pouyan Jahangirifor many helpful discussions throughout the course of this project. Specialthanks to Ehsan for proofreading this thesis.I would like to extend my appreciation to other colleagues and friendsat PPC, including but not limited to Hamed Ghasvari, Amirhosein Salim-ian, Hatef Rahmani, Dr. Frank Saville, Dr. Abbas Nikbakht, Dr. MousaNazhad, Daniel Patterson, and Nicholas McIntosh. I owe a great deal ofappreciation to my family for their unconditional love and support through-out my years of study. Special thanks to my mother, Farkhondeh, and mybrothers and sisters. Thank you for all you did for me and I hope I havemade you proud.I would like to pay special tribute to my loving wife, Solmaz, for hersupport, patience, and understanding throughout this project. Lastly, Iwould like to thank my son, Adrian, for his beautiful smiles and being bymy side while putting this thesis together.xviDedicationTo Solmaz,For all her love and support.AndTo the memory of my father, Hamid.It is to his standard I strive. I hope he would be proud.xviiChapter 1IntroductionForests are a critical natural resource in Canada and the pulp and paperindustry is of interest in countries that benefit from the forest as a naturalresource. Canada’s forest industry is a $58 billion in revenue annually, asreported by Forest Products Association of Canada (www.fpac.ca). Thisis significant since it represents 2% of the country’s GDP. Pulp productionis one of Canada’s largest export industries and British Columbia’s largestwith $7 billion in exports in 2014. Employing new techniques to optimizethe production process of this industry is of significant economic importance[1].In the pulp and paper industry, fractionation is defined as the separationof fibres into two or more fractions with different properties. The fibrecharacteristics have a major impact on the properties of the finished paperproducts. Therefore, it is beneficial to be able to control the fibre size usedin the papermaking process. Fractionation can tailor the final properties ofthe pulp towards its end-use. In theory, companies can buy any material fortheir products with optimal physical properties but in practice, it is limited.Fractionation of the final or semi-finished fibres could thus be one way tooptimize the use of fibres for specific applications [2].This project aims to assess the possibility of a newly-introduced particlesorting method of micro-fibrillated cellulose (MFC) suspensions. There isa need to fractionate MFC in a simple manner that enhances process effi-ciency and product quality [3]. A number of groups have recently examinedthis using different approaches but have been met with limited success inscaling-up the process. The objective of this study is to address these short-comings. We do so by exploring a methodology recently advanced in theliterature by Madani et al. [4]. We first examine this batchwise method in abenchtop laboratory centrifuge, then we design and build a continuous unitand evaluate its performance.This thesis is presented in 7 chapters. Chapter 2 presents backgroundon the MFC characterization, yield stress fluids, novel gel fractionation,and micro-particle separation techniques and ends with a summary of theliterature and the project objectives. In Chapter 3, we perform a series1of batch-wise centrifugation tests to develop the criteria for motion of theindividual classes of particles.Chapter 4 presents a process and mechanical design for a continuous ma-chine. It starts with an overview of the design, followed by design principlesfor each component. Next, the experimental set-up and loop are explained.A theoretical study is presented in Chapter 5 to aid in the operation ofthe device. We study the fully developed flow field of layered viscoplas-tic fluids in swirling annulus flow. Finally, in Chapter 6, we demonstratefractionation using the continuous device and try to achieve a continuousseparation by generating similar results to those obtained in the batchwisepart of the study. Conclusion, limitations and future work is discussed inchapter 7. The method used in this thesis for particle fractionation is intro-duced by Madani [8] and Martinez et al. [110]. The simulation results arethose of reported by Al-Shibl [144]. Any result from these works are citedappropriately.2Chapter 2BackgroundHydrocyclones and pressure screens are two traditional methods used forfractionation in the pulp and paper industry (see Figure 2.1). In pressurescreens, the separation is done based upon the size of the particles, moreprecisely their lengths [5–7] with varying degree of success [8]. Accumulationof contaminants and long fibres on the screen are the main reasons for thelow efficiency of pressure screens, which cause very high pressure drops.Multi-stage screens are used to improve the separation performance [9, 10].Hydrocyclones, also known as centrifugal cleaners, are extensively used ina variety of industries as solid-liquid and liquid-liquid separation devices, aswell as particle classifiers. Similar to screens, hydrocyclones have been usedin the pulp and paper industry to remove undesirable particles and unsatis-factory fibres from slurries. Hydrocyclones have the capability to fractionatefibres according to their thickness (like earlywood/latewood) specific surface,fibre length and coarseness. Plugging, increased thickening factors (rejectmass / feed mass ), short residence time, low capacity and high energy lossesare the main disadvantages of this apparatus [11]. The motion of particles isvery complex inside a hydrocyclone. The presence of boundary turbulence,long-range hydrodynamic interactions and flocculation are effects that makethe study of hydrocyclones highly complex [8]. More information about thecomplexity of this device can be found in [12–17].2.1 Micro Fibrillated Cellulose (MFC)Throughout this work, several particle systems will be used to test the frac-tionation. However, the ultimate objective is to achieve fractionation of anewly introduced cellulose material obtained from fibres called Micro Fib-rillated Cellulose or MFC [18–20]. MFC suspensions are a mixture of high-aspect ratio cellulose fibrils, with a broad length distribution [21–24], createdthrough a combination of chemical and mechanical treatments. MFC sus-pension displays a gel-like behavior at a high concentration as depicted inFigure 2.2. MFC is reported to have a high aspect ratio (the ratio of lengthto diameter) and thus, has been widely used in biocomposite technology3(a) Hydrocyclone (b) Pressure ScreenFigure 2.1: Units currently exist for fractionation purposes, (a) a hydrocy-clone [11] and (b) a pressure screen [7][24–26]. These features make these materials attractive as strength addi-tives in paper and composites [27–31]. Furthermore, the length and aspectratio distributions of the reinforcing MFC dramatically affect the strengthproperties of the resulting composites [21–23, 32].To address the properties of this material, we take a closer look at asingle wood fibre. A single fibre with a width of 10 − 50 µm (dependingon the source) is shown in Figure 2.3 with its corresponding layers. Theselayers are called Middle Lamella (ML) Primary wall (P1) and secondary(S1, S2, and S3) walls. The primary and secondary walls consist of cellulose,hemicellulose, and lignin. A closer look at the secondary wall reveals mi-crofibrils which are aligned parallel and packed densely in a flat helix in thislayer. This wall with a thickness of 300 nm (Spruce wood) contains mostof the cellulose mass [34, 35]. In the S1 layer, microfibrils are oriented per-pendicular to the main axis of the cellulose(see Figure 2.4). This cellulosematerial is presented in the fibres in the form of microfibrils with a diameterof 10− 20 nm (Spruce wood). The smallest morphological units in a fibre,elementary fibrils (EF), are the main elements of microfibrils that have adiameter of 3− 35 nm, depending on the source [3, 36, 37].Both the microfibrils and elementary fibrils are considered as cellulose4Figure 2.2: (a) MFC suspension (2 wt %) produced by mechanical treatmentin a homogenizer. (b) SEM images of the MFC suspension at the sameconsistency at a magnification of 20 k and 50 k. Reproduced from [33].nanofibrils. However, various terminologies have been used for micro/nanocellulose material in the literature. Recently a list by the Technical Associ-ation of the Pulp and Paper Industry (TAPPI) is proposed to address theterms and definitions of cellulose nanomaterial and its size range (TAPPI WI3022) [38, 39]. The abbreviation and applicable size range of each sub-groupare presented in Figure 2.4e. There are two types of cellulose nanomateri-als, nano-objects and nano-structured. The nano-object category is dividedinto two subcategories, namely cellulose nanocrystals (CNCs) and Cellulosenanofibres (CNFs). CNCs are needle-shaped, short, nanoscale in diame-ter and 100 − 500 nm in length and CNFs are flexible, long, nanoscale indiameter and microscale in length.2.1.1 Production and CharacterizationBleached kraft pulp is most often used as a starting material for MFC pro-duction. Mechanical treatment devices such as homogenizer, microfluidizer,grinder and refiner can be used for the production of the MFC. These me-chanical treatments may be as large as 70 MW/ton, depending on the tech-nique [18–20, 28, 40, 41].Disk refiners [42, 43] and grinders [44, 45] are two conventional devicesfor mechanical pre-treatment in the production process of MFC. The refin-ing process helps to peel the fibre’s cell wall, which causes an increase inits volume and specific surface [46]. As a result, this process makes the mi-crofibrils more accessible for further treatment and thus, it is commonly usedbefore the CNF production as well. However, the refining technique is also5Figure 2.3: The hierarchical structure of wood, showing: the middle lamella(ML), the primary wall (P), the outer (S1), middle (S2) and inner (S3)layers of secondary wall. With a closer look at the secondary wall of thewood fibre, cellulose (C), hemicellulose (H), and lignin (L) can be seen.The microfibril (MF), elementary fibril (EF), crystalline domain (Cr) andamorphous domain (Am) is also shown here. Reproduced from [3].reported as a single mechanical treatment for CNF production. Karandeet al. [47] employed a disc refiner to produce CNF from cotton fibre sus-pension, where, as a result, the average fibre diameter dropped from 25µm to 242 nm after 30 passes in the refiner. Refining results in a highlyheterogeneous suspension, and thus, the product is referred to as cellulosemicro-/nanofibrils or micro-/nanofibrillated cellulose (MFC). The particlesystem that we are intended to examine our fractionation method is pro-duced by refining. We call this material MFC, and from now on, any MFC isrelated to a highly refined pulp suspension at various refining energy levels.In the refining technique, various specific refining energy (SRE) can resultin various degrees of fibrillization, which can be achieved by changing thegap of a refiner disc. A further increase in the refining energy results in a6(a) (b)(c) (d)CellulosenanomaterialNano- ObjectsNano-StructuredCellulose microfibril (CMF)Width:10-100 nmLength:0.5-50 umCellulose microcrystal(CMC)Width: 10-15 um L/D < 2Cellulose nanofibrill (CNF)Width: 5-30 nm L/D > 50Cellulose nanoceystal (CNC)Width: 3-10 nmL/D > 50(e)Figure 2.4: Images of S1 wall layer of a single fibre. (a) Primary wall ofa eucalyptus pulp fibre at low magnification (5 k). The fine structure ofthe fibril arrangement cannot be seen at this magnification but is revealedat higher magnifications. (b) An Image of micro-fibrils in the S1 wall layeroriented perpendicular to the main axis of the cell (25 k). In (c) the samefibre with higher magnification is shown (50 k). (d) A high-resolution image(100 k) of the complex, fractal micro-fibril structure found within the S2layer. Reproduced from [3]. (e) Standard terms for cellulose nanomaterials(TAPPI W13021) reproduced from [38]7Figure 2.5: SEM micrographs of mechanically refined cellulose fibre atvarious refining energy. (a) Original pulp (b) 500, (c) 1000 and (d) 2000kWh/ton [48].much finer fibre, and a more microfibril cellulose structure [24]. Figure 2.2and 2.5 shows micrographs of mechanically refined cellulose fibre producedby grinding and refining.The characterization of MFC particle size can be divided into sepa-rate methods. High-precision morphology characterisation such as high-resolution microscopy, (scanning, transmission or atomic force microscopy),[49, 50] aiming for a fundamental understanding. However, when rapid char-acterization of properties is of interest, techniques such as optical transmit-tance, dynamic light scattering, rheology, water retention and mechanicalproperties of films or composite handsheet papers are reported in the liter-ature [8, 51, 52]. Figure 2.6 shows the average particle size as a function ofenergy consumption for a grinding process. The particle size was measuredusing Malvern Mastersizer which employs a laser diffraction technique forsize measurement.As described by Eriksen et al. [41] and later by Syverud et al. [53], anexponential decay function can be fitted to the results shown in Figure 2.6:APS = 24.53 + 139.8e−0.02EC (2.1)8Figure 2.6: Average particle size as a function of energy consumption forkraft pulp using grinding technique.Where APS is the average particle size (µm) and EC (MWh/t) is the en-ergy consumption during grinding of MFC made of kraft pulp. The modeldescribing the average particle sizes shown in this figure gives size down toapproximately 24 µm. However, the average value is based on the distribu-tion curve ranging from 0.1 to 120 µm. The Mastersizer device measuresthe size as a diameter of a sphere having equivalent volume as the measuredparticle [53].Given the high energy consumption of the current MFC productionmethods and the inherent size distribution of manufactured MFC, new piecesof equipment are constantly designed or developed to make the process moreefficient. Typically, this is achieved through a fractionation method, whichis explained in the following section.2.1.2 FractionationThe methods explained in the last section generally yield a wide size dis-tribution of produced MFC with some non-fibrillated residual fibres. Thus,fractionation can be employed to retrieve the undesired large fragments andunrefined fibre particles. There are minimal works done in the MFC frac-9(a) (b)Figure 2.7: MFC characterization with ultra-filtration fractionation. Thereare two optional channels in the device which utilizes this method; one with(a) rotating fractionation element and another with (b) cylinder tube unit.The rotating fractionation element has an interchangeable screen unit insidewith a net type of screens ranging from 150 to 0.1 µm. Formation of fillercake is a challenge in this technique; thus, the ultrasound cleaning systemwas used to prevents filter cake formation [54].tionation area. Tanaka et al. [54] developed a fractionation method basedon ultrafiltration system to characterize nano/micro-size cellulose particles.The device that was developed by them is very similar to a Bauer McNetttechnique currently being used for fibre characterization in the pulp andpaper industry (see Figure 2.7). In their technique, an MFC suspensionwith an initial concentration of 0.1% (25 g solid in 25 kg suspension) andin 50 oC temperature and feeding rate of 9 kg/min was fractionated usinga combination of screen and membrane filters. This process is reported tobe time-consuming since each stage takes about 9 hours on average to beconducted. What is clear is that this technique may be feasible for MFCcharacterization but probably not for production -maybe- because only onetrial takes about 1-2 business days to fractionate 25 g of MFC. A similartechnique was employed using ceramic membranes reported by Zhu et al.[55]. In their technique, the pulp suspension with an initial concentrationof 0.1 wt.% was fractionated, and results were characterized using SEMimaging.More recently, a work published by Chinga-Carrasco et al. [56] studiedthe screening using a Valmet laboratory equipment (TAP03, screen slotwidth of 0.2 mm and applied speed of 1000 rpm) classifier to remove theresidual fibres from 0.4 wt.% MFC aqueous suspension, which resulted in a100.2 wt. % suspension, although processing time is not reported.Each technique explained above has advantages and disadvantages; how-ever, processing time and low solid content of fractionation remain the maindrawback of these techniques.2.1.3 State of MFC SuspensionParticle concentration in a suspension can be in dilute, semi-dilute or concen-trated state. The key to this concept is Crowding number, which has beendeveloped by Kerekes and Schell [57]. It is shown that for mono-dispersedsolid cylindrical fibres, Crowding number, N, is given by N = 2/3 Cv(l/d)2where l is the fibre length, d is the diameter of the fibre, and Cv is thevolume concentration. For wood fibres, N can be written asN =piCmLw26w(2.2)where Cm is the concentration of solid material in suspension in (kg/m3)and Lw is an interaction length assumed to be equal to the length-weightedfibre length average of the fibre length distribution, i.e.Lw =∑nili2∑nili(2.3)Here, fibre length and aspect ratio is the critical parameter. It is verydifficult if not impossible, to measure it for highly refined pulp with a com-plicated morphology such as MFC. In a study conducted by Varanasi et al.[58] to estimate the cellulose nanofibril width, a combination of microscopicmeasurements equipped with image analysis is performed. However, it wasfound to be challenging to determine the length of the particles due to en-tanglement and difficulties in characterizing both ends of each fibrillated orsemi-fibrillated fibres [58]. The second method to estimate the aspect ratioand the suspension state is sedimentation method. This method was pro-posed by Martinez et al. [59] for wood pulp fibres and was later repeated forMFC/NFC by Varanasi et al. [58], Zhang et al. [60] to estimate the tran-sition consistency (gel point) of the suspension from dilute to semi-dilute.Another method is also to study the suspension rheology and estimate theyield stress. Yield stress occurs as fibres form a continuous network becauseof contact with other fibres. It is shown that a dilute fibre suspension willdisplay no yield stress. In work by Varanasi et al. [58], yield stress was’measured as a function of solids concentration in order to determine the11transition from a dilute fibre suspension to a semi-dilute suspension.’ Theirdata showed that the transition concentration from dilute to semi-dilute wasabout 2 kg/m3. The aspect ratio values were also calculated using both theyield stress and sedimentation methods and showed reasonable agreementwith each other.2.2 Fractionation in MicrofluidicsInterest in the particle separation is by no means limited to the pulp andpaper operations. It has been a key element in industrial and biochemicalapplications. When it is more about identification and analysis of specificparticles, microfluidics has been actively adopted because of its ability tomanipulate micro-particles precisely [61]. The main application of this re-search work is to evaluate a novel technique to fractionate microparticles;thus, we will examine other separation devices outside of the pulp and paperdomain for micro-size particles separation.Techniques for separating micro-size particles contain two main cate-gories which are based on whether an external force is applied or not. Activemethods use an external force, and because of this, the separation efficiencyand selectivity are high. However, they have a limited throughput due tolimited flow rates. There is no external force involved in passive methods. Itutilizes distinctive particle characteristics such as size and density and alsoparticle-particle interaction, flow field, and channel structure. While thishas a simple design, relatively simple fabrication, and high throughput, itsselectivity is lower compared to the active techniques [61].One of the earliest active separation methods is the field flow fraction-ation (FFF), which requires a precise injection of fluids. It is based uponthe difference in particle retention times in the separation channel. In thismethod, both small and large particles move to the outer wall due to anexternal force and form a thin layer on the wall. The larger particles movealong the fast-moving streamlines, whereas the small particles flow withslow-moving streamlines. This is used to achieve separation. In a differentapplication, if the particle size is large enough, the lift force acting on theparticle tends to move it away from the wall at a distance greater than theparticle diameter. Therefore, bigger particles exit from the channel first [63].Field Flow Fractionation has successfully been employed for characteri-zation and separation of cellulose nanofibrils [65, 66]. However, these unitsoperate at < 1 mL/min.In applications where energy input is most important, passive sorting12Figure 2.8: Particle sorting system using pinched flow. This mechanism isalso combined with a curved section to add centrifugal force for enhancedsedimentation [62]techniques are recommended, whereas, active separation method is usefulwhere higher fractionation efficiency is of critical concern. Some of the pas-sive techniques employ external forces to enhance fractionation performance.This is called combined technique [63].A third technique that is related to our work is pinched flow fractionation[62]. This method is a passive sorting technique that employs characteristicsof laminar flow for particle sorting. In this method, the fluid containing theparticles which we call ’dirty’ fluid, is focused by a clean fluid, as shown inFigure 2.8 . The flow channel includes a section called ’pinched segment’. Tobe able to use the pinched section, the particles have to be aligned with oneof the sidewalls. This is achieved by controlling the flow rates of both cleanand ’dirty’ fluids. In laminar flows, particles tend to follow the streamlinesthat pass through their center of mass. For smaller particles, these stream-lines are closer to the wall, whereas it is closer to the channel center forlarger particles. Thus, separation will occur in the pinched segment. Thismechanism can also be combined with a curved section to add centrifugalforce for better sedimentation and the possibility of separation based on size13Figure 2.9: Hydrodynamic amplification of a gravity-driven mass-dependentparticle separation system. Sheath fluids are acting as clean fluid to focuspoly-dispersed particle suspension in (A). As can be seen in (B) and (C),sedimentation of the particles is amplified by expanding the channel geome-try. (D) shows the final stage of fractionation. The separation demonstratedin [64] was performed at a total flow rate of about 1 mL/h. The size barsin the picture represent 500 µm.[63].Gravity and sedimentation can be utilized for fractionation in microflu-idics as well. The device used in this technique consists of three inlets, twoclean fluid which act as a sheath liquid for better sample focusing, a sep-aration channel and collectors (see Figure 2.9 ). Spherical beads becomealigned with channel and parallel to the gravity in focusing channel.In otherwords, the particles are focused to the center of the channel by flows of cleanfluid (Figure 2.9A). After being tightly focused, particles enter the separa-tion channel. The upper wall of the separation channel is perpendicularto gravity whereas the lower wall gradually expands. Due to the wideningchannel geometry, the mean flow velocity becomes smaller and the parti-cle sedimentation occurs due to gravity. Owing to asymmetrically wideningchannel geometry, larger particles reach the lower channel wall faster due tolarger sedimentation velocities experience (Figure 2.9B and C). This methodoperate at 1 mL/h flow rate [64]. There is abundant literature related tomicro-particle separation (See [63, 67, 68]). Here the most relevant studies14Table 2.1: Comparison between active and passive separation methods[63].Method Active PassiveExternal force Yes NoSeparation efficiency High LowThroughput Low HighDesign Simple ComplicatedEnergy input High LowSelectivity High Lowand methods were explained.ComparisonBased on the operating principles, separation techniques may be categorized.Passive techniques are used where energy input is most important, whereasactive separation method is suggested where higher fractionation efficiencyis required. Adding an external force can further improve the performanceof the passive techniques [63]. A comparison between these two methodscan be found in table 2.1.Almost all the techniques are suitable for very low flowrates i.e. ∼1 mL/min. Thus, the challenge with these devices is scaling-up to industrialcases, and this is what we address in this thesis.2.3 Particle Motion in Newtonian FluidsWe start with the description of a simple particle separation mechanismthrough settling. Consider an isolate rod-like particle, in an unbound fluid,settling slowly due to gravity. It is shown that the settling velocity canonly be used for separation under the creeping flow, in an extremely di-lute suspension, and with constant particle orientation. Otherwise, long-range hydrodynamic interactions disturb the flow field until recirculationor swirling like behavior is apparent. Disturbances in the suspension maybe due to the presence of other particles [69–75], which cause recirculationand swirling like structures at elevated Reynolds number [76]. Furthermore,preferential particle orientation exists during settling at high Reynolds num-ber [77, 78]. Therefore, it can be concluded that chaotic behavior is evidentdue to the long-range hydrodynamic interactions which can be even worse15in any industrial suspension and Reynolds number. Madani attempted todevise a novel separation principle which was not hindered by long-rangedisturbances. The proposed technique is based on controlling the thresholdof the particle motion in a yield stress fluid [4].2.4 Yield Stress FluidsAn everyday example of yield stress fluids is hair gel, as well as workingfluids in geophysical and industrial settings such as oil and cement. Thedirect effect of having yield stress is that if such fluids are subjected to stress,which is less than their yield stress, they behave like solid; otherwise, theydeform and flow. Thus, it can be assumed that once shear stress is applied,yield stress fluids exhibit a potential response: deformation or plastic flow.The first and simplest model for describing this behavior is explained initiallyby Bingham. In the tensorial form the constitutive equations for a Binghamfluid are: {τij =(µ+τyγ˙)γ˙ij τ > τyγ˙ij = 0 otherwise(2.4)and the norms of the tensors γ˙ and τ asτ =(∑ 12τij)2and γ˙ =(∑ 12γij)2(2.5)Here µ is plastic viscosity, τ is deviatoric stress tensor and γ˙ is strain ratetensor. By relying on the von Mises yield criterion, yielding occurs once thesecond invariant of the stress tensor at each point exceeds the yield stressof the fluid.The Herschel-Bulkley model, as a more generalized model, takes theshear-thinning behavior of the fluid into account:{τij =(Kγ˙n−1 + τyγ˙)γ˙ij τ > τyγ˙ij = 0 otherwise(2.6)where K and n are the consistency and power-law index, respectively. Thismodel includes a power-law shear-thinning behaviour after yielding (whenn < 1) and is widely used and accepted due to its flexibility for fittingexperimental data. The power-law index is found to be between 0.2-0.8 formany practical viscoplastic fluids [79]. However, time dependency in terms16of viscoelastic and thixotropic response is a behavior of real yield stressfluids that can not be described by these models [80]. This means for realviscoplastic fluids, the effective viscosity is a function of the shear historyof the fluid [81]. The non-ideal behaviour of the yield stress fluids is widelystudied in terms of viscoelasticity, shear banding, and hysteresis; see [82–85].In this work, we used Carbopol powder for preparing the viscoplasticfluid. The Carbopl solution is a transparent fluid which makes it easy tooperate with when conducting experiments. This polymer has a molecularweight of 104,400 g/mol and its rheology has been extensively characterizedTaghavi [86]. Herschel-Bulkley model can be considered as a good approxi-mation to describe its flow curve, and no significant thixotropic behavior isreported for this viscoplastic fluid.2.5 Particle Motion in Yield Stress FluidsThe batchwise fractionation technique works based on controlling the thresh-old of the particle motion in a yield stress fluid. To elaborate on this ideafurther, consider an isolated spherical particle settling in a yield stress fluid.In this case, the particle needs a net applied force to be greater than theforce due to the yield stress of its surrounding fluid to initiate the motion.The force can be defined as a critical force that must be large enough toovercome the resistive force due to the yield stress (Equation 2.7).F =FaD2τy>AeD2(2.7)F is a dimensionless force, Fa is the applied force, D is the particle diameterand τy is the yield stress. Since the fluid rheology can determine the yieldstress, thus the key to the solution for the separation problem is Ae. This isthe surface area over which the force due to yield stress is applied. Deter-mining the yielding surface is an open research topic in both numerical andexperimental fluid mechanics.Several works have been done to determine Ae through simulation [87–92]. Andres [87] through a numerical analysis reported that this area isrelated to the projected area of a particle. One of the most pioneer workswas done by Beris et al. [88] in which the position of the yield surface of asettling sphere in a Bingham fluid was calculated. Beris and his colleaguesBeris et al. [88] showed that there are two yielded surfaces; a kidney-shapedsurface along with two triangular-cusps in the front and back of the spheres.Recently, Chaparian [93–95] studied the velocity magnitude and yield sur-17Figure 2.10: Speed contours and yield surfaces of two different shape par-ticles. Gravity is upward and the white lines represent the yield surfaces.Reproduced from [93]face for different shapes and orientations of particles in a yield stress fluid.It was confirmed that the shape and orientation of the particle dictate theshape of the unyielded envelope. However, it is not unique, and we canhave the same unyielded envelope for different shape particles, i.e. differ-ent geometries can be cloaked inside the same unyielded envelope. Figure2.10 shows the speed contours and yield surface of two different geometrieswhich have the same unyielded envelope around them. Another key find-ing of Chaparian is the effect of the particle-particle interaction and thecomparison that he made in both the viscous and yield stress fluids. Theexistence of the hydrodynamic interactions in the viscous fluid was observedeven at large distances from a particle, whereas in yield stress fluids, thestress decays much faster. Therefore, if the particle is far away enough, itmay behave like an isolated particle in a yield-stress fluid. If the particles arefar away from each other, then they have their own Ae. However, when thedistance between the particles decreases, a single yielded envelope will formand eventually, unyielded fluid bridges connect the particles which result indifferent Ae compared to the case with two separate particles[95]. This isdepicted in Figure 2.11.Additionally, experimental works proved the presence of the yielding sur-face too. The experimental results have slight discrepancies from numericalworks due to the non-ideal rheological behaviour of a real viscoplastic fluid[96–98]. However, the signature of the yielding surface was observed in theexperimental works too. In recent work, Putz et al.[98] experimentally esti-mated the area through flow visualization and showed that the shape of theyielded surface approximated that of an ovoid spheroid with its major axis18Figure 2.11: Speed colourmap and yield surfaces of two identical particles.(a) When the particles settling in yield stress fluid, if the particles are far-away from each-other then both are moving in their yielding envelope andare separate from each other. (b) When the distance between the particles isdecreased, a single yielded envelope will form and eventually unyielded fluidbridges connect the particles. The white lines represent the yield surfaces.Reproduced from [95]approximately five times greater than the particle radius.We now turn our attention to the critical force for the onset of motion.This force was calculated by Beris et al. for a sphere in Bingham plasticFc =V∆ρgD2τy≈ 7pi2≈ 11 (2.8)where, V and ∆ρ are volume and density difference of the particle, re-spectively. This non-dimensional force is approximately three times greaterthan that given by Andres [87] (Fc = 4.8) and is closer to the experimentalmeasurements of [99–101],i.e. 16 < Fc < 25. These numbers were later re-ported by Madani et al. [4] to be between 12 and 26 for spherical particles.They then measured the critical force for rod-like particles in two differentorientations, i.e. parallel and perpendicular to the applied force. It wasshown that the critical force, Fc, strongly depends on the diameter, orien-tation and density of the particle (see Figure 2.14 ). Ahonguio et al., [102]also conducted a study on spherical particles and successfully measured theplastic drag coefficient as a function of Oldroyd number (Oldroyd number isthe ratio of the plastic force to the viscous force). Similarly, others reported19g𝑙⊥(a) χ = 0.25g𝑙⊥(b) χ = 4Figure 2.12: Geometrical aspect ratio and orientation of a rectangular par-ticle in 2Dthe drag coefficient such as Tokpavi et al. [103] for a 2D disk, Nirmalkar etal. [104] for a 2D square and Putz and Frigaard [105] for a 2D ellipse andChaparian for variety of shapes [106].To highlight the effect of the particle orientation on the critical force, weconsider what Chaparian and Frigaard [94] have calculated for a rectangularparticle, parallel and perpendicular to the gravitational force. Here, the dragforce on a cylindrical particle settling in an unbound viscoplastic fluid canbe written as:FD = CD l⊥τy , l⊥ =√piχ−1/2 (2.9)For two orientations depicted in figure 2.12, we will haveCase (a) : χ = 0.25, CD = 11.22, l⊥ = 3.5, FD = 40τyCase (b) : χ = 4, CD = 17.09, l⊥ = 0.89, FD = 15τyWhat we learn from their findings is that in idealized problem of sedi-mentation of a particle in Bingham fluid, in order to be able to separate par-ticles with random orientations, parameters have to be selected in a way that((4ρV gFD)a,b)1for particle #1 is different than the value of((4ρV gFD)a,b)2for particle #2. It may include the density difference, the size of the particleor the yield stress.20We now turn our attention to the essential task of dynamics of particlessuspended in yield stress fluids. There exists extensive technical literatureon the particle motion in viscoplastic fluids. However, we only cite here thepublications more related to the application related to our work. In workdone by Merkak et al. [107, 108], the particle behaviour in both the yieldedand unyielded regions is studied and shown that particles located in the plugregion have translational motion while they experience both translationaland rotational motions when located entirely or partially at the shearedzone. This is an exciting finding because we want the particles to move onlyin the lateral direction with respect to the axial motion of the viscoplasticfluid (At least for spherical particles). Siqueira et al. [109] also presenteda numerical investigation on a series of spherical particle suspension in aviscoplastic fluid. Their simulation showed the effect of suspension bulkconcentration, plastic number (τy/τw where τw is the wall shear stress) andpower-law index in the velocity profile. They observed a particle flux in thepositive radial direction that eventually completely depleted the plug flowregion from particles, so that the plug flow zone became free of particle. Theparticle-free plug region near the pipe center was found to be a function ofregularized viscosity function, and it takes an enormous amount of timedue to the extremely slow particle diffusion across the very viscous fluid.Such behaviour was not observed or captured in the Merkak et al. [108]experimental work.2.6 Madani’s Fractionation MethodMadani et al. [4] used the threshold explained in the last section as aseparation aid and demonstrated this separation principle by suspendinga number of different classes of particles in a gel of sufficient strength tohold the particles against the action of gravity, and then subjecting theseto a prescribed centrifugal force of sufficient strength to initiate motion inone class of particles, but not in the other. This technique was successfullyemployed to separate different spherical (based on size and density) and rod-like particles. A demonstration of his experiment is depicted in Figures 2.13and 2.14.Madani continued his work and showed a sufficient distinction in the crit-ical force to create a separation of nylon and cellulose fibres, and speculatedthat this process could be scaled and made continuous in spiral-Poiseuilleflow. This idea was presented in a patent explained in [110] with highlightsdepicted in Figure 2.15. Their proposed apparatus includes a body rotatable21Figure 2.13: A demonstration of fractionation of a bidispersed suspensionof cylindrical particles. (a) An image of the suspension before the com-mencement of the centrifugal force. (b) The state of the suspension afterthe centrifugal force has been applied. Reproduced from [4].about an axis of rotation. The body of the device comprises an inner walland an outer wall rotatable in unison. The inner viscoplastic fluid containsparticles and is introduced to an outer viscoplastic fluid. At the end of thedevice, the suspension is divided into two fractions, i.e. accept and reject.This proposed device was never realized. Among several mechanical designissues that were identified in this device, high friction on the sealing surfaceswas found to be the most challenging. A large rotation radius was used tocreate sufficient centrifugal force, which also caused in a substantially highpower required to spin the rotating parts. A rough calculation revealed thatthe power required to spin this device was about 120 hp, which was notfeasible considering the strength of the parts.2.7 Industrially Available Centrifugal SeparatorsThe centrifugal separators are used for separation/classification in mining,petroleum and pulp and paper industries [111].We considered several industrially available centrifugal separators, andthe most related case was chosen to study. It was done to evaluate thepossibility of utilizing the device to demonstrate Madani’s technique con-tinuously. A contactor design of CINC company (www.cincind.com) for asingle stage separation is shown schematically in Figure 2.16. In this device,22Figure 2.14: (a) An illustration of the batchwise separation methodology ad-vanced by Madani and his co-workers [32] for cylindrical particles of equaldimensions (diameter D = 3.2 mm and length L = 9.6 mm) but of differentdensities (yellow colored cylinders: ρ = 8.4 g/cm3 and silver-coloured cylin-ders: ρ = 8.0 g/cm3. Initially, the rods are at equal radial positions fromthe axis of rotation and experience the same acceleration field. This imageis of the particles before the commencement of the centrifugal force. In (b),the position of the particles is shown after the application of a rotation rateof up to 300 rpm for 5 minutes. As shown, the particles with greater densitymove to the outer periphery while the other class of particles remains sta-tionary. (c) Measurement of the critical force Fc = ∆ρV Rω2/τyD2 to causethe initiation of motion in cylinders with various aspect ratio L/D and ori-entation, defined as either with the long axis parallel or perpendicular to thedirection of the centrifugal acceleration. The legend, in this case, defines Dfor each class of particle. Reproduced with permission.23Figure 2.15: The proposed apparatus for continuously fractionating par-ticles contained within a viscoplastic fluid. Reproduced from a patent byMartinez et al. [110].initially mixed two immiscible fluids flow into the annular mixing zone inletports at the left (more dense phase inlet) and right (less dense phase inlet).The mixing zone which is the region between the rotating parts and stator(in green), helps in developing a turbulent mixing aid, while the mixtureflows by gravity to the bottom of the mixing zone and then to the inlet ofthe rotor. Inside the rotor, the dispersion band creates a vertical cylinderin the middle of the separating zone. This dispersion band breaks underthe centrifugal force, and as a result, the heavier phase moves out to therotor wall and flows upward through the underflow to the upper weir andthen finds its way to the collector. The lighter phase moves in towards thecenter of the rotor and flows up to the lower weir. Typically, at normalrotor speeds in this device, the centrifugal forces are much greater than thegravity forces, i.e. 100-400 g. [113].With substantial modification, this device could be used as our continu-ous separator. Two inlets need to be separated from each other before theseparation zone as only one of the streams is particle-rich. The exit weirdesign must change because in the current design the dense phase fluid will24Figure 2.16: Sketch of an annular centrifugal contactor. This centrifugalcontactor operates as follows: 1-Flows of immiscible liquids enter the annularmixing region. 2- Mixing occurs and dispersion forms an annulus by shearinduced by the spinning rotor. 3-Stationary vanes under rotor break rotationand force liquid into the hollow rotor 4- Rotor acts as centrifuge separatingphases and pumps fluid upward. 5- Phases flow over weirs into collectorrings and out. Reproduced from [113].have to move towards the center of rotation (against the centrifugal force)in order to flow past the dense phase weir and into the heavy phase slinger.The centrifuge is open to the atmosphere, and there is always a free surfacebetween the fluid and air. In order to avoid this free surface, the devicehas to be sealed, which requires substantial modifications with the currentdesign.2.8 Hydrodynamic Instabilities and Entry LengthIn the proposed apparatus by Martinez et al. [110], for continuously frac-tionating particles, flow field must be in the axial laminar state for efficientoperation [114]. We need to understand how the bounds for instability ofthe base flow(s) change due to addition of a centrifugal force to the pressuredriven annular Poiseuille flow. Thus, an active scientific topic concerning25the multilayer fluids is the flow stability. Stability in fluids has been intro-duced about a century ago by Kelvin, Reynolds, Taylor, Rayleigh and othersand then developed during the last 30-40 years for non-Newtonian fluids forthe similar geometries. Later industrial motivations shifted the studies to-wards the multi-fluid flows to study the effect of different flow parameters,including density differences, flow-rate and the yield stress on stabilizing themultilayer flows [81].The preliminary studies of Madani et al. [114] confirmed the stability ofthe flow over a wide range of Reynolds number and rotational accelerationin a spiral Poiseuille flow of Bingham fluids in an annular gap. We drawour hope from this finding and suggest to modify the technique to introducea continuous method for particle fractionation in viscoplastic fluids. Beforethat, we want to take a closer look at other sources of possible instabilitiesin a viscoplastic multilayer flow. We start with the instabilities caused bya yielded interface. This type of instabilities is found to occur in the eventof having yielded velocity profiles of both fluids sharing the interface. If wedecide to vary the velocity in the multilayer fluids, then Kelvin-Helmholtzinstabilities must also be considered. Any density difference in the case ofmultilayer fluids may also cause instabilities, especially (maybe) when themultilayer fluids are in density unstable configuration.We start with viscoplastic fluid flow in a rotating duct. It was first stud-ied by Bittleston and Hassangar [115] by considering a flow in a concentricannulus where the axial flow was combined with radial flow due to the ro-tation of -only-inner cylinder. Bingham plastic model was used to solve theproblem both numerically (full geometry) and analytically (only in a simpleslot). The main finding of the study was a critical rate at which the plugregion disappears. Their work can be a benchmark study in generating anystability map in our work. Similarly, Nouar et al. [116] and Escudier et al.[117] solved the fully developed problem using the Herschel-Bulkley model.Later, a comprehensive parametric study on Bingham number and radiusratio of a circular geometry was done by Liu and Zhu [118]. The laminarfully developed problem was solved for a vertical concentric and eccentricannuli geometry with the rotating inner cylinder. The reported results wereunique because it was shown that the rotational effect on the flowrate, ata fixed pressure gradient, is likely to the effect of changing axial volumetricflowrate in a non-rotating case. Another related parameter to our study isthe position of plug region which was studied by Wang in 1997 [119] and1998 [120] through a finite element method in various geometries in orderto track the yield surface and mobile plug zones. There exist literature onthe spiral Poiseuille flow of solid body rotation [8] and spiral Couette flow26of two independently rotating concentric cylinders[121] which offers relatedinsights. Their results showed that the rotation of the outer cylinder hadstabilizing effects. Another finding related to our work is that island instabil-ities, which exists in the spiral Couette flow of Newtonian fluids, disappeardue to the effect of yield stress. Later, Madani [8] investigated the linearstability of spiral Poiseuille flow in an annular gap. His main findings are:First, the flow is linearly stable for all Bingham numbers bigger than zeroand second, the position of the yielded surface is only a function of pressuregradient at constant rheology.The second category is related to the interfacial instabilities of multi-layer fluids which mainly caused by yielded velocity profile. Here we onlyconsider the instabilities in multilayer viscoplastic fluids, and we start withviscoplasticly lubricated multilayer flow advanced by Hormozi et al. [122].She advanced the original idea and showed that a multilayer viscoplasticfluid can be stable if an unyielded region exists at the shared interface. Inother words, the shear stress has to be below the yield stress of one of thefluids at sharing interface [123–125]. This is very promising for our design aswe intend to use two (or one) viscoplastic fluid in the continuous machine.In the third category, we review the stability in the case of density differ-ence between fluids, and we only consider non-Newtonian fluids. We reviewthis topic as we intend to extend the original separation idea into two ormore fluids in the batchwise mode. Studies done in this area are mostly re-lated to oil industry [126–130]. Perhaps the most related study is the workof Frigaard and Crawshaw [127]. In this work, the mechanically unstablesituation of a heavy yield stress fluid resting on top of a light one in a longpipe is studied. It was shown that this situation can be stabilized if thefluids have sufficiently high yield stresses for a given fluid density difference,pipe diameter and pipe inclination.The fourth category is Kelvin-Helmholtz instability which happens be-tween two parallel fluid layers moving at different speed [131–134]. Thebasics of this instability are explained by Charru [135] using the Bernoullieffect. When two fluids move with different velocities, due to the shapeof a perturbed interface and therefore, reduction of the area perpendicularto the flow, a pressure difference between two fluids occurs which amplifiesthe perturbation [81]. It appears that this type of instabilities needs to beconsidered in our proposed system.Finally, we also want to consider the entry length of viscoplastic fluids.This phenomena is studied for Newtonian fluids for different geometries[136–139]. The related finding is that the entrance length for the annulargeometry of Newtonian fluid flows is shorter than the corresponding pipe27flows under the same Reynolds number. Correlations were proposed forpipe flow entrance length of viscoplastic fluids in the laminar regime byVradis et al. [140] and Min et al. [141]. The low Reynolds number casewas best studied by Poole and Chhabra [142] and Ookawara et al. [143].They considered the entry length as the axial distance where the velocity atthe radial position of 95% of the plug radius reaches 99% of the calculatedmaximum velocity (at the same radial location.) Their findings can provideinsights into our design as the entry length can be estimated by Re and Dh.2.9 SimulationUtilizing the method introduces by Bittleston and Hassager [115] and ad-vanced by Madani [8], the fully developed region of spiral Poiseuille flow wassolved by Al-Shibl [144] for different flow parameters and rheologies. Similarwork is done by Poole and Chhabra [142], and the hydrodynamic entrancelength is estimated for the spiral-Poiseuille flow. More importantly, Kelvin-Helmholtz instability was considered and found that it is not evident due tothe presence of the walls for spiral multilayer Poiseuille flow. Additionally,the stability of the density stable and unstable multilayer fluids is studiedfor this type of flow. It was found that in case of density stable (Inner fluidin annulus lighter than outer fluid), or iso-dense case, the flow is alwaysstable. However, the density unstable case destabilized the flow but it couldbe stabilized again by increasing the yield stress. Next, the exit region ofthe annulus is studied to predict the flow behaviour near the exit area andhow the flowrate combination of the inner and outer fluids could affect theinterface position and maybe the fractionation efficiency. This result wascombined with the findings from solving the fully developed region resultedin a stability map and an operating window which is shown in Figure 2.17-f. Besides, Madani’s batchwise results were used to estimate the startingcriteria and residence time of a given particle in spiral-Poiseuille flow in anannulus. These results can not be used as the stress state of the fluid wasnot considered in the calculations.2.10 Literature Summary and motivationThere is a need to separate (particle-particle) or fractionate micro-fibrillatedcellulose suspensions (MFC) in a simple manner that enhances process effi-ciency and product quality [3]. A number of groups have recently examinedthis using both classic laboratory or micro-fluidic approaches [54, 55, 63,28Inner radiusriOuter radius(a)(e)(b)(d)(c)(f) (g)Figure 2.17: A summary of work done by Al-shibl [144] to simulate thebehaviour of multilayer spiral-Poiseuille flow. The considered annulus isshown in (a). Included in this figure are the volume fraction distribution andlengths (before, inside and after separation zone) which resulted in the axialvelocity profile development shown in (f). The simulations are run at Rez =149.3, Reθ = 7.88, B(1) = 0.155 and B(2) = 0.093. The interface behaviourat the exit region is also presented at different ri and flow rate combinations:(b) ri = 0.84, Q1 = Q2 = 2.98, (c) ri = 0.75, Q1 = Q2 = 1.22, (d) ri =0.72, Q1 = Q2 = 0.96 and (e) ri = 0.69, Q1 = Q2 = 0.75. The results of thissimulation combined with solved fully developed problem (at z = 0.3m) isshown in (g) as an operating diagram. Here, the residence to settling timeratios are shown in blue lines, interface locations in black dashed lines anddimensionless pressure drop rate in solid black lines . Particle diameter is2.5 mm, particle and fluid density 7800 and 1000 kg/m3 respectively, innerand outer fluid plastic viscosity 1 Pa.s, inner and outer fluid yield stress 10and 6 Pa and 40 rad/s rotational speed. The operating window is set at40% of unyielded inner fluid.29145, 146] but have been met with limited success in scaling-up the process.MFC suspensions are a mixture of high-aspect ratio cellulose fibrils, witha broad length distribution [21–23], created through a combination of chem-ical and mechanical treatments. The energy applied during the mechanicaltreatments may be as large as 70 MW+h/ton (280 kJ/g) [18–20, 28, 41].This physical make-up leads to a complex rheological behavior with the sus-pensions showing strong stress/strain-rate relationships. We find that thesematerials have been rapidly adopted as a strength additive in the paper,polymer composites, or in foamed cellulosic materials [27–30].Particle fractionation of these suspensions may allow for either reducedenergy usage during production or enhanced service performance. In recentwork, Madani et al. [32] proposed a novel principle for the separation ofthese suspensions based upon a centrifugation technique. For illustrativepurposes, Madani demonstrated this principle by suspending two differentparticles in a weak gel and then subjecting these to a prescribed centrifugalacceleration. Madani tested the robustness of this process with papermak-ing suspensions and indeed found a unique separation based on either lengthor coarseness (mass per unit length). In related work, he showed a sufficientdistinction in the critical force to create a separation in MFC and speculatedabout that continuous operation may be achieved with pressure-driven flowsuperimposed upon solid-body rotation, i.e. spiral-Poiseuille flow [8]. Usinglinear stability, Madani [8] argued that this class of flow is well-posed forscale-up as the critical Reynolds’ number for the onset for the transition toturbulence increases with rotational acceleration. Our work is motivated bythese findings and the objective is to address the above-mentioned short-comings in MFC fractionation.In this thesis, we build upon the work of Madani by designing a continu-ous prototype. To aid in the design, we develop a predictive tool to estimatethe operating window for the prototype by solving the equations of motionfor (layered) spiral Poiseuille flow. We also develop calibration curves in abatch-wise centrifuge to understand the force required to separate a hard-wood Eucalyptus MFC suspended in a weak gel. This data serves to set thecentrifugal acceleration required for the prototype. Finally, we present ourprototype and report on a continuous separation of the MFC.2.11 ObjectivesThe vision of this work is• To extend batctwise technique and use one ormore fluids for particle30separation.• To develop a lab scale continuous device to test the possibility of frac-tionation of particles through the use of viscoplastic fluids in the con-tinuous method.• To demonstrate this methodology on a novel class of materials emerg-ing in the pulp and paper industry, namely Micro-fibres.To fulfil this vision, we set the following project objectives:1. To understand the separation in one fluid of an industrially availableparticle system.2. To understand the stability of multilayer viscoplastic fluids, with dif-ferent rheology, in a centrifugal field and consider the possibility ofparticle fractionation under the stable conditions.3. To design a continuous lab scale device.4. To demonstrate separation in this device.Through the first and second objectives, we hope to have a better under-standing of particle separation in one or more fluids. This provides knowl-edge that can assist in designing a continuous machine to achieve the nextobjectives.31Chapter 3Batchwise SeparationThis chapter is presented in three major sections. In the first section, webegin the examination of the separation principle verifying Madani’s originalexperiment to sort MFC. In this case, we examine the separation of a poly-disperse suspension in a laboratory centrifuge. The underlying question orthe need, which motivates the work in the first section of this chapter, is tounderstand the yield (mass%/mass%) of the particles that can be recovered.This was never reported previously for MFC suspension. Next, we wouldlike to explore variations of this principle to help aid in the design of acontinuous device. The idea which we want to explore in the second sectionof this chapter is if we can improve upon the efficiency of the original idea in”one fluid” and increase the yield by layering two fluids. Thus we continuethe work by examining the stability of multilayer fluids in the centrifugalfield. In the last part, we employed several particle systems to examinethe layering approach in the batch-wise mode. The motivation behind thissection is to test the feasibility of the batchwise separation of industrialparticle systems in the layered fluid.In other words, our primary goal in this chapter is to determine thecritical force to separate MFC. This data will be used to guide the selectionof the operating point and prototype design. A secondary motivation in thischapter is to explore: (i) the robustness of layering fluids in a centrifuge andask the question of when they will mix, especially when the layered fluidsare of different density, and (ii) are there operating methodologies to createunique separations. Finally, this approach will be examined on industriallyavailable particle systems.3.1 Feasibility of MFC Fractionation3.1.1 Material and MethodIn this section we examine the fractionation of MFC suspension producedfrom bleached Eucalyptus Kraft pulp through refining (BEKP-MFC) ina 0.05 (±0.02) to 0.16 (±0.04) wt/wt(%) Carbopol solution. The MFC32was obtained from Fibria Cellulose (www.fibria.com.br) and the experi-mental procedure follows that reported by Madani [8]. In brief, we mixed0.1 wt/wt (%) BEKP-MFC into a 50 mL Carbopol solution. The mixturewas placed into a centrifuge for a range of time and rpm. The upper 20 mLand lower 30 mL of the suspension were recovered for the microscopic andparticle size analysis. Experiments were conducted with centrifuge times ofup to 15 minutes and with the rpm ranging from 150 to 13200. In order toobtain the mass yield, the upper 20 mL suspension (accept) was carefullyrecovered, and the mass was measured. The same procedure was followedto obtain the mass of the Carbopol solution under the same g-force. Then,the mass yield was calculated using the following equationFractionation Y ield =ma −mcpmo −mcp × 100 (3.1)here, ma is the accept mass, mcp is Carbopol mass and mo is the mass of theoriginal suspension before fractionation, all from 20 mL volume. To obtaina size distribution, the suspension was prepared and carefully dispersed inwater. As reported by Brodin and Theliander [147], it is important tobreak up fibre agglomerates without causing further disintegration of thesample. Ultrasonics (at lowest tip displacement 1 of 2 µm )-taking care notto fibrillate microfibres- was applied to help the dispersion, although therewere not large agglomerates of particles.The size distribution test was performed using a Malvern Mastersizerunit (www.malvern.com) which utilizes a laser diffraction technique. De-vices which employ Laser diffraction technique have been used by severalresearchers for the fibre and/or fibril size analysis [48, 145, 147–154]. Mas-tersizer has a detection range from 0.02 to 2000 µm, and assumes sphericalparticles when calculating the particle size. Thus, the particle size reportedin the size distributions should be considered as relative since both fibresand fibrils have high aspect ratios (length to width relation) and deviateconsiderably from spherical geometry. During our measurement procedure,the background was first measured with only water in the sample dispersionunit, using automated routines. A few drops of the sample were drippedinto the sample dispersion unit, which was equipped with a propeller stir-rer. The light extinction-level was monitored, and the sample was added1In the device, the scale of ultrasonication is expressed in terms of tip displacementrather than Watts input, which can have varying dispersive power dependent on theviscosity and gas content of the dispersant. Tip displacement can be accurately measured.It is directly proportional to the ultrasonic energy used to disperse the sample. Doublingof the tip displacement quadruples the shear stress.33Figure 3.1: An example of the flowcurve data for 0.16% Carbopol solution.until the light obscuration reached a certain threshold. Five data collectionswere made on the same sample, and the results were averaged. Between eachsample, the dispersion unit was cleaned with water. The analysis softwaresupplied with the instrument was used to extract the data. The softwarecalculated the volume-weighted percentage on a user-defined logarithmic x-axis as well as volume percentage [155]. It should be noted that the particlesize was reported as the volume-weighted mean particle diameter d(4,3)),defined by the following equation:d(4,3) =∑nidi4∑nidi3 (3.2)where ni is the number of particles with diameter di [156].Rheology of CarbopolRheology tests were conducted to determine the yield stress of the Carbopolsolution. It was performed using a Bohlin CVOR digital rheometer in acontrolled stress-shear rate mode. The device and procedure are similar tothose explained in [86]. In brief, the rheometer is a cone and plate type,with 40 mm cone diameter 60 mm plate diameter, 4◦ cone angle and 150µm34gap at the cone tip. To avoid any possible slip, both cone and plate wereroughened with a thin layer of sandpaper (400 grit roughness). Herschel-Bulkley model fits well the shear behavior of Carbopol. This rheologicalmodel is stated as :τ = τy +Kγ˙n (3.3)where K, τy and n are fluid consistency index, yield stress and power-lawindex, respectively. The yield stress value can be determined using therheometer data through the shear stress value at the global maximum of theviscosity. Then, we subtract the yield stress value from the remaining shearstress data, which leads to finding the best fit for the power law curve. [86]A test to obtain the flowcurve data for 0.16% Carbopol solution shows thefollowing values for the model: τ = 14.51 + 5.86γ˙0.3983, see Figure 3.1.State of suspensionWe measured the gel point of the MFC suspension in order to estimatethe state of the suspension. BEKP-MFC was prepared with consistenciesranging from 0.1-0.42%, in a 200 mL measuring jar. The suspension wasagitated and allowed to settle for at least 48 hours, then the height of thesediment in the cylinder was measured. The results of the sedimentationtest are presented in Figure 3.2. A graph of consistency versus the ratioof sediment height to initial suspension height was plotted and fitted witha quadratic equation, similar to what Martinez et al. [59] and Varanasiet al. [58] reported. This equation is found to be y = 0.242x2 + 0.14x withR2 = 0.99. The linear term of the fit gives the gel consistency i.e. 0.14%.The consistency which we chose to perform fractionation is 0.1%, whichconfirms that the state of the suspension is not in the concentrated state.3.1.2 ResultsWe begin the discussion of the results by characterizing the suspension.In Figure 3.3(a), a microscopic image of the suspension is shown with thecorresponding fibre size distribution, shown in Figure 3.3(b) as determinedby Mastersizer.Included in this figure is the fibre size distribution after centrifugation at13000 g-force (accept). As can be seen from this figure, despite not achiev-ing a distinct separation, the size distribution has improved. It is importantto note that the laser diffraction technique for size measurement ’providesan equivalent diameter based distribution assuming that the light scattering35Figure 3.2: Sedimentation data of BEKP-MFC. The linear term of the fitgives the gel consistency. The procedure reported in [58, 59] was closelyfollowed to generate the data points.pattern of the material is identical to that of spherical particles. For mi-crofibrils with a high aspect ratio, this approach leads to values that can beused only for the comparison between samples and not as a direct measureof the real size of the material’ [152]. The Volume percentage is shown inFigure 3.3(b) is reported for the particle size ranging between 0.02-1000 µm.However, the volume-weighted mean diameter of each ”particle size distribu-tions” is reported as D in Figures 3.3 (c) and (d). Where we extend Madani’swork is that we attempt to measure the yield of the fractionated particles.Madani only reported the fibre size mean value of a commercial MFC sus-pension and addressed the effectiveness of the separation by examining thestrength enhancement in the paper after additions of the fractionated MFC.Here, we will study the relation between particle size and the mass yieldafter fractionation.To study the effect of the centrifugation time, we also recovered the par-ticles in the top 20 mL of the centrifuge tube and measured D value incomparison to the original sample. Looking back again at the principle ofthis technique explained in the Background section (see equation 2.8), wecan scale two different series of variables, one driving force, i.e. RCF/τy36Figure 3.3: (a) A Scanning Electone Microscopy image of BEKP-MFC at15000x magnification. (b) The particle size distribution of suspension beforeand after centrifugation at 0.1% consistency and 10 minutes of centrifugationtime. (c) The particle size measured on BEKP-MFC suspension, with aninitial value of 128 µm, as a function of RCF/τy at 0.1%. This concentrationwas found to be below the gel point [58]. RCF is calculated by dividing Rω2by earth’s gravitational acceleration and τy is the measured yield stressdivided by a characteristic yield stress of 1 Pa. For the batchwise tests,a 2.5 mL of a 2 wt/wt % suspension of the MFC was mixed into a 50mL of a Carbopol solution with a yield stress of ranging between 3-15 Pa.Particle size (D) was measured using a Malvern Mastersizer 2000 which mayintroduce artifacts if the sample is fibrillated. Here, batchwise results areshown in (◦) for 5 minutes and in (×) for 15 minutes centrifugation times.(d) A measure of the ratio of the mass of recovered MFC in the gel aftercentrifugation to the initial mass of MFC (yield) . This test was performedgravimetrically and the uncertainty in the estimate is estimated to be 5%.370-10 0-20 0-30 0-40 0-50Bin Volume (mL)30405060708090100Cumulative Yield (%)g-force=1500g-force=2650g-force=3000Figure 3.4: Cumulative mass yield of MFC made from bleached eucalyptuskraft pulp (BEKP-MFC). Here, the Carbopol concentration is 0.05 (±0.02)%, MFC consistency is 0.1% and centrifugation time is 5 minutes.where RCF is Rω2/g and particle diameter (D). Assuming constant den-sity difference, we may report one versus another. The results are shownin Figure 3.3(c), where, we find that the particle size decreases somewhatlinearly with increasing the driving force. The procedure was repeated fortwo centrifugation times, i.e. 5 and 15 minutes to study its effect on theparticle size. The particle size is found to be smaller at longer centrifugationtime at constant driving factors. After careful recovery of several replicatesamples, we were able to establish a reasonable estimate of the mass yield.The results are shown in Figure 3.3(d). Equation 3.1 is used to calculate thefractionation yield at different g-force, yield stress and centrifugation times.The test was repeated for 0.1%, 0.25% and 0.5% consistencies. At 0.1%MFC suspension, there is a linear correlation between fractionation yieldand measured particle size. In this case, the different fractionation yieldvalues were obtained by increasing either the centrifugation time, rotationalrate or yield stress values. The fractionation yield versus D is also reportedfor higher consistencies, i.e. 0.25% and 0.5%. The fractionation yield valueis found to be lower by about 10% and 30% at 0.25% and 0.5% wt/wt con-sistencies, respectively compared to 0.1% wt/wt consistency. One possiblereason could be higher particle-particle interactions or the formation of fibre38(a) (b)Figure 3.5: A comparison between the size and shape of the original andfractionated BEKP-MFC. (a) is TEM image of fractionated reject at 20000xmagnification and (b) is TEM image of fractionated accept at 200000x mag-nification.networks at higher consistencies [4]. No conclusions can be drawn from thesignificance of these results as we would need to consider a particular processor product. What can be said from these findings is that these results pointto the feasibility of a new separation technique in MFC production as thefractionation yield varies between 10% and 50%.We continue by reporting the distribution of the mass yield within every10 mL of the tube after centrifugation for a range of g-forces between 1500-3000. Figure 3.4 summarizes the results for three g-forces within this range.As expected, increasing g-force moves more particles to the bottom of thetube and increases the mass yield at given bin volume value.Finally in what we find the most surprising result is that we found smallquantities of nano-fibrillated cellulose in the fractionated fibres. We wereunable to quantify the mass of these particles but were able to use Trans-mission Electron Microscopy (TEM) for characterization and image analysis.Sample images are given in Figure 3.5 and the results of image analysis areshown in Figure 3.6. Our measurements show 20 times and 7 times dropin diameter and length in fractionated results, respectively. A closer lookreveals that around 70% of the number of fractionated particles have a di-ameter below 20nm (see Figure 3.6d) and 35% have length below 10nm (seeFigure 3.6b). In these figures, TEM images were analyzed using ImageJsoftware, the length and diameter of particles are measured and recorded tocalculate the frequency of each size.390 2000 4000 6000 8000 10000Particle Length(nm)05101520Frequency(Reject)(a) Length distribution of MFC reject0 100 200 300 400Particle Length(nm)02468Frequency (Accept)(b) Length distribution of MFC accept0 200 400 600 800 1000 1200Particle Diameter(nm)0510152025Frequency (Reject)(c) Diameter distribution of MFC reject0 20 40 60 80 100 120Particle Diameter (nm)051015202530Frequency(Accept)(d) Diameter distribution of MFC acceptFigure 3.6: A Comparison between size distribution of reject and accept ofBEKP-MFC fractionated at 13000 g in one fluid with a 15 Pa yield stress.We started this chapter by benchmarking Madani’s concept using a dif-ferent MFC suspension than what he tested and were able to reproduce hisresults by achieving separation. We then extended his results by estimatingthe yield. In the next section, we will extend his original idea further, usingmultilayer fluids, in order to achieve higher yield values.3.2 Extending the Original Idea Using MultilayerFluidsTo extend the original idea using multilayer fluids, we will first identify thebounds of stable-layered fluids in batchwise experiments using a benchtopcentrifuge. Then various configurations will be examined to improve the40(a) t=0 (b) t=∞Figure 3.7: Highlights of Madani’s concept for fractionation: (a) beforecentrifugation using one fluid (b) after centrifugation. In this method, theseparation is achieved at the top of the cylinder but not at the bottom.separation efficiency in both bidispersed and tridispersed nylon particle sus-pensions.The idea which we would like to explore is if we can improve upon theefficiency of Madani’s concept for the design of a continuous unit. Madani’sconcept can be highlighted in Figure 3.7. Here we see the initially bi-disperseparticles being suspended in a viscoplastic fluid. After centrifugation, thelarge particles migrate to the bottom of the cylinder. Clearly, we haveachieved separation at the top of the cylinder but not at the bottom. Hence,the yield of the separation would be low, and we would need to re-fractionatethe bottom portion.In this section, we would like to test the possibility of increasing the yieldof the separation, immediately, without the need for a second centrifugation.Here we explain two concepts:(a) Two fluids: In this case we utilize the fractionation with a suspensionlayered onto a second fluid (see part (a) in figure 3.8). Once force isapplied, targeted particles move from the upper to the lower fluid.(b) Multiple fluids: Here we would like to examine if we can creat a one-step separation for a tri-disperse suspension. Here, target particlesmove from the upper solution. A portion of the particles stop in themiddle layer. The largest particles proceed to the lower fluid. (seepart (b) in figure 3.8)41(a)(b)Figure 3.8: Extensions to the original separation concept. In (a), a bi-disperse suspension is fractionated into two separate fractions after cen-trifugation. Once the force is applied, the targeted (heavier) particles moveto the lower fluid. In (b), a tri-disperse suspension is fractionated into threefractions in a one-step centrifugation. The lightest particle is trapped in theupper fluid, a portion of particles stop in the middle layer and the largestparticles proceed to the lower layer.The key scientific challenge is to assess the stability of the layered fluidsduring centrifugation. Ideally, the fluids should not mix. There is evidencein the literature that this is possible. We draw hope from the study ofFrigaard and Crawshaw [127] who examined an exchange flow of two initiallylayered viscoplastic fluids under the action of gravity. Given the geometryand notation as depicted in Figure 3.9a, the authors advanced the criterionthat these flows are stable when τy is large enough.As a result the objectives of the work in this section are to(a) Confirm the criteria for the stability given by Frigaard and Crawshaw[127] through experiment.(b) Demonstrate, qualitatively, the potential of fractionation in layeredfluids.423.2.1 Establishing Stable Layered FluidsIn this section we aim to establish a bound for stability, experimentally, toconfirm the procedure given by Frigaard and Crawshaw [127]. We considertwo fluids, namely, a viscoplastic fluid of density ρ(1) and yield stress τ(1)ylayered on top of a Newtonian fluid of density ρ(2). The apparent viscositiesof the two fluid do not need to be considered as this parameter, primarily,sets the time required for mixing and not the criteria for stability. For ourwork, the viscoplastic fluid will always be layered on top of the Newtonianfluid. We do so as the viscoplastic fluid will, eventually, carry the particles tobe separated. Because of this, only two distinct cases need to be considered,i.e. ρ(1) > ρ(2) or ρ(1) < ρ(2). This is shown schematically in Figure 3.9. In(a) the heavier fluid is on top of the lighter fluid, and the fluid will naturallywant to exchange positions due to the buoyancy effect. However, stabilitymay be achieved in this configuration, through the yield stress. A simpledimensional analysis suggests the existence of a static situation whenτ(1)y(ρ(1) − ρ(2)) gD > τy,dl (3.4)where g is the acceleration due to gravity, D is the inner diameter andτy,dl is the dimensionless ”yield number”. In Figure 3.9 b, we expect theconfiguration to remain stable. To examine this hypothesis we tested thestability of Carbopol in a 50 mL centrifuge at various concentrations, layeredonto the water with a clean interface, whose density has been adjusted usingsugar. Both the density stable and unstable configurations were tested.To aid in visualizing the results, a small quantity of rhodamine B dye wasadded to the Carbopol. The centrifuge tube was half-filled with the heavierfluid when vertical and upside down. The lighter fluid was then added atthe top through a small hole at the bottom of the tube, taking care not todisturb the interface. The tube was kept stationary in the density stablevertical position before centrifuging the sample to make sure that it remainsstable under the influence of gravity. Then the samples were placed in abenchtop centrifuge which rotated for one minute. The time was foundto be long enough because samples that were rotated up to three minutesand five minutes showed a negligible difference with the samples which wererotated up to one minute. A qualitative experiment is shown in Figure 3.10.This is initially density unstable, i.e. (ρ(1) > ρ(2)) where the fluids exchangepositions under the centrifugal force. Since the centrifuge operates at anangle to the horizontal, the final interface position is not horizontal. Here,43𝜏𝑦(1), 𝜌(1)𝜌(1) > 𝜌(2)𝑔𝜏𝑦(2), 𝜌(2)𝜏𝑦(1), 𝜌(1)𝜏𝑦(2), 𝜌(2)𝜌(1) < 𝜌(2)Figure 3.9: Schematic of two different possible configurations of layeredfluids. In (a) for yield stress fluid, it is expected that a sufficiently largeyield stress, (τ(1)y ) stops the gravity-driven flow. We anticipate (b) to bestable.for fixed inclination and interface, it must be expected that the dimensionlessyield stress interacts in determining the limits of static stability.Before proceeding further, we need to describe the criterion used to es-tablish stability. We imaged the intensity of the color of the centrifuge tubesto establish an intensity profile as a function of height. We considered thearea of mixing between two fluids under the influence of centrifugal force andany movement of the fluid-fluid interface was not regarded as instability. Weconsidered a case unstable when this area is greater than 30%.Figure 3.11 shows the marginal g-forces for different yield stresses anddensity differences. A line can be drawn to highlight the borders of stablelayered fluid. It is re-emphasized that each point plotted in figure 3.11 cor-responds to a sequence of experiments and represents at least three trials.The results are shown in this figure clearly indicate that the experimentalcharacterization of the (density unstable) static state in terms of stabilitymap is feasible. The theoretical yield stress gives margins of stability whichproportionally changes with changing g-force and density differences at con-stant yield stress. It is expected that a similar set of experiments carriedout for a different diameter or yield stress, would result in similar behaviourto that shown in Figure 3.11. From this, we find that in the density stableconfiguration, the fluids are stable for the range of g-force created by ourcentrifuge. Under initially density unstable case, we find stability to occur44CarbopolWaterWaterCarbopol(a) (b)Figure 3.10: A demonstration of density unstable double-layered fluid. (a)An image of the layered fluid is given before the commencement of thecentrifugal force. The centrifuge tube was first half-filled with the heavierfluid (Carbopol gel) and then sealed and inverted. While in the invertedposition, a small hole was made in the bottom of the tube and used tocarefully fill the lighter fluid, taking care not to disturb the interface. Thesamples were then placed in the centrifuge which rotated for one minute.We performed approximately 300 experiments in which we varied the densitydifference ∆ρ = ρ(2)−ρ(1) ∈ [−0.05, 0.05] kg/m3 and yield stress τ (1)y ∈ [3, 15]Pa. (b) The state of the fluids after the centrifugal force has been applied.The lighter fluid switched position with the heavier fluid (Carbopol).whenτ(1)y(ρ(1) − ρ(2)) gD > 0.37 (3.5)These results are similar to the findings given by Frigaard and Crawshaw[127].3.2.2 Establishing a Separation in Layered FluidsHaving established that, it is indeed feasible to layer fluids and have themremain stable, we now attempt to repeat Madani’s experiment reportedin [8] but with layering. Here we first develop a calibration of the forcerequired for motion of spheres with various initial diameters, in differentCarbopol concentrations. This is shown in Figure 3.12 as an attempt to45Figure 3.11: Stability map of a density unstable multilayer fluid inside a 50mL centrifuge tube when the top fluid has yield stress. The experimentsare conducted at density difference ∆ρ = ρ(2) − ρ(1) ∈ [−0.05, 0.05] kg/m3and yield stress τ(1)y ∈ [3, 15] Pa and constant D. Here, the stable resultsare shown in (◦) and unstable in (×).separate different diameter spheres, initially suspended in Carbopol, layeredover a sugar-water solution. For this experiment, the layered fluids werein a density stable configuration. A schematic of the geometry is shownin 3.12(a) and a qualitative image of the separation is presented in Figure3.12(b). The critical force is calculated using the method described in [8].A comparison with Madani’s results (re-plotted here) shows a similar trendand range for Fc. The difference, in this case, is the method of reporting- our results represent an upper bound of the estimate while Madani [8]results are a lower bound. His results are shown with x in Figure 3.12(c).We continue by examining the separation in a three-layer fluid. Using asimilar procedure to that mentioned above. In this case, we are attemptingto separate three different diameter spheres. Here a higher yield stress solu-tion is layered under a lower yield stress solution. Below these, is a higherdensity sugar-water solution.The top fluid density and centrifugation time were kept constant. Afterchoosing a particle size, the minimum g-force was determined under which46the biggest size particle passes all three fluids. Next, the medium-size par-ticle was chosen and the middle fluid yield stress was changed so that themiddle size particle stopped in the fluid. Finally, we checked to make surethat the big size particle still travels all the way down leaving the small sizeparticle trapped in the top fluid. As shown in Figure 3.13, a separation wassuccessfully achieved. In this figure, a 3, 6 and 12 mm spherical particleswere successfully separated at 120 rpm. The top, middle, and bottom fluidyield stresses were set at 15, 7 and 0 Pa, respectively.Finally, we would like to demonstrate that we are able to create a sep-aration of poly-disperse suspension by fractionation, sequentially. Here weused a nylon fibre suspension with three different particle sizes and createda sequential separation as shown in Figure 3.14 and 3.15. The suspensionused was a 0.1% nylon fibre suspended into Carbopol solution with yieldstress about 10 Pa. Similarly, the bottom fluid density was adjusted by theuse of the sugar-water solution. The size distribution test was done using aMalvern Mastersizer unit as explained in the previous section.Figure 3.15 shows the measured particle size distribution. The particlesize of the original sample was 160 µm, which decreased to 46 µm after thefirst stage of fractionation. The second stage of the fractionation was con-ducted using the same procedure but at an increased g-force which causeda decrease in the particle size by more than a half and was measured to be22 µm. We continued by examining the yield and attempted to measure themass in the bottom portion of the centrifuge (only at the second stage ofthe sequential procedure) and compared it to the results obtained from onefluid technique. After careful recovery of several replicate samples, we wereable to establish a reasonable estimate of the mass yield. The results showedthat the yield is 24%(±3) at the top and 76%(±5) at the bottom when weused the ”two fluids” technique. These values are found to be 12%(±2)at the top and 88%(±6) at the bottom portion when only the ”one fluid”technique was employed. This is due to the presence of the small particlesin the bottom portion of the centrifuge tube before the commencement ofthe centrifugal force.3.3 Batchwise Fractionation in Multilayer FluidsWe continue by examining the layered separation technique on three differentsuspensions related to the pulp and paper industry:1. A waste stream of pulp mill in order to recover fibre47Figure 3.12: (a) A schematic of the geometry used in the batchwise cen-trifugal tube. (b) A representative example of a separation of 3 mm and9 mm diameter spheres. In the left panel, the spheres were placed at thetop of the gel and then subject to an acceleration of 75 g for two minutes.In the right panel, we see that the large size spheres have migrated to thebottom of the tube. In this case, the bottom fluid is a sugar-water solutionconsidered to be a Newtonian fluid. The yield stresses are set at τ(1)y = 15Pa and τ(2)y = 0 Pa and the density of each fluid is ρ(1) = 1002 kg/m3 andρ(2) = 1010 kg/m3. In this study, the yield stress was determined using aKinexus Ultra rotational rheometer (Malvern Instruments, Worcestershire,United Kingdom) rheometer. (c) A calibration curve of the critical force toinitiate motion for isolated spheres both in the batchwise and continuousdevices. These data as collected under density stable conditions. For thebatchwise case, we placed a single particle in a 50 mL centrifuge tube filledwith the same fluids as in (a) and then spun at a fixed angular velocityfor two minutes in a benchtop centrifuge (Eppendorf 5804) with 10 rpmstep sizes. At the end of the experiment, the position of the sphere was in-spected and if still in the top fluid then the test was repeated by increasingthe speed of the centrifuge. The procedure continued until the particle ob-served in bottom fluid and then Fc was calculated. For the continuous case,we suspended 100 of same size spherical particles in 50 L of 0.16% Carbopolsolution (τ(1)y = 15 Pa, ρ(1) = 1001 kg/m3). The outer fluid was a 0.16%Carbopol solution (τ(2)y = 15 Pa, with a density of 1010 kg/m3 through theaddition of sugar. Centrifugation proceeded at the range [10-1750] rpm andat a flowrate (Q1, Q2) = (20, 40) mL/s. The particles were observed at theoutlet of the device until all the particles were removed from the inner fluid,then the rotational speed was recorded. This method will be described inthe last chapter in more detail. 48(a) Before (b) AfterFigure 3.13: A demonstration of three-layer separation of 3, 6, and 12 mmdiameter spheres. The spheres were initially suspended in 0.16% Carbopolsolution (τ(1)y = 15 Pa, ρ(1) = 1002 kg/m3) which was layered on a 0.1%Carbopol solution, colored pink through use a rhodamine dye, (τ(2)y = 7 Pa,ρ(2) = 1010 kg/m3). The bottom fluid was a 2% sugar water solution withρ(3) = 1020 kg/m3. (a) An image of the initial state where the three differentspheres are stably suspended in fluid 1. (b) An image of the position of thespheres after 2 min of centrifugation at an acceleration of 460 m/s2 (about46g)2. Northern Bleached Softwood Kraft pulp to recover MFC (NBSK-MFC)3. CarboxyMethyl Cellulose in order to recover small fibres (CMC)Each of these studies were qualitative in nature in which we demon-strated the feasibility of the two layer process, and the quality of the sus-pension.3.3.1 Waste Stream RecoveryIn the first trial, we attempted to separate a waste pulp stream obtainedfrom Celgar pulp. The suspension had previously been cleaned by fourstages of Noss cleaner, and the sample recovered was directly before dis-charge. The sample contains fibre with a length distribution given in Figure49Feed Continuous lineTop PortionDashed lineTop PortionDotted lineBottom PortionBottom PortionFigure 3.14: A schematic of the fractionation methodology to achieve asequential separation of a 0.1% (wt/wt) nylon fibre suspension. The nylonfibre suspension was composed of equivalent length fibres (160 µm) but ofthree different diameters 14, 27, and 43 µm. The nylon fibres were suspendedin 0.12% Carbopol solution (τ(1)y = 10 Pa, ρ(1) = 1002 kg/m3) which waslayered on a 2% sugar solution (ρ(2) = 1020 kg/m3) in a density stableconfiguration. Centrifugation proceeded at an acceleration of 70000 m/s2for two min in the first step and then 110000 m/s2 for two min in the secondstep.3.17. A Fibre Quality Analyser (www.optest.com) was used to obtain thelength distribution. The major components, other than fibres, were sandand seemingly bark (see Figure 3.16).The separation proceeded by mixing 0.1% (wt/wt) of the suspension into0.16% (wt/wt) Carbopol, and layering over a 30 mL sugar solution. Thesugar-water solution was prepared by mixing 0.3% of the oven-dried sugarinto the water. The suspension was placed into the centrifuge at 1600 g for5 minutes. The procedure is shown in Figure 3.18.We observed that heavier sands moved to the bottom and fibres remainedat the top. Three aspects of the suspension are examined to determine howthe separation mechanism was performed. First, we were able to recover theidentical fibre length distribution as in comparison to the initial pulp (andmarket pulp, see Figure 3.17). Second, we compared the tensile strength ofa composite hand-sheet made from these fibres. We found that the marketpulp has a strength of 27.7 kNm/kg whereas the recovered fibre was 23.7kNm/kg. Finally, we observed that the top and bottom sections of the cen-trifuge tube exhibited a distinct difference in composition (see Figure 3.19).50101 102 103Particle Size ( m)024681012Volume%First stageSecond  stageOriginalFigure 3.15: The particle size distribution of original and fractionated sam-ples of a poly-disperse nylon fibre suspension. After the first step of cen-trifugation, the nylon fibres were sampled from the top layer of the tube, todetermine their size. After the second centrifugation at a higher rate, weachieved excellent separation with only small fibres remaining in the sus-pension. The continuous line represents the original sample whereas thedashed and dotted lines represent the top portion of samples after the firstand second stages of fractionation, respectively.3.3.2 Fractionation of NBSK-MFCIn this study, we refined a market NBSK pulp in an LC-refiner up to 1000kWh/t energy. This process, as explained before, changes the morphology ofthe fibres (see Figure 3.20 for SEM images after refining). Then a suspensionof 0.1% (wt/wt) consistency of the produced ”MFC” (we call it NBSK-MFCfrom now on) was fractionated in a 0.16% Carbopol solution at g-forcesranging from 1000-13000 for 5 minutes using two fluids technique. Similar towhat is described for BEKP-MFC in Section 3.1.1, the gel point (explainedin section 3.1.1) was measured by conducting a sedimentation test. Thegel pint of NBSK-MFC was found to be about 0.2% (±0.03%) consistency,hence, any consistency below 0.2% will be in the dilute state. The bottomfluid density was adjusted again using the sugar-water solution to achievedensity stable multilayer fluid. After centrifugation, the top fraction wasanalyzed using Mastersizer, and the rest was retained for further testing.51(a) (b)Figure 3.16: Characterization of the particle suspension obtained from thewaste stream of a pulp mill. (a) Scanning Electron Microscopy (SEM) im-ages of debris and (b) fibres in the waste stream. Visual observations revealthe presence of regular fibres mixed with debris.0 2 4 6 8Length Weighted(mm)00.511.522.5FrequencyOriginalAcceptFigure 3.17: Illustration of typical fibre size distributions from the fibrequality analyzer (FQA). Blue dots represent the frequency of original sus-pension and the circle points represent the frequency of suspension after thecommencement of the centrifugal force (Accept).52Waste Pulp2 Fluids@ 1600gSand and Debris 14% (wt/wt)Accept fibres86% (wt/wt)Figure 3.18: Schematic of the procedure used to separate sands and debrisin the waste stream of a pulp mill, from lightweight papermaking particles.(a) (b)Figure 3.19: Optical images of the top (a) and bottom (b) portion of cen-trifuge tube after fractionation. A distinct difference in the composition canbe seen between the top and bottom.53(a) Unrefined (b) 1000 kWh/tFigure 3.20: Characterization of the particle system. (a) is an SEM imageof unrefined NBSK pulp suspension. This suspension is then highly refinedby a disc refiner up to 1000 kWh/t. (b) is an SEM image of this suspension.Figure 3.21 shows the particle size distribution of two different samples,the pulp which was refined up to 1000 kWh/t (original) and the samplefractionated at 13000 g (fractionated). As a result of centrifugation, thelarge unrefined particles should move to the bottom portion leaving thesmaller particles at the top of the tube. Note that due to the large numberof fines in the refined suspension, the FQA was replaced with a MalvernMasteresizer to be able to detect fines and small particles in the suspension,which may introduce artifacts if the sample is fibrillated.It can be seen from Figure 3.21 that the centrifugation shifts the sizedistribution to the left, removing more of the big fibres from the top portionof the suspension. A visual comparison of the particles in the original andaccept portion can be made using SEM images in Figure 3.22.The benefit of fractionation can be evaluated by an indirect method, i.e.tensile strength measurement. It has been long thought that the strengthof paper can be controlled by the fibre strength, bonding degree of the fibrenetwork and the strength of the bonds. Mechanical interlocking due to anincrease in the surface area of the particles plays an important role here[19, 29]. Due to MFC large specific surface area, well-dispersed cellulosefibrillated fibres improve the bonding between fibres by distributing thestress peaks under loading. The more fibrillated the particles and the smallerthe particles, the better is the contact area. We examined the benefit offractionation by reporting this indirect measure, the tensile strength gain,when re-introduced into market pulps (both NBSK and TMP, See Figure54500 1000 1500 2000Particle Size ( m)0123456Volume %OriginalBatch-wiseContinuousBauer McNettFigure 3.21: Particle size distribution of NBSK-MFC suspension refinedup to 1000 kWh/t (Original). Included here is particle size distributionafter fractionation in two fluids at 0.1% consistency, and subject to theacceleration of 130000 m/s2 (13000 g) acceleration for two minutes. Inthis case, the bottom fluid is a sugar-water solution considered to be aNewtonian fluid. The yield stresses are set at τ(1)y = 15 Pa and τ(2)y = 0 Paand the density of each fluid is ρ(1) = 1002 kg/m3 and ρ(2) = 1010 kg/m3.The third graph is the particle size distribution of the samples obtainedafter fractionation in a Bauer McNett classifier. TAPPI T233 standard wasclosely followed and fibres retained in the last stage were collected. Thecontinuous line is the result of fractionation in the continuous device whichwill be explained later in this work.55(a) (b)(c) (d)(e) (f)Figure 3.22: Scanning Electron Microscopy (SEM) images of the highlyrefined NBSK pulp suspension refined up to 1000 kWh/t (NBSK-MFC). In(a) and (b) the original particles are shown before fractionation. (c) and (d)are the particles collected from the bottom portion of the centrifuge tube,which is called ’reject’. Sample particles collected from the top portion or’accept’ are shown in (e) and (f).560 2 4 6 8Content Percentage (%)30405060708090Tensile Index (kNm/kg) OriginalFractionated in two fluidsR100 Bauer McNettR200 Bauer McNett(a) BEKP-MFC in kraft Pulp0 2 4 6 8 10Content Percentage (%)2030405060Tensile Index (kNm/kg) OriginalFractionated in two fluids(b) BEKP-MFC in TMPFigure 3.23: A comparison between different percentages of the fraction-ated and non-fractionated MFC re-introduced to NBSK and TMP pulp.Panel (a): The changes in the tensile strength of MFC reinforced compositehandsheets at different percentages. Included here is the tensile strengthof handsheet reinforced by adding 5% MFC of R100 (retained behind mesh100) and R200 of Bauer McNett classifier. Panel (b): The tensile strengthof a composite handsheet made from the same MFC but introduced to TMPpulp.3.23). As shown, both pulps experienced a significant gain in the tensilestrength. However, the incremental advantage of using this technique wasclearly evident with the NBSK. Included in this figure is a separation of theMFC using Bauer-McNett separator, the gold standard for lab separations.No significant increase in the tensile strength was seen.This finding is consistent with the size distribution comparison betweengel fractionation and Bauer McNett classifier. Figure 3.24 shows the parti-cle size of the fractionated samples using both the gel and Baurer McNettfractionation techniques. It is important to note that the Bauer McNettclassifier misses a large portion of the ”small” particles in the fractionationprocess, possibly due to its pore sizes. We found that the gel fractionationtechnique resulted in a more significant drop in the particle size, comparedto the Bauer McNett technique. On the other hand, the size distribution inour technique is narrower compared to the standard Bauer McNett method.Thus, more control on the final product is available in this technique.57Original 28 48 100 200Mesh Size0100200300400500D (m)(a) Bauer McNett0 5000 10000 15000R 2/g50100150200250300350D (m)(b) Gel FractionationFigure 3.24: Fractionation of NBSK-MFC using two separate methods. Inpanel (a) the particle size of the fibres retained at each screen of a BauerMcNett classifier is shown. In panel (b) the particle size is reported for thesame suspension which is fractionated using gel fractionation in batchwisemode and two fluids.3.3.3 Carboxymethylated CelluloseSeveral strategies are proposed in the literature as pretreatment methodsin the MFC production process, e.g. enzymatic pretreatment [157], andcarboxymethylation [158]. Carboxymethylation has a substantial effect onthe liberation of fibrils in the process of MFC production [158, 159]; how-ever, Carboxymethyl cellulose (CMC) can also be referred to a water-solublepolymer achieved from the fibre (as a final product and depending on thedegree of polymerization).The last particle system which was chosen for fractionation is carboxymethy-lated particles to assess the methodology explained earlier in this chapter onthe possibility of fractionation in two fluids in a sequential procedure whichis demonstrated in Figures 3.14 and 3.15.We used the sequential fractionation technique at 2000 and 3000 g-forceand continued with ”one fluid” technique to remove the soluble part of CMC.As a result, the size of the large and small particles was measured to be 208µm and 130 µm, respectively. Figure 3.25 shows the state of the suspensionbefore fractionation and the fractionation procedure is depicted in Figure3.26.Figure 3.27 shows the particle size distribution of the accept and re-ject portion of the suspension after centrifugation. Clearly, fractionation isachieved as the top portion contains no particles larger than 410 µm. Fig-58Figure 3.25: Optical image of Charboxymethylated fibres before fractiona-tion which contains a wide range of particle size.CMC suspension2 Fluids@ 2000Top Portion2 Fluids@ 3000Top Portion1 Fluid@ 13000Bottom PortionSoluble PartTop PortionBottom PortionParticle size=155 µmParticle size=208 µmParticle size=130 µmFigure 3.26: A schematic of the procedure which we used to fractionateCMC particles. Both ”two fluids” and ”one fluid” strategy are used in asequential method to obtain fractionation results.5902468100 200 400 600 800Volume %Particle Size (µm)Figure 3.27: The particle size distribution of original and fractionated CMCsamples. The continuous line(—) is the original size distribution and thedashed line(- - -) is the result of two-stage fractionation in two fluids, asdemonstrated schematically in Figure 3.26.ure 3.28 shows the optical images of the top and bottom portion of CMCsamples. At the top portion, the particles are smaller than the particlespresent in the pre-centrifugation samples.3.4 SummaryWe started this work by benchmarking Madani’s original method using adifferent MFC suspension than what he tested. Indeed, we were able, in astraightforward manner, to reproduce Madani’s results by achieving sepa-ration. Here we fractionated a hardwood (Eucalyptus) MFC (BEKP-MFC)manufactured by Suzano in their pilot plant facilities in Brazil. The MFCwas produced through mechanical refining with the final particle size of 128µmeasured by Malvern Mastersizer 2000. We followed the experimental pro-cedure reported by Madani [8], generated a calibration curve and showedthat the average fibre size of the fractionated portion decreases linearly withcentrifugal force and time. After careful recovery of a number of replicatesamples, we could establish a reasonable estimate of the yield Y represent-ing the ratio of the mass recovered to the initial mass. We found that yielddecreases linearly with particle size.In the second section, we tested to see if we can extend Madani’s batch-wise procedure and include layering. We began by examining the effect60(a) Top (b) BottomFigure 3.28: Optical images of the Carboxymethylated particles taken fromthe top portion of the second stage.of density difference in the layered fluids on interface stability. We foundthat when the density of the lower fluid is greater than the upper fluid,i.e. ρ(2) > ρ(1), the fluids are stable and do not mix during centrifugationover the acceleration of 130000 m/s2 (13000 g) applied for approximatelyfive minutes. More importantly, when the fluids were ordered in oppositeconfiguration, i.e. when the upper fluid had a greater density than the lowerfluid (ρ(2) < ρ(1)), stable operation was more problematic. Under this config-uration, we characterized the stability of the interface by using a rhodaminedye in the upper fluid (only) and examining the change in its position af-ter centrifugation. We observed that stable operation can only be achievedwhenτ(1)y(ρ(1)−ρ(2))gD > 0.37. This finding is similar to a theoretical estimatereported by Frigaard and Crawshaw [127] for an exchange flow of viscoplas-tic fluids. When we conducted experiments outside of this bound, the fluidswere observed to mix with the mixing-time dictated by apparent viscosityof the fluid. Finally, when operating within this bound, we repeated thecritical force measurements by Madani et al. [32] methodology and wereable to obtain similar results. We noticed a difference which was due to themethod of reporting - our results represent an upper bound of the estimatewhile Madani et al. [32] results are a lower bound. In the next series ofexperiments, we asked the question if there are unique operating strategiesoffered by layering. We performed two separate experiments. In the firstexperiment, we explored a time-varying centrifugal force and applied a fixedrotational rate and then increased its value to a higher rate after a knownlength of time. By doing so we successfully separated a tri-disperse nylon61fibre suspension and achieved excellent separation with a higher yield, com-pared to one fluid technique. In perhaps the most unique demonstration ofthis layering technique, we separated a tri-disperse suspension by using threefluid layers. These initial findings points to the potential novel operatingmethodologies for this technique.In the last section, we performed several qualitative tests to assess theusefulness of the gel fractionation technique. Here we demonstrated thatindeed we could achieve separation simply and robustly in a layered fluid.In perhaps the most significant finding was that our technique was able tofractionate an MFC to achieve a more considerable gaining strength thanthat fractionated in the current lab standard (Bauer-McNett).62Chapter 4Process and MechanicalDesign of Continuous DeviceIn the previous chapter, we demonstrated that the separation can be achievedusing two viscoplastic fluids. The results were however based upon batch-wise testing. A continuous process must be developed for this method to gainindustrial significance. Flowrates, pressure drop within the device, requiredcentrifugal force (rpm), interface position of two fluids, the residence time,settling time and the device length are inputs to the design. These need tobe determined for various combinations. Throughout this chapter, we de-sign a fractionator and demonstrate how to select its key components. Webegin with an introduction to address the essential design elements required,followed by a section to elaborate on the challenges. Designed componentsare explained in the next section. The chapter is concluded with the finaldesign and its corresponding experimental flow loop.4.1 IntroductionFigure 4.1 shows a simple configuration for a micro-size particle fractiona-tion device that utilizes the ”two-fluids” method and an external force as amanipulator. SPLITT, introduced by Lenshof and Laurell [146], is a simpleactive method that consists of three elements: 1-an external force, 2- a ’cleanfluid’ with no particles, and 3- a particle-rich ’dirty’ fluid’. It has two inlets,one stream is to introduce particles and the other is for carrier or ’clean’fluid, and one splitter that separates two streams up to the region in whichthe external field acts. The effect of the field is more significant on the largerparticle than that on the smaller ones. Thus, the larger particles move intothe clean fluid and hence, separation occurs[146]. The SPLITT method, inmany ways, represents the basics of our thoughts on a continuous separationmethod. We combine the improved novel fractionation method explained inthe last chapter and SPLITT method ( centrifugation acts as the externalforce). This extends the batchwise separation method into the particle sep-63Figure 4.1: Split-flow lateral-transport thin (SPLITT) separation introducedby Lenshof and Laurell [146].aration in layered spiral Poisouille flow. A rotating annulus is replacing thechannel to generate centrifugal force. Building on the presented results inthe last chapters, we propose a design and use of Madani’s modified methodto examine the possibility of continuous fractionation.The new configuration requires layered fluids flow next to each otherwithout mixing. We know that stable viscoplastically lubricated flows canbe achieved in parallel multilayer flows of two yield stress fluids [122]. Thisstability was observed at certain speeds for two viscoplastic fluids or oneviscoplastic fluid and one Newtonian fluid. This occurs when an unyieldedplug region existed on one side of the interface. Thus, our design hypothesisbuilds upon one more literature finding: Multilayer viscoplastic fluid flow ispossible and can hold a stable interface if at least one of the fluids is un-yielded. A comprehensive numerical study of the spiral multilayer Poisuilleannular flow for the purpose of fractionation is also presented by Al-Shibl[144] and explained in Chapter 2 of this document. In brief, he focused onthe stability of the flow in conjunction with the fractionation requirementand showed that spiral multilayer Poisuille viscoplastic flow can be stablefor both annulus and continuous fractionation geometries. He argued thatdensity current is not a factor in density stable and iso-dense cases. He re-ported entrance length of the annulus and reported that to be shorter thanthe equivalent Newtonian flow. These will be discussed in more details inthis chapter.4.2 Essential Elements of the DesignFigure 4.2(a) illustrates the schematic of our initial design of the fractionatordevice. In this design, inner fluid or ’dirty fluid’ contains particles andenters the device from the side and flows into the annular chamber. The64Figure 4.2: (a) A schematic of the key components required for the designof the continuous device. In this device we refer to fluid (1) as the innerfluid (2) as the outer fluid. Particles are introduced into the system influid (1). If the applied centrifugal force is greater than the critical force,they settle in the radial direction and are received in fluid (2). If not, theycontinue their travel in fluid (1). (b) A cross section of the engineeringdrawings to build the continuous device. (c) The computational domainand the simulation of concentration profile of the layered solutions [144].The density maps represent the concentration of the fluids. Red in thiscase is fluid (1) and Blue is fluid(2). This simulation was conducted withR = 0.0476 m, κ = 0.368, ω = 40.22 rad/s. The rheological properties of thefluid were set at τ(1)y = 10 Pa, µ(1) = 1.083 Pa.s and τ(2)y = 6 Pa, µ(2) =1.083Pa.s. (d) An image of the laboratory device.65properties of this fluid are shown with superscript (1). The other fluid,’clean fluid’, enters also from the side of the device then finds its way tothe annulus. The separation zone is the region between the bottom splitterand top splitter. The two fluids are pumped through the device, and theirflowrates can be controlled. Once the inner and outer fluids reach two sides ofthe splitter, they flow in the parallel direction and then enter the centrifugalseparation zone of the rotor. We form a vertical spiral Poisuille flow betweenthe top and bottom splitter. The big particle flowing in the plug regionof the inner flow will move from the inner fluid to the outer fluid due tothe centrifugal force. The separated bigger particles move outward andflow upward before exiting through the reject pipe. The separated smallerparticles remain stably trapped in the plug region and move vertically withthe fluid. Eventually, both small and big particles move out of the machinedue to the applied pump pressure.4.3 Design ChallengesBesides the conditions specified above, other additional points must be con-sidered to design the fractionator.1. We need to keep the shear stress as low as possible while flowing insidethe machine so that the particles stay in the plug flow region, e.g. localflow field near the exit.2. The chamber has to be pressurized to avoid any free surface. Thus, asealing system is required.3. Particles will not be going against the gradient,i.e., the particles haveto move from small radii to big radii at all times. Thus, the chamberrequires sealing at its smallest radius near the entrance and the biggestradius near the exit.4. There are manufacturing and sealing limitations, e.g. fluid entrancecan not be the same as that in Figure 4.2(a).4.4 Key ElementsSplitter or SeparatorWe want two fluids to stay unmixed before the separating zone so the splittertakes place between inner fluid and outer fluid. This part has to be designed66in a shape to introduce two fluids undisturbed to each other. Feeding twofluids using a long separator smooths out flow fluctuations and provides amore constant flow rate to the separating zone of the machine. The Nu-merical simulations of Al-Shibl [144] investigated the interface position andconfirmed that under fully developed conditions the interface position shouldnot be affected by the g-force (unless there is a density difference betweenthe two fluids). The computational domain and the simulation of concentra-tion profile of the layered fluids are shown in Figure 4.2(c). He showed thatthe interface position is not dictated by the sizes of the inlet jets where theyare introduced. Additionally, the presence of the outlet separator has animportant effect on the fractionation efficiency. It is not surprising that theinterface position changes with the flow-rate ratio. Furthermore, as shownin Figure 4.2(c), the interface is located at a radial position slightly abovethe distance of the outlet splitter. He showed that this occurs due to thedifference between shear stress near the separator wall (high shear stress)and around the middle of the outer fluid’s outlet gap (low shear stress)[144].Figure 4.3 shows the interface position as a function of flow-rate ratio.The flowrate needs to be chosen such that the interface in the fully developedregion of the separation zone is radially located below the outlet separator.Such flowrate enhances the fractionation efficiency by making sure smallparticles do not leave the device in reject (or big particles from accept.)Separating ZoneThe separating zone is a determining factor for fractionator throughput. Assuch, it plays a key role in scaling-up any fractionator design. The volumeof this zone is an essential design feature where separator centrifuges usuallycharacterized by the diameter of the rotor. The maximum ratio for rotorlength relative to the inside diameter is typically 2.2 as reported by Leonard[113].The entry length needs to be taken in to account if the fully developedflow is considered. This length for the inertial flow is the distance fromthe inlet (tip of the separator in this case) where the flow field no longerchanges in the axial direction and is called the fully developed region. Thevelocity profile and wall shear stress are both constant, and the pressuredrop varies linearly with the axial direction downstream of the entry length.The criterion to estimate the entry length can be set at which the axial flowvelocity reaches 98% of its fully developed value. Figure 4.4 shows the entrylength required for fully developed laminar pipe flow of yield stress fluids[160]. The entry length of an annulus was found to be shorter compared to670.5 1 1.5 2 2.5 3Q1/Q20.60.650.70.750.80.85Interface Position (r i)Figure 4.3: Interface position at different flow-rate ratio obtained from [144]Newtonian fluids (in the same annulus) at the same Reynolds number [144].The entry length was found to be approximately 0.32 for two fluids.Assuming Re ∼ 1 and the geometrical and fluid properties as Table 4.1,the mean velocity 0.0166 m/s and the flowrate inside the annulus will be6.8 L/min for each stream. Thus, the entry length is estimated to be Le =0.32× 0.060 = 0.0192 m which seems reasonable. We choose the separationzone to be 150 mm to maintain the aspect ratio.We also calculated an estimate for the range of the flow-rate. Our targetparticle is a spherical nylon particle with 1 mm diameter and a density of1134 kg/m3. After calculating the residence time, the maximum flow-ratewhich allows the particle to move radially to the outer fluid was determinedto be around 20 L/min.SealingAs discussed previously, the chamber has to be pressurized to avoid any freesurface due to the centrifugation force. Seals must be selected in such away that the maximum torque on the shaft does not exceed the strengthof the rotating parts. This was found to be a very challenging part of thedesign due to the large sealing surface and the number of required seals.The details of the sealing are explained in Appendix A.68(a) (b)Figure 4.4: (a) Entrance length required for fully developed laminar pipeflow of yield stress fluids the entry length is shown with XD [160] (b) En-trance length for Newtonian and yield stress fluids in an annulus of radiusratio of 0.8. The entry length is shown with Le [144].Table 4.1: Fluid and geometrical propertiesProperty Unit ValueFluid Density m3/kg 1000Plastic Viscosity Pa.s 1Annuls Inner Diameter m 0.0421Annulus Outer Diameter m 0.1023Mechanical PowerMaximum torque and nominal rpm are used for the mechanical power cal-culations. The selection of the proper sealing system led to a reasonabletorque required for rotation. The details of the calculation are presented inAppendix A. The von Mises stress and displacement of the shaft calculatedand checked for failure using the Solidworks design tool. Details are alsopresented in Appendix A.69PD Pump PD PumpFlow MeterFlow Meter“Dirty” Tank Clean TankFlow MeterFlow MeterAccept RejectFigure 4.5: A schematic of the flow loop4.5 Device DescriptionFigure 4.2(b) shows a cross-section view of the inside of the device. Moredetails are given in Appendix A, but in brief, the device is designed tobe in a vertical position, the inner and outer fluids entrances are designedto address the aforementioned design challenges. The bottom separator isconnected to the inner fluid pipe and the top separator is attached to theshaft. Figure 4.2(d) illustrates the constructed device, driving motor andthe supporting structure. The motor is mounted directly on the device shaftwhich is a 3 phase, 5 hp, 1750 rpm controlled by a variable frequency drive.4.6 Flow LoopThe flow loop consists of two positive displacement pumps (www.seepex.com)and two 65 L tanks of both ’dirty’ and clean fluids. Given Re ∼ 1, settlingtime of a 1 mm nylon spherical particle and thus its residence time, thepump range were selected to be between 0.15 L/min to 2.5 L/min. Themaximum entry length has to be about 20 mm as calculated before. Theflowrates are monitored and measured using two low flow rate flow-meters(www.omega.ca). The flow-meters range selected to cover the pump flowraterange. A schematic of the flow loop is shown in Figure 4.5.70The device pressure drop is measured using an Omega pressure trans-ducer (www.omega.com). Both the pressure and flow-rate data are stored ina matrix from each individual sensor and are outputted to a text file when”save data” button is activated in the Labview interface. The rotationalrate of the driver is controlled manually by the VFD (Variable FrequencyDriver) indicator.4.7 SummaryWe decided upon a centrifuge with an outer radius of R = 5 cm controlled bya variable frequency drive, and mechanically balanced, so that the rotationalrate can be set as 1750 rpm. The flow of each inlet fluid is generated by avariable-frequency driven (VFD) positive displacement pump from an inletreservoir of approximately 65 L capacity to an outlet reservoir of the samecapacity. The pump can provide a maximum flow rate of 40 mL/s, withwater as the working fluid, and with set the length of the device L = 15cm to achieve an adequate residence time to achieve separation. For 0.1 %(wt/wt) feed suspension, we anticipate a production rate of 24 kg/d. Withthese estimates, we created the engineering drawing for the prototype anda cross-section of this is shown in Figure 4.2(b)71Chapter 5Fully Developed Flow inContinuous DeviceThe design of the device was based on the assumption that the stress state ofthe interface is only criteria for flow stability in an annulus. An unansweredscientific question here is about the bounds of stability and how it changesdue to the addition of a centrifugal force to the pressure-driven annularPoiseuille flow. In this part, we examine the flow in the device, where,internal and external walls are rotating to create the centrifugal force. Theflow is analyzed assuming the fully developed flow conditions and under anaxial pressure gradient. This analysis will help us to choose proper rheologyand flowrates for the inner and outer fluids to achieve a better fractionation.It also can provide insight into fluid behaviour, particularly when the axialflow is combined with solid body rotation.Throughout this chapter, we present the work done in analyzing the fullydeveloped flow field inside the device. First, two research works publishedon the spiral Poiseuille flow are highlighted. Then the rheological modeland governing equations are reviewed. Finally, the solution methodologyand results are presented. The difference between our work and previouslypublished work of Madani [8] and Al-Shibl [144] is the difference in the rhe-ology of the fluids and also a different operating condition that we intendedto run the device.5.1 BackgroundFully developed fluid flow in a rotating annulus with an axial pressure gradi-ent of a Bingham plastic is investigated by Madani [8]. He reported that thewidth of the plug region is not diminished with the rotating rate. He alsoreported that the position of the yield surfaces depends only on the Bing-ham number and the plug region is not affected by the swirl component(Bingham number is the ratio of yield stress to viscous stress). In an earlierstudy, Bittleston and Hassager in one fluid [115] combined the rotation of72AAwzSECTION A-ASCALE 1 : 2R kRrA AB BC CD DE EF F8877665544332211DRAWNCHK'DAPPV'DMFGQ.AUNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES:   LINEAR:   ANGULAR:FINISH: DEBURR AND BREAK SHARP EDGESNAME SIGNATURE DATEMATERIAL:DO NOT SCALE DRAWING REVISIONTITLE:DWG NO.SCALE:1:5 SHEET 1 OF 1A3WEIGHT: Assembly for stability analysisFigure 5.1: A cross-section view of the fractionatorthe inner cylinder and the pressure gradient, and considered the annularflow of Bingham fluids. They confirmed that at sufficiently large Binghamnumbers, i.e. large ratios of the yield stress to the axial pressure gradient, aplug zone existed near the stationary (outer) wall. Moreover, it was claimedthat no plug region formed when the inner wall moved faster than a ’criticalrate’. This finding is in support of our choice of creating centrifugal force byrotation both the inner and outer walls. Later, Al-Shibl [144] extended thework for two isodense Bingham fluids in spiral Poiseuille annulus. Here weuse the method introduced by Bittleston and Hassager which later extendedby Madani and also Al-shibl to solve the flow field for two Herschel-Bulkleyfluids.5.2 Fully Developed Problem: Spiral PoiseuilleFlow in AnnulusFigure 5.1 presents the fraction geometry of annulus with the inner andouter radii of κR and R respectively , where 0 < κ < 1.We consider a multilayer flow where two or more Herschel-Bulkley flu-ids flow with their interfaces aligned parallel to the flow direction. Eachindividual fluid has unique rheological properties. The Herschel-Bulkley flu-ids considered have the consistency index Kˆ(m), the power-law index n andyield stress τˆ(m)y for each fluid m=1,2,3.... The location of each fluid can bedefined apriori of its upper boundary rml . Hence, each layer is defined in theregion (r(m−1)l , rml ). For simplicity in the analysis we drop the superscriptm and assume that the properties vary as a function of radial position only.Let u the velocity vector,τ the stress tensor and γ˙ the rate of stress tensorwhich are defined as73γ˙ =√12γ˙ : γ˙ and τ =√12τ : τ (5.1)Hereinafter, dimensional parameters are presented with a hat notation,while the parameters without hat notation will be non-dimensionalized. Thebest rheological model for Carbopol is the Herschel-Bulkley model, whichcan be written as follows:{ˆ˙γij = 0 τˆ ≤ τˆyτˆij =( τˆyˆ˙γ+ Kˆ ˆ˙γn−1)ˆ˙γij τˆ ≥ τˆy (5.2)The momentum equation for a fully developed laminar flow with rotationcan be written as,ddrˆ(rˆ2τˆrθ)= 0 (5.3)1rˆddrˆ(rˆ ˆτrz)= Gˆ (5.4)where Gˆ is the pressure drop per unit length. The norms of ˆ˙γij and τˆij areˆ˙γ =(12∑ˆ˙γij ˆ˙γij) 12=1√2(ˆ˙γ2rθ + ˆ˙γ2rz) 12 (5.5)τˆ =(12∑τˆij τˆij) 12=1√2(τˆ2rθ + τˆ2rz) 12 (5.6)whereˆ˙γrθ = rˆddrˆ(uˆθrˆ)(5.7)ˆ˙γrz =ddrˆ(uˆz)(5.8)If we scale the equations using the following characteristic valuesrˆc = Rˆ Kˆc = Kˆ(1) (5.9)uˆc =√(κωˆRˆ)2+(GˆRˆ(n+1)Kˆ(1))2/nτˆc = Kˆc( uˆcRˆ)n ˆ˙γc = uˆcRˆ(5.10)74The equations in dimensionless form reduce toddr(r2τrθ)= 0 (5.11)1rddr(rτrz)= G (5.12)τˆij =(τˆyKˆc(uˆc/Rˆ)nKˆc(uˆc/Rˆ)nˆ˙γuˆc/Rˆuˆc/Rˆ+Kˆ ˆ˙γn−1Kˆc(uˆc/Rˆ)n−1Kˆc(uˆc/Rˆ)n−1) ˆ˙γijuˆc/Rˆuˆc/Rˆ(5.13)τˆij =(B.Kˆc(uˆc/Rˆ)n−1γ˙+Kγ˙n−1Kˆc(uˆc/Rˆ)n−1)γ˙ij(uˆc/Rˆ) (5.14)τˆij = Kˆc(uˆc/Rˆ)n(Bγ˙+Kγ˙n−1)γ˙ij (5.15)τij =(Bγ˙+Kγ˙n−1)γ˙ij (5.16)n and K vary with fluids 1,2,3,... so similar to B, are a function of r. Hence,the dimensionless form of the Herschel-Bulkley model is:{γ˙ij = 0 τ ≤ B(r)τij =( B(r)γ˙ +K(r)γ˙n(r)−1)γ˙ij τ ≥ B(r) (5.17)γ˙ =(12∑γ˙ij γ˙ij) 12=1√2(γ˙2rθ + γ˙2rz) 12 (5.18)τ =(12∑τijτij) 12=1√2(τ2rθ + τ2rz) 12 (5.19)whereγ˙rθ = rddr(uθr)(5.20)γ˙rz =ddr(uz)(5.21)with the following dimensional groups75G =ˆGRˆτˆcB(r) =τˆy(r)τˆcK(r) =Kˆ(r)Kˆcγ˙ =ˆ˙γ(uˆc/Rˆ)(5.22)the momentum equation of 5.11 and 5.12 can be integrated to yieldr2τrθ = C1 (5.23)τrz =Gr2+C2r(5.24)to eliminate γ˙ we first ”square” the stress-strain relationship, i.e.{γ˙2ij = 0 τ ≤ B(r)τ2ij =( B(r)γ˙ +K(r)γ˙n(r)−1)2γ˙2ij τ ≥ B(r) (5.25)and then sum the terms{ ∑γ˙2ij = 0 τ ≤ B(r)∑τ2ij =( B(r)γ˙ +K(r)γ˙n(r)−1)2∑ γ˙2ij τ ≥ B(r) (5.26)This expression can be reduced by the definition of the norm to{γ˙2 = 0 τ ≤ B(r)τ2 =( B(r)γ˙ +K(r)γ˙n(r)−1)2γ˙2 τ ≥ B(r) (5.27)or γ˙2 = 0 τ ≤ B(r)γ˙ =(τ−B(r)K(r))1/nτ ≥ B(r) (5.28)substituting this result as well as equation 5.23, and5.24 into equation 5.17yields the final system of equation:ddr(uθr)=0 τ ≤ B(r)C1r3(τ−B(r)Kτn)1/nτ ≥ B(r) (5.29)76ddr(uz)=0 τ ≤ B(r)(Gr2 +C2r)( τ−B(r)Kτn)1/n, τ ≥ B(r) (5.30)whereτ =1√2((C1r2)2+(Gr2+C2r)2) 12(5.31)with the boundary conditions ofuθ(κ) = κRˆωˆuˆcuθ(1) =Rˆωˆuˆcuz(κ) = 0 uz = 0 (5.32)5.3 Method of SolutionThe axial velocity can be obtained by solving a boundary value problem andemploying a built in function in Matlab [8, 118]. The details of the methodcan be found in Appendix B.5.4 ResultsStable multilayer viscoplastic flow can be achieved with a certain stress stateat the interface, owing to the yield stress of the viscoplastic fluids [122, 125].Holding the applied shear stress below the yield stress means that the fluidwill not deform and there will be plug flow. This plug area is also neededto fractionate particles; otherwise the media will not have yield stress to actas our separation aid. We use the same definition as in [144] and divide theflow into two subcategories from the stability point of view:• Flow is unstable when the applied shear stress at the interface is higherthan the yield stress of each fluid: both fluids are yielded at the inter-face• Flow is stable when the applied shear stress in one or two of the fluidsat the interface is lower than the yield stress value, which creates anunyielded region in at least one side of the interface.As shown in Figure 5.2(b), for a given set of operating conditions [G, ri] =[0, 45000]× [0.5, 0.9] we solve for the total volumetric flowrate in each layer77(a) (b)Figure 5.2: (a) A schematic of the geometry used to estimate the fully-developed flow field. Two cross-sectional views of the flow field are displayed.In the upper panel, we highlight the uθ component. In the lower panel,we see the uz component (b) Flow stability and operating diagram. Thedashed lines represent operating conditions for equal interface position ri.The continuous lines represent the pressure drop per unit length of G. Forthis example, the yield stress of the fluids are set at τ(1)y = τ(2)y = 15 Pa,consistency and power law index is 5.86 and 0.3983, respectively and 1000rpm rotational speed. The uncolored area represents the stable region whilethe colored area shows the unstable region{Q1, Q2}. Using the stability criteria, at each solution point we determinethe stability of the flow, i.e. whether the layers will mix (unstable) or not(stable) to create the contour plot shown in this figure.First observation that can be made from this figure is that for two iden-tical viscoplastic fluids, the interface is stable when the inner and outer fluidflowrates are approximately equal. The interface becomes unstable at higherflowrates for both streams. It is also unstable when the interface position isclose to the shaft (ri = 0.5) or close to the outer rotating wall (ri = 0.9).In addition to the operating point, we need to check one last parameter,the settling time of the particle. We know that the axial length is (somewhat)equivalent to time in the batch-wise centrifuge. Thus, we compare the axialresidence time, i.e. tz ∼ L(1 − κ)2R2/Q1, with the time for a particleto settling (at a known settling velocity us) from the inner radius to theouter radius, i.e. tr ∼ (1 − κ)R/us, and demand that tz  tr for efficient78operation. Thus, as a last ”rule of thumb” this needs to be checked, for aselected particle, to make sure that the tz is always bigger than tr for anefficient separation. Likewise, we repeated this procedure for a series of yieldstress and pressure drop values to create groups of ”rule of thumbs”. Wesummarized our findings in the following section.5.5 SummaryWhat is evident is that not all operating conditions result in stable oper-ation. We find that there is a subset of all potential operating conditionsin which this methodology will work and this critically depends upon rhe-ology and radii. We have repeated this calculation for other fluid and radiicombinations and our findings can be summarized into a number of qual-itative ”rules of thumb”. By increasing yield stress we increase the regionof stability and simultaneously increase pressure drop required to maintainthe desired flow rate, and more importantly, the critical force to initiatemotion. Any change in the flowrate and rheology will also affect the particleresidence time and the time for the particle to settle Thus, as the last ”ruleof thumb” this needs to be checked, for a selected particle, to make surethat the tz is always bigger than tr for an efficient separation.79Chapter 6Fractionation in ContinuousDeviceTrials to separate ideal shape particles in the continuous device are presentedin this chapter. Additionally, fractionation is examined using both nylonfibres and industrial particle systems.This chapter consists of two major sections. In the first section, resultsfor the fractionation of idealized shape nylon (spherical and fibre) suspen-sion(s) are presented along with speculative discussions of the observed trendbehaviour. And finally, we turn our attention to our primary motivation ofthis work and develop a calibration curve for fractionation of the BEKP-MFC suspension.6.1 Material and MethodFractionation trials were conducted in the machine using three differentparticles as listed in Table 6.1. The nylon particles were obtained fromMcMaster-Carr ( www.mcmaster.com), and MFC is similar to what ex-plained in section 3.7 of chapter 3, i.e. BEKP-MFC.An experimental trial begins with preparing the Carbopol solution. Forthe idealized test where the spherical particles were used, the Carbopolsolution was prepared first, and then the particles were added to the solution.A unique procedure was followed to keep the pH of Carbopol constant,whereas the yield stress was adjusted by changing the concentration of theTable 6.1: Particles tested in the fractionatorMaterial Shape Size rangeNylon Spherical 1.6-3.2 mmNylon Fibre 1.5 & 15 denierBEKP-MFC Random < 1 mm80Carbopol. First, 0.14% of Carbopol powder was dissolved in deionized waterfor 60 minutes at a specific mixer rpm (about 125). Then for each gram ofCarbopol 0.285 gram NaOH was dissolved in deionized water. Finally, theNaOH solution was added to the Carbopol solution and the mixer was set at300 rpm for 24 hours. This time helps in de-gasification of the solution. Inpreparing the suspension for the idealized fractionation, 100 spherical nylonparticles (of each size) with diameters between 1.6 mm and 3.2 mm with adensity of about 1140 kg/m3 were suspended inside 10 L of above mentionedCarbopol solution. After centrifugation in the device, all the particles werecollected from the ’accept’ and ’reject’. Finally, the number of each particlewas recorded.In preparing the fibre suspension, 50 grams of (oven-dried mass) fibreswere suspended into one L of deionized water and were mixed. The sus-pension was first mixed before it was added to 49 kg of Carbopol solutionto obtain 0.1% (wt%/wt%) suspension and then mixed for 60 minutes at125 mixer rpm. Next, the NaOH solution was added and monitored using apH meter until the suspension became neutralized. Finally, the mixer wasset at 300 rpm for 24 hours for de-gasification purposes. After fractionationat different rpms the samples were collected from both ’accept’ and ’reject’streams.RheologyA Consistent test procedure was used to characterize the fluid rheology. Us-ing a parallel plate geometry in shear stress control mode (MCR501,www.anton-paar.com) rheological parameters were determined through regression to apower-law fluid model [122]. The rheology is similar to what is discussed inChapter 3.6.2 Idealized SeparationFractionation trials were conducted in the machine with the nylon sphericalparticles ranging in diameter between 1.6 mm and 3.2 mm. The sphereswere suspended in the inner fluid, and identical Carbopol solution was usedas the outer fluid. The procedure is similar to the batchwise trial describedin Section 3.2.2, but is performed in the continuous method.816.2.1 Mono-dispersedThe particles with 1.6 mm diameter were first suspended in the inner fluidtank and then pumped to the machine by the progressive cavity pump. Thepumps were selected in such a way that rigid particles with diameters upto 4 mm can pass through the entire loop. The flowrates at the two inletswere set based on dye test results explained in Appendix C.3. The dye testsuggested that the flowrate combinations of 1.2 L/min for the inner fluidand 2.4 L/min for the outer fluid can be suitable.The measurements were carried out by collecting and counting the par-ticles before and after centrifugation. For instance, the number of particlesin the inner fluid and ”accept” were recorded for every single rpm in Fig-ure 6.1. It is evident that particles of 3.2 mm diameter have moved fromthe inner fluid at about 600 rpm while the 3.2 mm diameter particles arecompletely migrated from the inner fluid at about 1200 rpm. A comparisonwith the fractionation results of the randomly oriented nylon fibres usingthis technique in bathchwise mode reported in [8] (Figure 2.12) shows asimilar trend. In this case, similar to nylon fibres, there is an rpm rangefor the complete removal of one set of particles from the inner fluid. Thisbehaviour occurs may be due to the randomly positioning of particles alongthe radial direction inside the inner fluid which results in experiencing dif-ferent critical forces. These results are promising and support the feasibilityof continuous separation in the machine.6.2.2 Bi-dispersedFractionation of different class spherical particles is determined using a com-plete continuous process. We calculated the critical force of individual par-ticles based on the results obtained in the previous section. Note that thiscritical force varies with particle size, but remains constant for the particleswith identical size and density. Particles with 1.6 mm and 3.2 mm diame-ters were chosen for centrifugation at 600 rpm using the calibration curvereported in Figure (6.1). Figure 6.2 shows the ratio of recovered particlesfrom the outlet of the machine. The test was done under constant rheolog-ical properties, flow-rates, and rotational speeds, as in section 6.2.1. Underthese conditions, the majority of the small particles flowed through the ’ac-cept’ (73%) while only 6% of the big particles remained in the inner fluid,and thus flowed through the ’accept’. On the other side, i.e., ’reject’, most ofthe big particles moved towards the outer wall along with 27% of the smallparticles. This number is higher than that obtained in the mono-dispersed820 500 1000 1500rpm020406080100 Retained in Inner Fluid (%) D=1.6 mmD=2.4 mmD=3.6 mmFigure 6.1: The ratio of the number of particles retained at the inner fluidof the continuous machine to the total number of particles. The inner andouter fluid flow-rates were set to be 1.2 L/min and 2.4 L/min respectively.Both the fluids have yield stress about 15 Pa.trial (Figure 6.1), where almost all of the particles stayed in the ’accept’ andthere was no small particle in the ’reject’.Referring back to work done by Chaparian [95], the inline motion andhydrodynamic interaction of particles settling in a viscoplastic fluid are stud-ied. It was shown that the plug regions can appear between the particlesand connect them together. This can change the yielding behaviour, sincethe combination forms a larger (and heavier) “particle.” Moreover, smallparticles (that cannot move alone) can be pulled/pushed by larger particlesor assembly of particles. This also can be true for a combination of twosame size particles in mono-dispersed suspensions. Although our device isvery different from that Chaparian studies, however, there might be a linkbetween his findings and our results. We think that these hydrodynamic in-teractions can affect the throughput of the continuous fractionation systemand needs to be addressed in future works.833.2 mm 1.6 mmDiameter020406080100Accept%(a) Accept3.2 mm 1.6 mmDiameter020406080100Reject%(b) RejectFigure 6.2: The number of spherical nylon particles collected from the ’ac-cept’ and ’reject’ in the continuous device. Two suitable particle sizes werechosen from the results presented in Figure 6.1 and fractionated in the con-tinuous device under the same flowrate and yield stresses as explained inthis figure.6.2.3 Nylon FibresWith the principle of separation shown for the ideal shape/size particles,i.e. spherical nylon particles, we attempted to demonstrate this principlewith a fibre-like particle system. As the size of these particles is smallerin comparison to the particles used in the previous section, we expect thatseparation occurs at relatively higher rpms. The results of this trial areshown in Figure 6.3. The portion of the fibres which were retained in theinner fluid or ’accept’ was recovered and the suspension consistency wasdetermined for each case. The orientation of the fibres can not be controlledin this experiment and may be considered randomly distributed. The resultsshow that the rpm required to cause the motion increase by increasing theparticle diameter (denier). Although a complete separation did not occur, apartial separation was achieved at about 1700 rpm, where almost 40% of the15 denier particles were stably trapped compared to 84% of the 1.5 denierparticles.As reported by Madani et al. [4] and Chaparian et al. [94] which isdiscussed in section 2.6, the critical force for the onset of the motion is notonly a function of the shape of the particle but also its orientation. Witha possible generalization of this finding to the more complex flow in ourgeometry, it can be hypothesized that the orientation of fibres might have anoticeable influence on the fractionation efficiency. In other words, one may840 500 1000 1500rpm020406080100Fibre in Accept (%)15 denier1.5 denierFigure 6.3: Calibration curve of different size nylon fibres. The fraction ofnylon fibre particles trapped in the inner fluid after the centrifugation inthe device. The nylon particles were of equal length (1 mm) and differentdeniers. The trial was performed at two different yield stresses 15 Pa (blackcolor) and 5 Pa (red color). The inner and outer fluid flow-rates were set at1.2 L/min and 2.4 L/min respectively with the same yield stress values.conjecture that at a fixed rpm, randomly oriented small and large particlesmight experience the same critical force.6.3 Continuous Fractionation of MFCTo test the industrial application of the continuous separation, we conducteda fractionation procedure using the same material studied in Chapter 3. Sim-ilarly, the suspension was prepared by adding the BEKP-MFC and sodiumhydroxide to the Carbopol Solution. A new dye test with same procedureexplained in Appendix C.3 was done at 100 rpm and 0.08 (±0.02) wt/wt(%)Carbopol concentration. Typical particle size distribution measurement re-sults are depicted in the Figure 6.4. Each curve represents three measure-ments of the distribution in ’accept’. The results presented here are forthe fibre concentration of 0.1% and Carbopol concentration of about 0.08%.The first observation that can be made from this figure is that the particle850 200 400 600 800 1000Particle Size ( m)012345Volume %OriginalRPM=30RPM=50(a)0 10 20 30 40 50 60rpm6080100120140D (m)(b)Figure 6.4: (a) Particle size distribution and (b) volume weighted mean di-ameter of BEKP-MFC fractionated in the continuous device. The inner andouter fluid flow-rates were set to be 1.2 L/min and 2.4 L/min respectively.Both the fluids have yield stress about 1 Pa.size drops by increasing the rotational speed. Also, at 50 rpm, the second’bump’ of the size distribution has been removed successfully causing partialfractionation.As the final step, we repeated Figure 3.3 of batchwise method andadded the results obtained from the continuous machine in Figure 6.5. Thetriangles(4) represent the continuous machine results which show a similartrend to those obtained from the batch-wise technique presented in chapter3 but at a lower threshold. This is an anticipated result because the geome-tries are different and thus, are under a different stress state. Despite this,we were able to achieve a separation at the same trend as the batchwisemethodology.6.4 SummaryTwo different particle suspensions were tested in the continuous device. Tobenchmark our calibration curves, we examined and measured the criticalforce to initiate motion for (monodisperse) spherical particle suspensions.Here, we find that the critical force to initiate motion shows a similar trendto the batchwise test but at a lower threshold. A similar finding was foundin the second test where we examined the separation of the hardwood MFC.We argue that this is an anticipated result as the two geometries are indifferent stress states. The extensional and viscous stress found in the con-86Figure 6.5: (a) The particle size measured on Eucalyptus MFC suspension,with an initial value of 128 µm, as a function of RCF/τy at 0.1%. Thisconcentration was found to be below the gel point [58]. RCF is calculatedby dividing Rω2 by earth’s gravitational acceleration and τy is the measuredyield stress divided by a characteristic yield stress of 1 Pa. For the batchwisetests, a 2.5 mL of a 2 wt/wt % suspension of the MFC was mixed into a 50mL of a Carbopol solution with a yield stress of ranging between 3-15 Pa.For the continuous tests, we suspended 2.5 L of 2% (wt/wt) MFC in 50 L of0.08% Carbopol solution (τ(1)y = 1 Pa, ρ(1) = 1001 kg/m3). The outer fluidwas a 0.08% Carbopol solution (τ(2)y = 1 Pa, with a density of 1010 kg/m3through the addition of sugar. Centrifugation proceeded at the range [10-1750] rpm and at a flowrate (Q1, Q2) = (20, 40) mL/s. Particle size (D) wasmeasured using a Malvern Mastersizer 2000 which may introduce artifactsif the sample is fibrillated. Here, batchwise results are shown in (◦) for 5minutes and in (×) for 15 minutes centrifugation times and the results ofthe continuous device are presented in (4). (b) A measure of the ratio ofthe mass of recovered MFC in the gel after centrifugation to the initial massof MFC. This test was performed gravimetrically and the uncertainty in theestimate is estimated to be 5%. The batchwise tests are displayed as circlesand the continuous as triangles. (c) Scanning Electron Microscopy image ofthe particles before fractionation and (d) after fractionation.87tinuous device contributes to the second invariant of the stress tensor whichwill lower the centrifugal force required to initiate motion. Despite this,we were able to achieve a separation at the same trend as the batchwisemethodology. Hence we have successfully scaled-up this process. This ispromising the application of the device for the fractionation of industriallyavailable particle systems.88Chapter 7ConclusionsIn this work, we presented a continuous methodology of sorting particlesby scaling-up a batchwise process. We designed this device in three stages.First, we solved the equations of motion for a fully-developed flow spiralPoiseuille field to determine the relationship between flowrate, pressure dropand interface position. We were able to assess the stability of the flow usingcriteria found in the literature to create a contour map representing the oper-ating window. Missing from this map, was a calibration curve of the criticalforce required to create the separation particular to MFC. This calibrationdata was acquired in the second step. In addition to this, we performed anumber of complimentary batchwise calibration curves to demonstrate thatthis process can be extended to three fluids - opening up the potential formore advanced separations. Given this we designed a continuous unit andverified its operation by computational fluid dynamics from literature. Moreimportantly, we performed two preliminary separations, using spheres andMFC and found that we could indeed separate these suspensions at the sametrend as the batchwise device. However, the critical force we determined waslower than that of the batchwise device due to the presence of elongationand viscous stress.In particular, the main findings concerning the objectives defined in Sec-tion 2.11 are detailed in the following:Objective 1We tested the feasibility of sorting MFC in a batchwise method. Indeed,we were able, in a straightforward manner, to reproduce literature resultsby achieving separation, generating a calibration curve and showing thatthe average fibre size of the fractionated portion decreases linearly withcentrifugal force and time. We also established a reasonable estimate of the”yield” representing the ratio of the mass recovered to the initial mass andfound that yield decreases linearly with particle size.89Objective 2We extended the batchwise procedure to include layering. Thus, we con-tinued by examining the effect of density difference in the layered fluidson interface stability and found that when the density of the lower fluid isgreater than the upper fluid, the fluids are stable and do not mix duringcentrifugation over the acceleration and time that we tested. Additionally,when the fluids were ordered in the opposite configuration we characterizedthe stability of the interface and observed that stable operation can onlybe achieved whenτ(1)y(ρ(1)−ρ(2))gD > 0.37. We performed a number of comple-mentary experiments to examine the possibility of particle separation understable conditions. When operating within stable bound, we were able tomeasure critical force for individual bi-disperse particles in two fluids. Wealso successfully separated a tri-disperse nylon fibre suspension and achievedexcellent separation with a higher yield, compared to one fluid technique.We then performed several qualitative tests to assess the fractionation ofMFC and demonstrated that indeed we can achieve separation simply androbustly in a layered fluid. Additionally, we showed that our technique wasable to fractionate the MFC to achieve a more considerable gaining strengthin a composite paper than that fractionated in the current lab standard(Bauer-McNett).Objective 3We designed the fractionator which includes a multilayer flow system undercentrifugal force. The device is mechanically balanced, sealed and success-fully meets other design challenges given in Section 4.3. Our theoreticalanalysis of the fully developed flow field inside the separation zone of thedevice confirms the possibility of reaching stable multiplayer fluid over therange of G, ri, Q1 and Q2 that we tested (See Figure 5.2). This analy-sis, along with the dye test reported in Appendix C.3, helped us to choosesuitable flowrates to achieve fractionation.Objective 4A series of experiments were carried out in the continuous device to deter-mine the possibility of particle sorting. We used both ideal and industrialparticle (MFC) suspensions and were able to estimate the critical force. Wewere also able to achieve partial separation and find that the critical force toinitiate the motion of spherical particles shows a similar trend to the batch-90wise test but at a lower threshold. We argue that this is an anticipated resultas the two geometries are in different stress states. However, we were ableto achieve a separation at the same trend as the batchwise methodology.A similar trend was observed in the MFC trials. Still, consistent with thebatchwise separation results, the size distribution confirmed the separation.Furthermore, the results collected from the mass yield of the particles werein-line with the values found for the batchwise method.7.1 Limitations and Future Work• Hydrodynamic interactions exist in this technique, however, the in-teractions are on a smaller scale since the fluid remains rigid awayfrom the yielded envelope around the particles, as explained in detailby Chaparian [106]. The fractionation trials that we conducted usingspherical particles were performed in an extremely dilute suspension.Although our results provide enough trend for one stage of fractiona-tion, we think the hydrodynamic interaction may diminish the sepa-ration efficiency in higher consistencies. This needs to be investigatedfurther through a systematic study.• We showed in the batchwise process that a tri-dispersed suspensionwith spherical particles can be fractionated into three suspensions.A device with three inlets/outlets can be designed to investigate thepossibility of sorting tri-dispersed suspension continuously.• The final product after fractionation consists of Carbopol with its cor-responding challenges to be removed from the particles. Other in-dustrially available yield stress fluids can be tested to determine thefeasibility of adding value in it by particle sorting.• It is shown that the designed lab-scale device is capable of improvingthe size distribution of the ’highly refined’ pulp suspension. Neverthe-less, the benefit of the device in terms of energy consumption duringfractionation remains an active question. No data is available from theliterature about energy consumption during other MFC fractionationtechniques to compare. In the current system, at the nominal flowrate,2.5 L/min, at 0.1% consistency, the electrical energy consumed wasobserved to be only 0.5 kW at 50 rpm. Considering the mass flowrateof solid particles (150 g/h)) and the mass yield in the accept (42%),the consumed energy is calculated to be about 5000 kWh/t . As a91result of this energy consumption, the particle size drops from 128 µmto 78 µm. One possible reason for high energy consumption could bethe operating of the fractionator under 0.1% consistency at a very lowflowrate. A comparison to the data reported by Syverud et al. [53] forenergy consumption during the grinding process shows the same rangeof energy consumption to reach the same particle size (see Figure 2.6).However, the analysis reported in Chapter 5 and [144] reveal the pos-sibility of running such a device under 60 times higher flowrate whichmay dramatically alter the energy consumption during fractionation.• The complexity of the morphology of the MFC particles results insubstantial nonideality in the particle separation capacity using thismethod. This also limits the concentration of the particles to staybelow the gel point which may affect a production/fractionation rate.• The laser diffraction technique for size measurement provides an equiv-alent diameter based distribution considering that the light scatteringpattern of the material is identical to that of spherical particles. ForMFC with a high aspect ratio, this approach may introduce artifactsand lead to values that can be used only for the comparison betweensamples and not as a direct measure of the real size of the material• Overall, it is of interest to provide a comparison between the previ-ously introduced methods in the literature and the current method forfractionation of MFC. Other techniques such as microfluidic separationdevice operate at excessive low flowrate (1 mL/h) and we anticipatethat the production rate would be very low. Conventional methodssuch as pressure screens, hydrocyclones and Bauer McNett classifiercould also be used to remove relatively long fibrils from MFC sus-pensions, however, it is shown that gel fractionation can gain largerreduction in fibril length in comparison to pressure screen and hydro-cyclone [114] and also Bauer McNett (Chapter 3 of this document)methods for the conditions that was tested. The only similar frac-tionation method developed by Tanaka et al. 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These are standard 114” and 2” seamless NPS pipe size, madefrom 304 stainless steel.A.1.1 Splitter or SeparatorWe want two fluids to be introduced only at the separating zone, hence thesplitter takes place between the inner fluid and outer fluid. It is mounted onthe shaft and designed in a shape that introduces two fluids to each otheras smooth as possible.A.1.2 Separating ZoneThe separating zone was chosen by considering fluid properties, desired g-force and standard aspect ratio. The maximum flow-rate to allow particlemove radially to the outer fluid was calculated to be about 20 L/min, basedon the 150 mm separation zone.A.1.3 SealingThe sealing is Turcon rotary seal obtained from Trelleborg company. Theseal is double-acting and can be exposed to pressure from both sides [161].The main advantage of this sealing system is low friction on the shaft, aswe expect high friction forces due to the big sealing surface areas on eachentrance, exit and both sides of the shaft. The sealing system consists of aseal ring of Turcon material, which is a combination of aluminum-magnesiumboride (BAM), and graphite filled material, which results in a low frictionfactor. The contact surface has two continuous grooves, which improves the109Figure A.1: Exploded view of entrance assemblyFigure A.2: Bottom and top splitters110 		 !"#$%&% '()*+,+* -(.#+/ (!012334 5	67	89:;<=>	?	>	?@A7	5B6C7D EF7	68D1	G	?AD	G5		H?1IJ	KIL= 2IMNO& IPQR SPQR 	ISTUVN WX%:O= WX%VNON .YMZO= &O&N NO%[ NO%N NOZN %O\: NTUV% %=XV\O= %NX&Z[ON .YM\O[ VO&N NO&N NO%[ NOWN &OW& %TUV& V:X%==O= %=XZ[[ON .YM%%ON ZO&N NO&[ NO&N %ONN VO[V %TUVV &NNX&[[O= V:XW[[ON .YM%[O[ WOVN NOVN NO&[ %OVN [OVV &TUVZ &[WXWZ=O= %&NXW[[ON .YM&%ON :O%N NOVN NO&[ %O:N \ONN &TUV[ W[NX===O= W[NX===O= .YM&:ON =O[N NOZ[ NOVN &O[N :OZN &]#-^ .$)_, *<-") (!!#--^$)+` -`#. (!*-. +a$*$#b)$$T+c,$dee'fOg*_#$))"#$)hIPQR * )#$`-aa$(.+c,$*<+*9-#*<$`#-)))$`* -(i-" <`--)$*<$($j*,+#!$#_#-9 ,$+` -`#. (!*-*<$`-,"a(kg^+ ,+c,$#+(!$k O$O9-#)<+9*l:NaamTUVVNN:NNXOng*_#$))"#$)hoPQRmp)$. +a$*$#*-,$#+(`$L:;9:qc-#$;#-.r (+#$+-9)$+,O0D	s7>t7sd+*$)* (9-#a+* -(+^+ ,+c,$+*///O*))O*#$,$c-#!O`-a&[Zu. * -(g"!")*&NN=Figure A.3: Seal, housing and shaft assembly of a standard Turcon sealspecific surface load pressure for better sealing. Figure A.3 shows the seal,housing and shaft assembly of a typical system. dN is the shaft diameter, D1and L1 are the groove diameter and length, S is the clearance between theshaft and the seal housing, r1 is groove radius and d2 is o-ring cross-sectiondiameter [161]A.1.4 DriverThe Motor above centrifuge can be mounted directly with a flexible couplingsystem to damp vibration generated from both sides. Gear-shaped couplingscan be used for high-speed and high-torque applications. A rubber centerallows flexing so that couplings can take on multiple types of misalignmentwhile damping vibration and shock. With no metal-to-metal contact, thereis no need for lubrication. All the bearings are kept out of any contact withthe liquid so that they have a normal long life. To select the right motor asthe driver, maximum torque and angular speed must be taken into account.The maximum torque is calculated at 15 N.m and the nominal rpmconsidered to be 1000, so the required mechanical power is 2 hp. The startingtorque of a 3 phase induction motor is about half the running torque henceconsidering all the mechanical losses in the drive system, a 5 hp, 3 phasemotor will suffice.Bending, torsion and axial stresses may be present in the rotating partsof the fractionator. Axial loads are comparatively very small at criticallocations of the shaft where bending and torsion dominate. Hence they willbe neglected in the calculation. It is also essential to consider the possibilityof static failure in the first load cycle. Thus, the maximum von Mises stress111(a) (b)Figure A.4: Displacement and von Mises stress on the shaft under designcases112Top SeparatorRotorBottom SeparatorOuter Fluid EntranceInner Fluid EntranceSupport PlateBottom BearingSealTop BearingShaftSupport PlateAcceptRejectSealSealFigure A.5: Section view of the fractionatorhas to be checked as a criterion for the shaft size, stress concentration,material and power [162]. von Mises stress and displacement of the shaftcalculated and checked using the Solidworks design tool. The results of adesign case can be seen in Figure A.4.A.2 Device DescriptionThe rotor of the fractionator, inner and outer fluids entrances are con-structed out of 4”, 114” and 2” NPS seamless standard pipe size, respectively.All the rotating parts have been made from stainless steel and most of thestator parts and seal housings are made from Aluminium 6061. see Fig-ure A.6. Figure A.5 shows a cross-section view of inside the device. Thereare 4 rotary seals associated with the shaft, two for fluid entrances and twofor fluid outlets. The stators are made of two identical halves with innerfluid and outer fluid entrance ports placed on each side.113 20.389  Up to slit  18.645 .004  4.450 h9 +-.000  .002.000-+1.000 h9   .002.000-+.750 h9   .0005.0000-+.750.003 19.389      5.463 + 6.821 .000     .000-4.450 h9 +.003 -1.630 h9  2.000  3.150  3.902 .004 .0000.750 .0005 +-  2.335 h9 +-.000 26.000 CHK'DAPPV'DMFGQ.A   ANGULAR:FINISH:TOLERANCES:EDGESNAME SIGNATURE DATEMATERIAL:DO NOT SCALE DRAWING REVISIONTITLE:DWG NO.SCALE:1:4 SHEET 1 OF 1A2WEIGHT: A12BH11 12345678910GFEDC10 812 6 4 2DRAWNFCAD111   LINEAR:9 7 5 3BEGHUNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN INCHESSURFACE FINISH:DEBURR AND BREAK SHARP Rotor AssemblyFigure A.6: Engineering drawing of rotor assembly with dimensions andmanufacturing tolerances. Here, the dimensions are given in inches.The bottom separator is welded to the inner fluid pipe which is boltedto the shaft. The rotor and its cap are welded together and are connectedto the shaft using three connecting vanes. The top separator is made inone piece and is connected to the shaft using set screws. A standard groovetakes place on the flange side of each stator and also between each flangewith the mating pair to ensure proper sealing between the stationary partsto eliminate leakage.The axial thrust (vertical) and radial forces are restrained using a taperedroller bearing. The assembly of the device and support structure is shown inFigure A.7. The motor is mounted directly on to the device shaft using High-Speed Vibration-Damping Flexible Shaft Couplings (www.mcmaster.com).The coupling housing is mounted between the device and the motor as asupport for coupling and motor. It is also made of a 6” thick wall stain-less steel pipe. The motor is a 3 phase, 5 hp, 1750 rpm (www.baldor.com)controlled by a variable frequency driver (www.abb.ca). The flow loop con-sists of two positive displacement pumps (www.seepex.com) and two 65litres tanks ”dirty” and ”clean” fluids. Considering Re ∼ 1 the pumprange was selected to be between 0.15 L/min to 2.5 L/min. Thus, the114Figure A.7: Fractionator, driver and support structure.maximum entry length has to be about 20 mm as calculated before and130 mm of separation zone can be available as a fully developed region.The loop flow-rate is monitored and measured using two low flow-rate flow-meters(www.omega.ca). The flow-meters range selected to cover the p[umpflow-rate range. The device pressure drop is measured using an Omega pres-sure transducer (www.omega.com). ”Analogue signal transmission was doneto the National Instruments USB Data Acquisition System (www.ni.com).The data was stored in a matrix after digitally filtered in a LabVIEW pro-gram and then outputted to a text file.115PD Pump PD PumpFlow MeterFlow Meter“Dirty” Tank Clean TankFlow MeterFlow MeterAccept RejectFigure A.8: A schematic of the experimental set-up loopInner Fluid TankOuter Fluid TankAccept TankReject TankFractionator Figure A.9: Experimental setup in the lab116Figure A.10: Piping and instrumentation diagram (P & ID) of the experi-mental setup.117Appendix BMethod of Solution for BVPA boundary value problem (BVP) can be solved using a built-in functionin Matlab. It solves boundary value problems for Ordinary DifferentialEquations by collocation and solvesdudr= f(r, u), g(u(a), u(b)) = 0, a ≤ r ≤ b. (B.1)here the approximate solution is a continuous function on each subintervals[ri, ri+1]. It satisfies the boundary conditions and the differential equations(collocates) at both endpoints ri, ri+1 and midpoint (ri + ri+1)/2 of eachsubinterval. These conditions result in a global system of nonlinear algebraicequations while approximating the exact solution over the whole interval.The boundary conditions are taken into account over the whole interval.The non-linear algebraic equations are solved iteratively by applying New-ton’s method. It is well known that the convergence of the Newton methoddepends critically on the closeness of the initial guess values. Although theinitial guess solution does not have to satisfy the differential equations oreven the boundary conditions, a reasonable initial value of the solution mustbe provided for the entire domain [163].118Appendix CDevice CharacterizationIn this Appendix, we begin with the characterization of the device by re-porting the pressure drop. Then, using dye test, flowrates for frac0tionationwill be determined.C.1 Material and MethodAn experimental trial begins with preparing the Carbopol solution. Thepreparation procedure is similar to what was demonstrated in the thesis. Aconsistent test procedure was used to characterize the fluid rheology, using aparallel plate geometry in shear stress control mode (MCR501, www.anton-paar.com) and the rheological parameters were determined through regres-sion to a power-law fluid model [122]. For pressure drop measurements, Car-bopol solution was pumped through the fractionator at constant rotationalspeed while the pressure and flowrate were measured. In the second sectiona dye test was run to examine the flowrates suitable for fractionation. Thedye (Rhodamine B) obtained from Sigma Aldrich (www.sigmaaldrich.com)was added to the inner fluid. Samples were collected from ’accept’ and ’re-ject’ to check the concentration. A confocal microscopy was used to measurethe light intensity, which was correlated to the dye concentration.C.2 Pressure DropThe first step in the assessment of the performance of the machine is tocharacterize the inlet and discharge flows by their pressure and velocityassuming uniform flows. To understand the behaviour of the device, theinner and outer fluids are pumped through the pipes and fractionator atdesignated flow-rates, and pressures were recorded. Hereafter, subscripts i,o, a and r refer to inner, outer, accept and reject, respectively ( Qinner isQi, Qouter is Qo, Qaccept is Qa and Qreject is Qr, see Figure C.1).For each combination of flow-rate and rotational speed, the pressuredifference was recorded and compared. It can be seen in Figure C.2, the119QiQoQaQrFigure C.1: Flowrates labelling of the device.pressure difference between entrance and exit increases by increasing flow-rate. The pressure difference drops for higher rotational speeds, and at somepoint, it reaches a negative value. To interpret this, once again we look at theenergy balance within the device. This scheme could be advantageous sincethe operation process requires a smaller external pump, while the machinecan pump itself.The basic thermodynamic measure of the energy stored in a unit massof flowing fluid is the total specific enthalpy (total enthalpy per unit mass)denoted by hT and defined ashT = h+12u2 + gz = e+pρ+12u2 + gz (C.1)where e is the specific integral energy, u is the magnitude of the fluidvelocity, and z is the vertical elevation assuming no other external forces andchemically inert process [164]. Assume the steady state operation for thefractionator with W˙ the net amount of work done on the fluid by externalmeans. Considering incompressible, inviscid flow the equation C.1 can bewritten as: (pρ+12u2 + gz)1−(pρ+12u2 + gz)2=W˙m(C.2)The net work, W˙ , is obtained by the multiplication of the applied torqueto the fluid and the rotational speed of the moving parts, i.e. W˙ = Tω. Con-sequently, in the case of an ideal fluid which is incompressible and inviscid,C.2 yields a relation connecting the total pressure rise across the machine,1200 1 2 3Flow rate (l/m)-10010203040P i - P a (kPa)RPM=0RPM=500RPM=1000RPM=1500RPM=1775Figure C.2: Pressure difference between inner fluid (Pi) and accept (Pa).The average value for Pi was found to be 70 kPaP2T − P1Tρ= Tω (C.3)Furthermore, the second law of thermodynamics implies that in the pres-ence of irreversible effects, such as those caused by viscosity, the equalityin equation C.3 should be replaced by an inequality, namely as ”less than”sign. Therefore, in the machine with incompressible fluids, the viscous ef-fects will lead to energy loss. So, we define a machine hydraulic loss factor,η (similar to pump hydraulic efficiency):P2T − P1Tρ= Tωη (C.4)Note that additional losses can occur, for example as a result of ”diskfriction” caused by the fluid dynamic drag on other non-active surfaces ro-tating with the shaft.To evaluate the pressure drop in the machine we conducted a zero rpmtest to examine the ”zero-omega” behaviour of the machine at different flow-rates. We measure the inner fluid pressure immediately before the machine(p1) and in the accept stream (pa).121ZmObjective LensConfocal Unit Laser unitCameraStageGlass surfaceFigure C.3: Sketch of the experimental set-up; Samples are between twoglass sheets and are separated using gaskets. Images are taken from thebottom to measure the intensity in the middle of the container. The con-tainer is 30mm × 30mm and the field of view is 2mm × 2mm from thecenter.C.3 Dye testThe concentration of the inner fluid at different flow-rate combinations andrpms were checked using Laser Induced Florescence (LIF). The objective isto trace the inner fluid to estimate the suitable to trace flowrate combinationfor fractionation. LIF is a known as a non-intrusive technique for measuringscalar concentration in fluids. In this technique, a laser is used to excite afluorescent,Rhodamine B, inside the fluid.The dye absorbs a portion of theexcitation energy and instantly re-emits a portion of the absorbed energy asfluorescence. The fluorescence is measured optically and used to infer thelocal concentration of the dye [165].C.3.1 Test ProcedureThe dye obtained from Sigma Aldrich (www.sigmaaldrich.com) was addedonly to the inner fluid. The fractionator was run at a specific rpm andflow-rate combination. Then samples were collected from all four inlets andoutlets for the LIF test. The test was carried out on a confocal microscope.In the set-up shown in Figure C.3, the confocal optical unit is attached to aninverted microscope (Nikon ECLIPSE Ti), and the imaging was done using a1220 0.2 0.4 0.6 0.8 1Normalized Concentration00.20.40.60.811.2Normalized IntensityCalibration CurveFigure C.4: Intensity-concentration calibration for LIF test(Zyla 5.5 sCMOS) camera. The field of view which is about 2mm×2mm wasilluminated using a 5 mW laser (MLC 400B Agilent Technology). Finallythe emitted light was passed through a 22 µm slit [166]. A 4x objective lens(CFI Plan Apo Lambda) was used. The objective lens can move verticallywhich makes it possible to focus on the specific surface between two glasssurfaces (Zm). Thus we could focus on the middle plane for all the tests. Theoriginal inner fluid samples were always used as a check test and were usedfor normalizing the images from each test. The magnitude of the intensityof the picture is averaged over the entire field of view and reported as arepresentative of the concentration of the dye in each sample.Borg and his colleagues showed that there is a linear relationship betweenthe image brightness and dye concentration [167] when concentration <0.2mg/l. So a calibration curve is needed as a Concentration-Intensity rela-tion guide. The results are shown in Figure C.4 which shows a fairly linearrelation between the intensity and concentration with R2 = 0.9983.C.3.2 ResultsThe inner fluid contains Rhodamine-Carbopol solution while the outer fluidis only Carbopol. In order to minimize possible chemical instabilities inthe experiment, the pH of both fluids were matched which also resulted in123the same values for yield stress. Figure C.5 shows the results for constantrotational speed, i.e. 1000 rpm. In each trial, Qi was kept constant whileQo varied. The flow-rates were measured constantly and three samples weretaken for each Qi and Qo combinations. The samples were then taken tothe confocal set-up to measure the dye concentration.To be able to trace the flow-rates entering by the inner fluid, we reporteda ratio of Qa/Qi with respect to Qo for Qi=0.4, 1.2 and 2.4 L/min. Close to1 means that the flowrates are equal in the the inner fluid and accept. In (b)we report QaCaQiCi which represents the trace of the mass of inner fluid. Thefirst observation that can be made from (a) and(b) is that for low values ofQi and high values of Qo bothQaQiand QaCaQiCi fractions are close to unity. Inother words, This means the mass entering the machine from the inner fluidport exits from the accept port of the machine (This is because QaCaQiCi = 1)and this is only Qi which is exiting from accept(This is because ofQaQi= 1).In particular, we can conclude that when QaQi = 1 andQaCaQiCi= 1 the interfaceof the two fluid is hitting the top separator, assuming the interface is stable.We believe these results can help us find suitable flowrates to achieve betterfractionation efficiencies.C.4 SummaryThe Continuous device is characterized through pressure drop and dye test.It was found that rotation of the parts in the fractionator helps maintain thepressure inside and outside of the machine. The Dye test can help to alignthe interface position and top separator assuming that the layered fluids arestable and no mixing occurs inside the machine.12400.40.81.21.60 1 2 3Qa/QiQ o00.20.40.60.811.20 1 2 3QaCa/QiCiQ o0123450 1 2 3Qr/QiQ o2.41.20.400.20.40.60.811.20 1 2 3QrCr/QiCiQ o(a) (b)(c) (d)Figure C.5: Flowrate and concentration ratio of the accept and inner flowwith respect to the outer flow. In this test, the outer flowrate was keptconstant and the inner flowrate was changed at constant rpm.125Appendix DOperations ManualThe following procedure has been developed for particle fractionation ex-periment using the experimental setup described in Chapter 5. Followingthese steps carefully can ensure repeatable data and safe operation of theequipment.Warning: The experimental setups can be a dangerous apparatus. Careneeds to be taken to prevent injury or damage to the equipment.Note: The procedure will take 2 hours followed by 20 hours of de-gasification wait time. We suggest to start the sample preparation in themorning and perform the experiment the next day.D.1 Start-up and Sample PreparationAll the parts of the loop is labelled and we use typographic conventions listedin the Table 2 for simplicity. The following start up procedure assumes thesystem is empty of water and all power and water supplies are turned off.Caution: To avoid any damage to the pumps both T1 and T2 mustcontain DI water and the V1 and V2 must be in open position. If the valvesare closed or tanks are empty you must stop the experiment and review thepump manual.1. Open V3, V4 and V5 valves to discharge T1 and T2 tanks.2. Close V1-5 valves.3. Open the DI water supply above both T1 and T2 tanks.4. After filling both the tanks up to 50 litters, turn off the DI watersupply valves and turn on the mixer. set the mixer speed at 125 rpmand let it mix for 15 minutes. This washes away any residue in thetanks.5. Open V8, V9, V10, V11 and V12 valves. Make sure that V13, V14and V15 are closed.126Danger: EXTREME ELECTROCUTION HAZARD. THE VFD ISWIRED WITH HIGH VOLTAGE LINE. DO NOT ATTEMPT THISIF THERE IS ANY SPILL ON THE ELECTRICAL DEVICES.6. Turn on power to both pump VFDs. Navigate the menus of the VFDdisplay to reach the set point feature.7. Set the VFD frequency to 20 Hz and press the green start button. Atthis point water begins flowing through the entire loop. Continue toflush the loop.8. Turn off the VFD.9. Open V13, V14, V15 and V3 to drain both T3 and T4 tanks.10. Open V1-5 valves to drain T1 and T2.11. Close valves V1-5.D.2 Sample Preparation1. Re-fill both T1 and T2 tanks up to 50 litters by opening DI water.Warning: In addition to safety goggles and gloves, you must put onbreathing masks before working with Carbopol powder in the nextstep.2. Weight 50 g of OD Carbopol powder.3. Dissolve 0.285 g NaOH in deionized water for each gram of Carbopol.4. Add 50 g of OD Carbopol powder to each of T1 and T2 tanks.5. Set the mixer speed at 125 rpm and mix for 1 hour.6. Add NaOH solution to the solution and set the mixer at 300 rpm for20 hours. It helps in degasification of the solution.Caution: The pumps have the capability of handling particles up to4 mm in diameter. The particles bigger than 4 mm may damage thepump.7. Add particles with diameter smaller that 4 mm into T1 and let itmix at 300 rpm for 15 minutes.8. Turn off the mixer and wait for 60 minutes before performing theexperiments.127

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