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Understanding rapid dewatering of cellulose fibre suspensions Paterson, Daniel Thomas 2016

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Understanding Rapid Dewatering ofCellulose Fibre SuspensionsbyDaniel Thomas PatersonB.A.Sc., The University of British Columbia, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)May 2016c© Daniel Thomas Paterson, 2016AbstractRapid dewatering of cellulose fibre suspensions is a fundamental process inmany unit operations in the production of pulp and paper. Understand-ing dewatering behaviour can be applied to optimizing designs of industrialequipment. In this project, we assess the suitability of a well-establishedmodeling approach, referred to as the base model, at capturing the onedimensional dewatering behaviour of cellulose fibre suspensions seen exper-imentally. This modeling approach requires two closure relationships deter-mined experimentally, i.e. compressive yield stress and permeability.Experimental equipment has been designed, constructed, and operatedto obtain the closure relationships and collect dewatering results for vali-dation of the model. Two experimental techniques, with close agreement,have been developed for the collection of compressive yield stress. Perme-ability results are obtained through Darcian permeation experiments. Twoapproaches, neglecting and accounting for flow induced compaction, weredeveloped. Results were found to fall within values seen in the literature.The base model provided good representation of ideal nylon fibre suspen-sion trials. These solid fibres are representative of the base models consti-tutive equation for an infinite solid phase rearrangement rate constant. Thebase model poorly represents the cellulose fibre suspensions’ dewatering be-haviour. The suggested source of discrepancy is the further dynamic dueto the dewatering of the individual porous cellulose fibres which results in afinite solid phase rearrangement rate constant. The base model is expandedupon in hopes of capturing this rate dependent behaviour. This extendedmodel, with the determined closure relationships, captured load versus solidvolume fraction profiles at varying dewatering rates better than the basemodel for cellulose fibre suspensions. Further improvements in representa-tion were seen through close representation of the solid phase velocity profilesfound experimentally during dewatering. Various cellulose fibre suspensionswere investigated to begin a catalog of different dewatering behaviours seenthrough variations in pulp production variables. Investigations includedvarying fibre species, pulping processes, levels of low consistency refining,and impacts of dewatering chemical additives.iiPrefaceMy contribution to the research project started with designing, construct-ing, and operating the experimental equipment necessary to collect requiredmaterial parameters of fibrous suspension that are input into a theoreticaldewatering model. I was also responsible for collecting the experimentaldewatering data to which the theoretical model is compared. A furthercontribution is through collecting the experimental data of a particle track-ing velocimetry experiment and analyzing frames collected to determine thesolid phase movement during dewatering. This work was to further validatethe theoretical model posed for capturing the dewatering behavior.Section 2.1.2, the scaling exercise in Section 3.2, and the expansion inSection 4.2 are paraphrased from a joint paper that is in the process ofbeing published: D.R. Hewitt, D.T. Paterson, N.J. Balmforth, and D.M.Martinez, Dewatering of fibre suspensions by pressure filtration, Physicsof Fluids, Submitted 2016. Various results in Chapters 3 through 7 arepresented in the paper as well. My contribution to this publication includedthe collection of experimental results for comparison to the theory, writingthe outline of the experimental setup and description of the experimentalmaterials sections. The remainder of the paper was written by D.R. Hewitt,N.J. Balmforth and D.M. Martinez.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Dewatering of Flocculated Suspensions . . . . . . . . . . . . 42.1.1 Base Model . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Extended Model . . . . . . . . . . . . . . . . . . . . . 92.1.3 Scaling the Extended Model Equations . . . . . . . . 112.2 Background Summary . . . . . . . . . . . . . . . . . . . . . . 122.3 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . 133 Compressive Yield Stress Py(φ) . . . . . . . . . . . . . . . . . 153.1 Literature: Py(φ) . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Methodology: Py(φ) . . . . . . . . . . . . . . . . . . . . . . . 193.3 Device Description: Py(φ) . . . . . . . . . . . . . . . . . . . 213.4 Experimental Protocol: Py(φ) . . . . . . . . . . . . . . . . . 233.5 Data Processing and Fitting: Py(φ) . . . . . . . . . . . . . . 243.6 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.7 Results and Discussion: Py(φ) . . . . . . . . . . . . . . . . . 253.8 Conclusions: Py(φ) . . . . . . . . . . . . . . . . . . . . . . . 30ivTable of Contents4 Permeability k(φ) . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Literature: k(φ) . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Methodology: k(φ) . . . . . . . . . . . . . . . . . . . . . . . 364.3 Device Description: k(φ) . . . . . . . . . . . . . . . . . . . . 424.4 Experimental Protocol: k(φ) . . . . . . . . . . . . . . . . . . 454.5 Data Processing and Fitting: k(φ) . . . . . . . . . . . . . . . 464.6 Results and Discussion: k(φ) . . . . . . . . . . . . . . . . . . 474.7 Conclusions: k(φ) . . . . . . . . . . . . . . . . . . . . . . . . 535 Dewatering Experiments and Model Comparisons . . . . . 555.1 Methodology and Experimental Protocol: Dewatering . . . . 565.2 Experimental Results and Discussion: Dewatering . . . . . . 575.2.1 Chemical Additives . . . . . . . . . . . . . . . . . . . 605.2.2 Low Consistency Refining . . . . . . . . . . . . . . . . 625.3 Base Model Results: Dewatering of Hard Particle Suspension 655.4 Base/Extended Model Results: Dewatering of Cellulose FibreSuspensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.5 Conclusions: Dewatering Experiments and Model Compar-isons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806 Model Validation Through PTV Analysis . . . . . . . . . . 816.1 Methodology and Experimental Protocol: PTV Analysis . . 816.2 Results and Discussion: PTV Analysis . . . . . . . . . . . . 826.3 Conclusions: Model Validation Through PTV Analysis . . . 877 Diffusivity Dˆ(φ) and Quantifying Dewatering Ability . . . 887.1 Results and Discussion: Dˆ(φ) . . . . . . . . . . . . . . . . . 887.2 Quantifying Dewatering Ability: Dˆ(φ) . . . . . . . . . . . . . 907.3 Quantifying Dewatering Ability: CSF . . . . . . . . . . . . . 927.4 Conclusions: Dˆ(φ) and Quantifying Dewatering Ability . . . 948 Summary and Future Work . . . . . . . . . . . . . . . . . . . 958.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99vTable of ContentsAppendicesA Compressive Yield Stress and Dewatering Experiments: Op-erator’s Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . 104A.1 Start-Up Procedure . . . . . . . . . . . . . . . . . . . . . . . 104A.2 Experimental Procedure . . . . . . . . . . . . . . . . . . . . 105A.3 Compressive Yield Stress: Specific Material Trial Details . . 106A.4 Dewatering: Specific Material Trial Details . . . . . . . . . . 107B Permeability Experiments: Operator’s Manual . . . . . . . 109B.1 Start-Up and Flush Procedure . . . . . . . . . . . . . . . . . 109B.2 Experimental Procedure . . . . . . . . . . . . . . . . . . . . 110B.3 Fibre Collection, Flush, and Shutdown Procedure . . . . . . 114B.4 VFD Operation Procedure . . . . . . . . . . . . . . . . . . . 115C PTV Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118D Information on Suspensions . . . . . . . . . . . . . . . . . . . 121D.1 Background on Cellulose Fibre Suspensions . . . . . . . . . . 121D.1.1 Softwood versus Hardwood Fibres (Series 1 Comparedto 9) . . . . . . . . . . . . . . . . . . . . . . . . . . . 122D.1.2 Difference in Pulping Process (Series 1 and 9 Com-pared to 5) . . . . . . . . . . . . . . . . . . . . . . . . 122D.1.3 Impact of Low Consistency Refining (Series 6, 7, and8 Compared to 5) . . . . . . . . . . . . . . . . . . . . 123D.1.4 Impact of Chemical Additives (Series 2, 3, and 4 Com-pared to 1) . . . . . . . . . . . . . . . . . . . . . . . . 124D.2 Preparation of Suspensions . . . . . . . . . . . . . . . . . . . 125D.2.1 Series 1 and 9 Preparation . . . . . . . . . . . . . . . 125D.2.2 Series 5, 6, 7, and 8 Preparation . . . . . . . . . . . . 125D.2.3 Series 2, 3, and 4 Preparation . . . . . . . . . . . . . 126D.2.4 Series 10 Preparation . . . . . . . . . . . . . . . . . . 127D.3 Physical Parameters of Suspensions . . . . . . . . . . . . . . 127viList of Tables3.1 Empirical Constants for Cellulose Fibre Py(φ) Functional FormsFound in Literature . . . . . . . . . . . . . . . . . . . . . . . 173.2 Series of Suspensions Investigated. . . . . . . . . . . . . . . . 253.3 Results: Fitted Py(φ) Empirical Constants . . . . . . . . . . . 274.1 Empirical Constants for Cellulose Fibre k(φ) Functional FormsFound in Literature . . . . . . . . . . . . . . . . . . . . . . . 344.2 Results: Fitted k(φ) Empirical Constants . . . . . . . . . . . 495.1 Results: Chosen  and λ(φ) Empirical Constants . . . . . . . 68A.1 Compressive Yield Stress: Specific Material Trial Values . . . 107A.2 Dewatering: Specific Material Trial Values (Pulp Fibres) . . . 107A.3 Dewatering: Specific Material Trial Values (Nylon Fibres) . . 108D.1 Details of TMP Low Consistency Refiner Trial . . . . . . . . 126D.2 Results: Suspensions’ Physical Parameters . . . . . . . . . . . 128viiList of Figures1.1 Valmet TwinRollTM Press . . . . . . . . . . . . . . . . . . . . 21.2 Twin Roll Press Nip Point . . . . . . . . . . . . . . . . . . . . 32.1 One Dimensional, Constant Rate Dewatering Model . . . . . 53.1 Select Py(φ) Values From Literature . . . . . . . . . . . . . . 163.2 Compressive Yield Stress Experimental System (CYSES) . . 213.3 CYSES Suspension Chamber and Permeable Piston . . . . . 223.4 CYSES Overall Layout . . . . . . . . . . . . . . . . . . . . . . 233.5 Results: Py(φ) (Series 1 Compared to Select Values FromLiterature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 Results: Py(φ) (Series 1, 5, 9, and 10) . . . . . . . . . . . . . 283.7 Results: Py(φ) (Series 2, 3, and 4 Compared to 1) . . . . . . 293.8 Results: Py(φ) (Series 6, 7, and 8 Compared to 5) . . . . . . 304.1 Select k(φ) Values and Forms From Literature . . . . . . . . 324.2 Permeability Model . . . . . . . . . . . . . . . . . . . . . . . . 374.3 Permeability Experimental System (PES), Section and Ex-ploded View . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4 PES Permeable Piston and Screen Spacer . . . . . . . . . . . 444.5 Results: k(φ) (Series 1 Compared to Select Values From Lit-erature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.6 Results: k(φ)/r2 (Series 1 and 10 Compared to Select ValuesFrom Literature) . . . . . . . . . . . . . . . . . . . . . . . . . 484.7 Results: k(φ) (Series 1, 5, 9 and 10) . . . . . . . . . . . . . . 504.8 Results: k(φ) (Series 2, 3, and 4 Compared to 1) . . . . . . . 514.9 Results: k(φ) (Series 6, 7, and 8 Compared to 5) . . . . . . . 535.1 One Dimensional, Constant Rate Dewatering Model (Re-shown) 565.2 Dewatering Rate Color Legend . . . . . . . . . . . . . . . . . 575.3 Results: Dewatering (Series 1, 5, 9, 10, and Select Curves) . . 595.4 Dewatering Trend Shape Explained (Series 10) . . . . . . . . 60viiiList of Figures5.5 Results: Dewatering (Series 1, 2, 3 and 4) . . . . . . . . . . . 615.6 Results: Select Dewatering (Series 1, 2, 3 and 4) . . . . . . . 625.7 Results: Dewatering (Series 5, 6, 7, and 8) . . . . . . . . . . . 635.8 Results: Select Dewatering (Series 5, 6, 7, and 8) . . . . . . . 645.9 Results: Dewatering vs. Base Model (Series 10) . . . . . . . . 665.10 Results: Fit of Base Model (Series 10) . . . . . . . . . . . . . 665.11 Results: Dewatering vs. Base/Extended Model (Series 1) . . 695.12 Results: Fit of Base/Extended Model (Series 1) . . . . . . . . 695.13 Results: Dewatering vs. Base/Extended Model (Series 2) . . 705.14 Results: Fit of Base/Extended Model (Series 2) . . . . . . . . 705.15 Results: Dewatering vs. Base/Extended Model (Series 3) . . 715.16 Results: Fit of Base/Extended Model (Series 3) . . . . . . . . 715.17 Results: Dewatering vs. Base/Extended Model (Series 4) . . 725.18 Results: Fit of Base/Extended Model (Series 4) . . . . . . . . 725.19 Results: Dewatering vs. Base/Extended Model (Series 9) . . 735.20 Results: Fit of Base/Extended Model (Series 9) . . . . . . . . 735.21 Results: Dewatering vs. Base/Extended Model (Series 5) . . 755.22 Results: Fit of Base/Extended Model (Series 5) . . . . . . . . 755.23 Results: Dewatering vs. Base/Extended Model (Series 6) . . 765.24 Results: Fit of Base/Extended Model (Series 6) . . . . . . . . 765.25 Results: Dewatering vs. Base/Extended Model (Series 7) . . 775.26 Results: Fit of Base/Extended Model (Series 7) . . . . . . . . 775.27 Results: Dewatering vs. Base/Extended Model (Series 8) . . 785.28 Results: Fit of Base/Extended Model (Series 8) . . . . . . . . 786.1 Results: Contour (Series 10 Low Dewatering Rate, 0.25 mm/s) 826.2 Results: Contour (Series 10 High Dewatering Rate, 3.0 mm/s) 836.3 Results: Velocity Profiles vs. Base Model (Series 10) . . . . . 846.4 Results: Contour (Series 1 Low Dewatering Rate, 1.5 mm/s) 856.5 Results: Contour (Series 1 High Dewatering Rate, 10.0 mm/s) 856.6 Results: Velocity Profiles vs. Base/Extended Model (Series 1) 867.1 Results: Dˆ(φ) Compared to Literature . . . . . . . . . . . . . 897.2 Defining Schematically φAvg and φPy . . . . . . . . . . . . . . 907.3 Results: Dˆ(φ) vs. Φ . . . . . . . . . . . . . . . . . . . . . . . 917.4 Results: CSF vs. Φ . . . . . . . . . . . . . . . . . . . . . . . . 937.5 Results Dˆ(φ) vs. CSF . . . . . . . . . . . . . . . . . . . . . . 94B.1 Permeability Experimental System Water Flow Diagram . . . 116ixList of FiguresB.2 Permeability Experimental System Hydraulic Fluid Flow Di-agram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117C.1 PTV Analysis Flow Diagram . . . . . . . . . . . . . . . . . . 119xAcknowledgementsTo start, I would like to thank the many individuals in the Mechanical andChemical & Biological Engineering Departments at UBC who have sup-ported and assisted me throughout this project. In particular, I would liketo thank my supervisor, Mark Martinez, for his guidance, mentorship, andassistance throughout this process, in addition to my co-supervisors NeilBalmforth and Duncan Hewitt for all their help and advice. Thank you toall my research assistants for their efforts towards this project.Special thanks are owed to my parents and family, for all their moralsupport and guidance throughout this lengthy educational pursuit. All thephone calls, visits, emails and letters have made me feel at home. Thankyou to my friends who have helped in many ways along the way.Finally, I would like extend my warm appreciation to Alicia Figueira, forall of her support, understanding, and companionship throughout this chal-lenging endeavor. Learning and growing together through our educationalpursuits has been a wonderful, exciting, and rewarding journey.xiChapter 1IntroductionThe forest industry is of significant importance to the Canadian economy.According to the Forest Products Association of Canada (www.fpac.ca),Canada’s forest industry as a whole is a $58 billion yearly revenue industryrepresenting 2% of our country’s GDP. The pulp and paper industry ac-count’s for $15.7 billion of the Canadian forest industry. Pulp productionis one of Canada’s largest export industries and British Columbia’s largest,with $7 billion in exports in 2014. Understanding and optimization of pulpand paper production techniques are of significant economic importance.A fundamental process in the production of pulp or paper is the dewater-ing. Large volumes of water are added to the fibres at the start of productionto produce a homogeneous suspension [1] and at intermediate washing op-erations. The aspect of production in which we aim to gain further insightinto is the process of dewatering flocculated suspensions of cellulose fibresby mechanical means, or mechanical dewatering. Evaporative drying is alsoused in the production of paper, however it is a very expensive operation [2]due to the high energy intensity needed to boil remaining water out of thesheet at the end of production. This high cost is what creates the desire tooptimize dewatering by mechanical means.Mechanical dewatering is seen in various operations. A few examplesinclude thickeners, wash presses, screw presses, and on the paper machineduring forming and pressing. The particular application that is of inter-est to this project is the operation of a twin roll press used in the washingof pulp suspensions. Twin roll presses provide displacement washing be-fore mechanically dewatering the suspension. The machine consists of twocounter rotating, permeable drums that sit within stationary cylindricaltroughs, which can be seen in the cross section view of Figure 1.1. The pulpsuspension is supplied to the tops of the drums and flows downwards fol-lowing the rotation of the drums within the gap between the drums and thetrough. Washing fluid flows radially inward through the suspension streamsto rinse the pulp from residue. The cleaned suspension streams then mergeand consolidate as the suspension passes through the nip point. The pulpsuspension then carries on to further processes.1Chapter 1. IntroductionPulp Suspension Stream Figure 1.1: View of Valmet TwinRollTM Press showing internals and asection view illustrating the flow path of the pulp suspension streams. Therotating drum directions are indicated by the black arrows. Figure adaptedfrom Valmet brochure, Valmet Corporation c© 2016.The mechanical dewatering that occurs in the nip point is the focus ofthis project. During particular operational conditions, the dewatering of thesuspension can be approximated as one dimensional dewatering in the radialdirection. The nip point is shown in Figure 1.2.This project aims at assessing the suitability of a well-established mod-eling approach [3, 4] at capturing dewatering behaviour of cellulose fibresuspensions. An extension is made to this approach as well to capture a fur-ther dynamic of the dewatering event. Suitability of this extended model isalso investigated. Experimental equipment was designed, constructed, andoperated to collect the material parameters required for the models, and thedewatering results for comparison. Numerous suspensions are investigatedto catalog various cellulose fibre suspensions dewatering behaviors.Chapter 2 presents background on the two modeling approaches and endswith a summary and the project objectives. Chapter 3 contains the workpertaining to the collection of the first of two material parameters needed forthe modeling validation, compressive yield stress Py(φ). The chapter startswith a literature review of compressive yield stress, followed by our method-ology of collecting the material parameter. A description of the experimentalequipment and procedure follows. The series of suspensions investigated arethen introduced. Next, the various experimental results collected are shownand discussed, and the chapter ends with concluding remarks. Chapter 4 fol-2Chapter 1. IntroductionDrum DrumNipTroughFigure 1.2: Enlarged view of twin roll press nip. Fluid flows radially inwards(denoted with blue arrows) through the permeable wall of the rotating drumsas the suspension streams converge and consolidate through the nip point.lows the identical format for the second of two material parameters required,permeability k(φ). Chapter 5 presents experimental and modeling work ofdewatering. The chapter begins with a brief description of the methodologyand experimental procedure, followed by a presentation and discussion ofthe experimental results. Next, comparisons of the experimental results toboth model results are presented and discussed. Concluding remarks follow.Chapter 6 presents a further validation attempt of both models through aparticle tracking velocimetry (PTV) analysis that was performed to com-pare experimental results to the models’ solid phase movement predictions.Concluding remarks follow. Chapter 7 focuses on diffusivity, a materialparameter dependent on compressive yield stress and permeability. Experi-mentally determined results are first compared to other materials found inthe literature, followed by an investigation into diffusivity’s suitability inquantifying a suspension’s dewatering ability and how it compares to an in-dustrially accepted parameter quantifying drainability, Canadian StandardFreeness (CSF). Summarized conclusions of each section and future workare found in Chapter 8. Various supplemental material can be found in theappendices, including equipment manuals, details of the PTV analysis, andinformation on the various suspensions investigated.3Chapter 2BackgroundWe are interested in understanding the mechanical dewatering (hereafterreferred to only as dewatering) of cellulose fibre suspensions in the nip pointof a twin press roll. This industrial dewatering problem has been simpli-fied down to a one dimensional, constant dewatering rate investigation of aflocculated suspension, shown schematically in Figure 2.1.The model consists of a cylindrical suspension chamber with a closedbase. A permeable membrane is located at zˆ = hˆ(tˆ) = h0 − Utˆ as shown inthe schematic where U is the speed of the permeable membrane (scalar), h0is the initial height of the suspension, and tˆ is time.To gain an understanding into this simplified dewatering event, we wishto develop a modeling approach that can capture experimentally collectedresults. In the coming section, the modeling efforts used in this project arepresented. Following a detailed discussion, a summary is provided, followedby the project objectives.2.1 Dewatering of Flocculated SuspensionsInterest in the consolidation of flocculated suspensions is by no means lim-ited to pulp and paper operations. Dewatering is a primary operation inmineral, chemical, and waste water treatment industries. A few examples ofresearch of dewatering in these industries include investigations into the im-pact of swelling clays on the concentrating efforts of coal mining tailings [5],the compaction of clay rocks in sedimentary basins for applications of un-derwater drilling [6], and investigation of dewatering of waste water sludgesfor optimization of filtration equipment [7].Due to the wide industrial interest, various attempts to capture dewa-tering behavior have been made. The compressive rheology modeling effortsby Buscall, White, and Landman are followed in this project [3, 4]. Thismodeling approach describes the behavior of flocculated suspensions in sed-imentation and compression from dilute, un-networked suspensions, all theway up to suspensions at maximum packing. Networking of suspensionsoccurs at a solid volume fraction, or solidity (φ), referred to as the gel point42.1. Dewatering of Flocculated Suspensions 𝒛𝝈( 𝒕) 𝒛 =  𝒉( 𝒕)Suspension 𝒛 = 𝟎Figure 2.1: One dimensional, constant dewatering rate model.(φg). At this concentration, a continuous network forms that can withstandand transmit a compressive load [8]. Gel points for cellulose fibre suspen-sions are below solidity (solid volume fraction) values of approximately 0.01(v/v) [9]. In this project, we limit our interest to initially fully networkedsuspensions. We are not below or near the gel point in the operations of atwin roll press, particularly in the press nip point where concentrations reachconsistencies (solid mass fractions) as high as 0.30-0.40 (wt/wt) [10, 11].The compressive rheology modeling approach uses a two-phase flow model.Assumptions include neglecting gravity, inertial terms, and viscous stressesin the fluid phase, except where they enter indirectly through Darcy’s law[12]. The individual phases are also assumed to be incompressible. Slip onthe wall limits motion to one dimension. This assumption has been shownexperimentally to be valid by Buscall et al. [13–16]. A further assumption isnegligible shear stresses in the solid network (shown to be a valid assumptionby Buscall et al. [14]).With these various assumptions, we arrive at the following simplifiedequations. We start with continuity expressions of the solid and fluid phase(Equations 2.1 and 2.2 respectively)∂φ∂tˆ+∂∂zˆ[φuˆs] = 0 (2.1)∂(1− φ)∂tˆ+∂∂zˆ[(1− φ)uˆf ] = 0 (2.2)52.1. Dewatering of Flocculated Suspensionswith φ as our solidity (solid volume fraction), and uˆs and uˆf being thesolid and liquid phase velocities respectively. We next introduce a Darcianexpression in Equation 2.3 and a conservation of total compressive stress inEquation 2.4, respectively(1− φ)(uˆf − uˆs) = −k(φ)µ∂pˆ∂zˆ(2.3)∂Pˆ∂zˆ= 0 (2.4)where k(φ) is the permeability of the suspension, µ is the fluid viscosity, andPˆ represents the total compressive stress.Permeability is an experimentally determined material parameter thatquantifies the resistance fluid flow experiences through a porous suspension.The total compressive stress is defined asPˆ = Pˆ + pˆ (2.5)where Pˆ represents the effective solid stress, or network stress, and pˆ rep-resents the fluid pore pressure. The network stress represents the solidnetwork’s resistance to uni-axial compression [8].In addition to the expressions introduced in Equations 2.1, 2.2, 2.3,and 2.4, we need a constitutive equation to relate the network stress Pˆto the solidity φ and the solid phase velocity uˆs. If the network flocculationis sufficiently strong, it can be observed experimentally that an appliedpressure to a suspension’s solid phase causes an irreversible consolidation,which depends on the normal stress acting on the network [17]. This impliesthat the suspension network posses an elastic limit that when exceeded,results in irreversible consolidation [3]. The simplest form of a constitutiveequation that would capture this consolidating behavior isDφDtˆ≡ ∂φ∂tˆ+ uˆs∂φ∂zˆ={λ(φ)[Pˆ − Py(φ)], if Pˆ > Py(φ)0, if Pˆ ≤ Py(φ)(2.6)which is posed by Buscall, White and Landman [3, 4]. λ(φ) is defined asthe solid phase rearrangement rate constant, or the dynamic compressibil-ity. Py(φ) is defined as the compressive yield stress. This expression givesconsolidation when the network stress is above the compressive yield stressPy(φ) and no consolidation when below. The compressive yield stress isthen an experimentally determined material parameter that quantifies themaximum network stress that can be withstood without consolidation.62.1. Dewatering of Flocculated SuspensionsNext, expanding the solid phase continuity, Equation 2.1, results in∂φ∂tˆ+ uˆs∂φ∂zˆ+ φ∂uˆs∂zˆ= 0 (2.7)which can be substituted into the constitutive equation, Equation 2.6, givingthe following expression for consolidationPˆ = Py(φ)− φλ(φ)∂uˆs∂zˆ. (2.8)This provides a rheological expression for the consolidation of the solidphase. This expression can be simplified further, according to Buscall andWhite, who present an argument that if the consolidation is physically lim-ited by the fluid movement past the solid phase, and not the moving ofthe solid particles relative to each other, then the dynamic compressibilityλ(φ) is of O(φ/µ) which is a large value (thus assume λ(φ) = ∞), makingthe second term on right of Equation 2.8 negligible. This assumption hasbeen used by many in the literature [3, 4, 6, 8, 18–22]. Thus, a simplifiedrheological expression is given asPˆ = Py(φ). (2.9)Equations 2.1 through 2.4, and 2.9 fully describe consolidation of a floc-culated suspension and constitute the compressive rheology modeling ap-proach. Required are a suspension’s material parameters of permeabilityand compressive yield stress, both of which are functions of solidity φ.There has been considerable interest in this modeling approach, howeveronly a few examples of validation, through comparison of experimentally col-lected dewatering data, can be found. One example was a comparison of thefinal equilibrium heights for a stepped constant pressure filtration, shown byde Kretser et al. [23], however consideration to how the model captured thetransient behavior was not given and agreement appears marginal. Anothercomparison between experiment and theory was done by de Kretser et al.[24] comparing the filtration time versus specific volume of filtrate squaredfor a single constant pressure filtration of zirconia. Final equilibrium be-havior was the focus of the authors’ validation efforts which showed goodagreement between theoretical and experimental values, however only briefdiscussion of the dynamic dewatering event is given which showed pooreragreement. Certainly further validation, particularly in capturing the dy-namics of dewatering, would be desirable to support this model.Compressive rheology, as presented here, is a well accepted method ofmodeling the consolidation of flocculated suspensions despite the limited72.1. Dewatering of Flocculated Suspensionsexperimental validation, and so it is a logical start point for this project’smodeling. Unfortunately, there is concern if it will capture the dynamicsof cellulose fibre dewatering. Pettersson et al. [25] found this method un-successful in capturing the dewatering behavior of cellulose fibres. Furtherdiscussion of this comes in Section 2.1.2 where the shortcomings of this ap-proach are addressed. Despite this, we wish to observe its effectiveness incapturing dewatering and hope to provide further validation for this wellused method.2.1.1 Base ModelWe formalize the equations of the compressive rheology modeling approachfor the experimental geometry, which will be referred to as the base model.The simplified model of the dewatering within the twin roll press is shownschematically in Figure 2.1.We start by combining our continuity expressions, Equations 2.1 and 2.2,and integrating with respect to zˆ. The boundary condition of the closed baseis used such that at zˆ = 0, uˆs = uˆf = 0. We arrive atuˆs = (1− φ)(uˆs − uˆf ). (2.10)Equation 2.10 is inserted into the Darcian expression, Equation 2.3, givinguˆs =k(φ)µ∂pˆ∂zˆ. (2.11)Next, Equations 2.4, 2.5, and 2.9 are substituted into Equation 2.11, arrivingat an expression of the the solid phase velocity in terms of φ asuˆs = −k(φ)µP ′y(φ)∂φ∂zˆ(2.12)where P ′y(φ) is defined as∂Py(φ)∂φ . Equation 2.12 is inserted into the solidphase continuity expression, Equation 2.1, to furnish the following non-lineardiffusion equation∂φ∂tˆ=∂∂zˆ(φk(φ)µP ′y(φ)∂φ∂zˆ)(2.13)with the following boundary and initial conditionsuˆs(0, tˆ) = 0 (2.14)uˆs(hˆ(tˆ), tˆ) =dhˆ(tˆ)dtˆ(2.15)82.1. Dewatering of Flocculated Suspensionsφ(zˆ, 0) = φ0. (2.16)At zˆ = hˆ(tˆ), the total compressive load is equal to the permeable pistonload, σ(tˆ). From the definition of total compressive stress, Equation 2.5,assuming the pressure drop through the permeable membrane is negligible,and Equation 2.9, we arrive atPˆ (tˆ) = σ(tˆ) = Pˆ + 0 → σ(tˆ) = Py(φ(hˆ(tˆ), tˆ)). (2.17)The load then is simply the value of the compressive yield stress defined forthe solidity at zˆ = hˆ(tˆ). This expression allows us to determine the loadpredicted by the model to compare to experimentally collected results.A third material parameter is introduced at this point which is dependenton compressive yield stress and permeability; diffusivity, Dˆ(φ) is a materialparameter defined asDˆ(φ) =φµk(φ)P ′y(φ). (2.18)Diffusivity is a solidity dependent solid diffusion coefficient [24], and can beused to compare suspensions’ dewatering performance. A high diffusivitywould correspond to a suspension that can consolidate easily. With Dˆ(φ) inEquation 2.13, we have∂φ∂tˆ=∂∂zˆ(Dˆ(φ)∂φ∂zˆ). (2.19)2.1.2 Extended ModelCellulose fibres differ from most particles found in suspensions that com-pressive rheology has been applied to. In general, cellulose fibres are hollow,tube-like structures that have weakly permeable walls [1, 26]. Uncompressedcellulose fibres have a hollow center (named a lumen) that is filled with thefluid of the suspension. During compression, fluid evacuates both the ex-terior space between fibres and the lumen of the fibres through pores inthe fibre walls. The flow of liquid out of the fibre, along with the cellu-lose polymeric nature, result in a visco-plastic behavior during compression[27]. This brings into question if the rheological expression for the networkstress of cellulose fibres is only a function of concentration. This concernis discussed by Pettersson et al. [25] as well. A more extensive rheologicalexpression, as proposed in the literature, is investigated for its suitability incapturing dewatering behavior of collapsible fibre suspensions. Expandingupon the compressive yield stress approach, introduced in the previous sec-tion, was done by D.R. Hewitt, a post doctoral fellow (PDF) from the UBC92.1. Dewatering of Flocculated SuspensionsMathematics department, who is a member of our research group. The fol-lowing modeling approach and extended model equations are paraphrasedfrom Hewitt et al. [12].To begin, we return to the constitutive equation shown in Equation 2.8.The simplifying assumption that λ(φ) =∞ provided by Buscall and Whiteseems less clear with the cellulose fibres being collapsible. If this assumptionis removed, we have a rheological expression with a rate dependency whichmay capture the dewatering of the individual fibres. The resulting, morecomplete, rheological expression is re-shown asPˆ = Py(φ)− φλ(φ)∂uˆs∂zˆ. (2.20)The exact form of the additional material parameter dynamic compress-ibility λ(φ), was beyond the scope of this project and the PDF’s work,however qualitatively we can suggest it is a parameter representative of theflow out of the hollow, porous fibres, thus is related to the permeability ofthe cellulose fibre wall. Alternatively, λ(φ) can be interpreted as the inverseof the dewatering time scale of the individual cellulose fibres (large valuesof λ(φ) represent very short dewatering time scales of the fibre). A crudemodeling of the flow out of a cellulose fibre during consolidation, shown inHewitt et al. [12], suggested that λ(φ) = (kf/µrL)φ−1 = Cφ−1, where kf , r,and L are the fibre wall permeability, fibre radius, and length respectively.These parameters are combined into C, providing a coefficient which is pro-portional to fibre wall permeability. This is a different scale of permeabilitythan that defined by k(φ).We formalize the equations for our experimental geometry with the morecomplex rheological expression, which consistutes our extended model. Weinsert Equations 2.5 and 2.20 into Equation 2.11, and arrive at a new ex-pression of the the solid phase velocity in terms of φ asuˆs = −k(φ)µ[P ′y(φ)∂φ∂zˆ− ∂∂zˆ(φλ(φ)∂uˆs∂zˆ)](2.21)which now is an implicit expression. When inserted into our solid phasecontinuity expression, Equation 2.1, we arrive at∂φ∂tˆ=∂∂zˆ(φk(φ)µ[P ′y(φ)∂φ∂zˆ− ∂∂zˆ(φλ(φ)∂uˆs∂zˆ)])(2.22)which, again, can be expressed in terms of diffusivity Dˆ(φ) as∂φ∂tˆ=∂∂zˆ(Dˆ(φ)∂φ∂zˆ− φk(φ)µ∂∂zˆ(φλ(φ)∂uˆs∂zˆ)). (2.23)102.1. Dewatering of Flocculated SuspensionsThe boundary and initial conditions remain the same, seen in Equations2.14, 2.15, and 2.16. The boundary condition for the load of the permeablemembrane is nowσ(tˆ) = Py(φ(hˆ(tˆ), tˆ))− φ(hˆ(tˆ), tˆ)λ(φ(hˆ(tˆ), tˆ))∂uˆs∂zˆ∣∣∣∣zˆ=hˆ(tˆ). (2.24)Recall: ∂uˆs∂zˆ ≤ 0 due to the permeable membrane’s direction. It should benoted that the extended model equations can be reverted to the base modelequations by reintroducing the assumption that λ(φ) is large.2.1.3 Scaling the Extended Model EquationsWe begin with dimensionless variables z, h, t, and u by scaling by the initialheight of the suspension h0, and by the speed of the piston U , respectivelyz =zˆh0, h =hˆh0, t =tˆUh0, u(z, t) =uˆs(zˆ, tˆ)U. (2.25)Permeability k(φ) and compressive yield stress Py(φ) are scaled by char-acteristic k∗ and p∗ values, chosen as the fitted functional form values ata solidity of 0.10 (v/v). We scale the load of the piston by p∗, giving thedimensionless termsK(φ) =k(φ)k∗, Πy(φ) =Py(φ)p∗, Σ(t) =σ(tˆ)p∗. (2.26)A dimensionless diffusivity is defined asD(φ) =φk(φ)P ′y(φ)k∗p∗= φK(φ)Π′y(φ). (2.27)Next we introduce γ, which is a parameter that relates the compressivestrength of the suspension to the viscous drag force from the fluid asγ =p∗k∗µh0U. (2.28)One final dimensionless parameter, that accommodates the coefficient of thedynamic compressibility, is =k∗µh02C . (2.29)112.2. Background SummaryEquation 2.23, after scaling, is defined as∂φ∂t=∂∂z(γD(φ)∂φ∂z−  φK(φ) ∂∂z(φ2∂u∂z))(2.30)with the following initial and boundary conditionsu(0, t) = 0 (2.31)u(h(t), t) = −1 (2.32)φ(z, 0) = φ0 (2.33)Equation 2.24 scaled isΣ(t) = Πy(φ)− γφ2∂u∂z∣∣∣∣z=h(t). (2.34)The scaled base model equations can be found by reinstating the assumptionthat the dynamic compressibility is a large value (λ(φ) =∞). This is doneby setting C to a large value, which simplifies Equations 2.30 and 2.34.2.2 Background SummaryInvestigating the dewatering of suspensions is not a new field. Extensive re-search has been invested in understanding dewatering, particularly throughtheoretically based modeling approaches. The compressive rheology mod-eling approach, developed by Buscall, White, and Landman, has been wellaccepted and constitutes the base model used in this project, consisting ofEquations 2.13, 2.14, 2.15, 2.16, and 2.17. Validation of this model throughcomparison to experimental results however is limited. Pettersson et al. [25]found this approach was unsuccessful in capturing the dewatering behaviorof cellulose fibres, and suggests that the network stress being only dependenton concentration was at fault.Work in extending the compressive rheology modeling approach has beendone by D.R. Hewitt, a PDF from the UBC Mathematics department whois in our research group. A more complex rheological expression, also previ-ously posed in the literature, which is dependent on another material param-eter, the dynamic compressibility λ(φ), is used to extend the compressiverheology modeling approach. This developed the extended model in thisproject, consisting of Equations 2.22, 2.14, 2.15, 2.16, and 2.24. Hope-fully this extension will be able to capture the second scale of permeability122.3. Project Objectivespresent in cellulose fibre suspension dewatering coming from liquid escapingthe porous, hollow cellulose fibres.Both the base and extended models require experimentally determinedmaterial parameters of permeability and compressive yield stress. In addi-tion to being inputs to the base and extended model, these material param-eters, particularity when combined into the dependent material parameterdiffusivity, provide comparisons of dewatering behavior between suspensions.2.3 Project ObjectivesTo start our understanding of the dewatering of cellulose fibres in the nippoint of a twin press roll, we present the following project objectives:• Develop equipment and protocol for collecting compressive yield stressPy(φ), permeability k(φ), and one dimensional dewatering experimentsat varied dewatering rates for cellulose fibre suspensions.• Test the suitability of the base and extended model equations for cap-turing the dewatering behaviour of cellulose fibre suspensions. Thiswill be determined by how well each model represents load versus av-erage solidity trends collected experimentally. The extended model’sadditional material parameter, λ(φ) is not determined experimentallyat this time, rather C, within the functional form, is used as a fittingparameter for the extended model curves. The extended model’s gov-erning equation and load, provided by the permeable membrane, arere-shown as∂φ∂tˆ=∂∂zˆ(φk(φ)µ[P ′y(φ)∂φ∂zˆ− ∂∂zˆ(φλ(φ)∂uˆs∂zˆ)])(2.22 re-shown)σ(tˆ) = Py(φ(hˆ(tˆ), tˆ))− φ(hˆ(tˆ), tˆ)λ(φ(hˆ(tˆ), tˆ))∂uˆs∂zˆ∣∣∣∣zˆ=hˆ(tˆ)(2.24 re-shown)where λ(φ) = Cφ−1. The base models equations can be found bysetting λ(φ) =∞. Base model validation is also investigated throughhow effective it can capture the dewatering behaviour of hard particlesuspensions.• Further validation of the model’s representation of dewatering be-haviour will be investigated in determining the base and extendedmodel’s abilities in capturing the solid phase movement of suspensionsduring consolidation.132.3. Project Objectives• Catalog various cellulose fibres’ dewatering behaviours.Through these objectives we hope to have a better understanding of onedimensional, constant rate dewatering of cellulose fibres. This provides aknowledge base that can then be built upon in the pursuit of fully under-standing the mechanisms at play in the nip of a twin roll press.14Chapter 3Compressive Yield StressPy(φ)Compressive yield stress, as introduced in Section 2.1, is a material pa-rameter that quantifies the network stress that can be withstood withoutconsolidation of the network. It is an input into both the base and theextended models, requiring experimental determination for the various sus-pensions that are to be investigated in this project. It can also provideinsight into how a suspension dewaters, particularly when combined intodiffusivity, which will be discussed in Chapter 7.Throughout this chapter, we present the work done in developing theequipment and protocol for collecting compressive yield stress. We beginwith a review of functional forms and several experimental techniques of col-lecting compressive yield stress found in the literature. We next introducethis project’s methodology for collecting results and our chosen functionalform. Following this, sections including a detailed description of the ex-perimental device, an experimental protocol outlining the procedure, and abrief description of processing and fitting of experimental data, are provided.Next, a materials section outlining the various suspensions investigated forcataloging dewatering behaviours is provided. Results collected are thenprovided, followed by concluding remarks.3.1 Literature: Py(φ)Compressive yield stress is the network stress limit that can be withstoodelastically by a suspension at a concentration φ. A load above the compres-sive yield stress results in irreversible consolidation of the network [4]. Theform of Py(φ) is an increasing function with φ due to the increasing numberof inter-particle contacts. The criterion necessary to measure compressiveyield stress is a sufficient concentration to form a continuous network [23],thus Py(φ) is only measurable in concentrations above the gel point (φg).Thus, Py(φ) → 0 as φ → φg and Py(φ) → ∞ as φ → φmp, where φmp153.1. Literature: Py(φ)0 0.2 0.4 0.610−2100102104φPy(φ)[kPa]Figure 3.1: Select Py(φ) values from the literature. Softwood chemicalpulp from Pettersson et al. [25] and Vomhoff et al. [27] are shown as ⊕ and⊗ symbols respectively. Suspensions of zirconia [23] (©), alumina [28] (),water treatment sludge [29] (N), and coal-mining tailings [5] (♦) are shownfor comparison.is the maximum packing solidity. Select results of compressive yield stressfrom the literature are shown in Figure 3.1 to illustrate the general trendfor various materials. Cellulose fibres are highlighted in blue in the figure.Various functional forms have been suggested for compressive yield stress.A simple power-law function has been used (eg. [13]) as a fit,Py(φ) = aφb (3.1)where a and b are fitting parameters. Buscall et al. found this as an ap-propriate fit for the experimental data for flocculated polystyrene latex [13].Simple power-law functions, however, are not able to capture the behaviorover a large range of solidities due to the change in behavior around the gelpoint and when approaching the maximum packing [23, 28]. Slightly morecomplex power-law functions have been suggested by various authors (eg.[4, 8, 22])Py(φ) = k [(φ/φg)n − 1] (3.2)Py(φ) = k(φ/φg − 1)n (3.3)163.1. Literature: Py(φ)Table 3.1: Empirical constants for Py(φ) functional forms for cellulose fibresuspensions found in the literature. Vomhoff et al. constants assume adensity of 1500 kg/m3 for the solid phase.Reference Details Functional Form ConstantsVomhoff et al. [27] Bleached softwood Py(φ) = aφb a = 7.9 · 104 kPapulp b = 4.0Pettersson et al. [25] Scandinavian fully Py(φ) =C1·φC2(1−φ)C3 C1 = 3.1 · 103 kPableached softwood C2 = 2.6pulp C3 = 3.2Py(φ) = k[φnφmp − φ](3.4)to capture the trend over a larger range of solidities where k and n arefitting parameters, and φg and φmp are the gel point and maximum packingvolume fractions respectively. Often φg and φmp are fitted parameters aswell. Channell et al. [28] used the functional form shown in Equation 3.3 tofit behavior of aggregated alumina.Turning back to the cellulose fibre literature results (shown in Figure3.1), Vomhoff et al. [27] used a general power-law of the form in Equation3.1, whereas Pettersson et al. [25] used the following expressionPy(φ) =C1 · φC2(1− φ)C3 . (3.5)The fitted results of Vomhoff et al. and Pettersson et al. are found in Table3.1.Various experimental techniques can be found in the literature for deter-mining compressive yield stress. Comparing results from the various tech-niques shows independence of process used, providing evidence that com-pressive yield stress is a true material parameter [21, 23].The simplest technique implemented involves sets of sedimentary tests.Experimentally, equilibrium heights of sediments (h∞) are found for varyingvalues of the product of the initial solidity and initial height of the suspen-sion (φ0h0) and plotted as φ0h0 versus h∞. Based on the solid phase force173.1. Literature: Py(φ)balance, the solidity at the base of the sediment is defined as [20, 30]φ =∂(φ0h0)∂h∞(3.6)and the solid pressure, equivalent to the compressive yield stress, asPy = ∆ρgφ0h0 (3.7)where ∆ρ is the difference in densities between the two phases. The mainlimitation of this process is not being able to obtain high values of solidpressure, thus the solidity range available with this technique is quite limited.One way to increase the available range of solidities using the same fun-damental principle is to determine equilibrium heights of sediments at vary-ing velocities in a centrifuge, which is a technique proposed by Buscall andWhite [3]. Of course, due to varying gravitational force due to radial loca-tion, the equations are a little more complex, however, with approximatesolutions provided by Green et al. [31], the solidity and solid pressure at thebase of the sample can be found from the following expressionsφ ≈φ0h0[1− 12R(h∞ + g dh∞dg)][(h∞ + g dh∞dg) (1− h∞R)+ h2∞2R] (3.8)Py ≈ ∆ρg[1− h∞2R]φ0h0 (3.9)for varying levels of g, the gravitational acceleration at the base of the sampletube, a distance R from the center of the centrifuge. Green et al. concludedthat these approximations would be accurate enough for most applications;they have been a well-used approach for finding the compressive yield stressof various materials (eg. [5, 15, 28, 32]).A different approach is through a technique of constant applied pressurefiltration. The experiment involves containing the suspension in a compres-sion cell, with a permeable boundary at one or both ends, and inducing aconstant uni-axial compression force on the suspension [23]. The suspensionwill dewater until a solidity (φ∞) is obtained homogeneously. Thus, we canfind the solidity and solid pressure from the final equilibrium height (h∞)of the compressed suspension and the applied constant pressure ∆P asφ =φ0h0h∞(3.10)183.2. Methodology: Py(φ)Py = ∆P. (3.11)This technique has been used successfully in many applications for find-ing the compressive yield stress (eg. [32, 33]). The technique also can beadapted to allow multiple tests of a single suspension sample, by incremen-tally increasing the applied pressure once a stable h∞ has been obtained fora particular applied pressure. This adapted technique allows much quickerdetermination of compressive yield stress for a range of solidities, and hasbeen shown to provide comparable results to single pressure filtration ex-periments [24, 34]. Others have used, or suggested, this technique as well(eg. [8, 18, 21]).Turning now to examples of cellulose fibre suspension techniques, Vomhoffet al. [27] used the stepped constant pressure technique, with the resultsshown in Figure 3.1. Kugge [35] also used a stepped constant pressure tech-nique for measuring compressive yield stress of cellulose fibre suspensions.Finally, Pettersson et al. [25] used a technique of compressing a suspensionat a low constant dewatering rate. If a sufficiently low dewatering rate isachieved, uniform compaction of the suspension will occur providing a di-rect measurement of compressive yield stress from the applied load. Resultsof this technique are shown in Figure 3.1. The experiment started witha 0.05 (wt/wt) consistency suspension, and was compressed by a movingpermeable membrane at a rate of 0.005 mm/s.3.2 Methodology: Py(φ)Two methodologies are used in this project for determining compressiveyield stress. The technique proposed by Pettersson et al. [25] was imple-mented as our main method. It involves running constant dewatering rateexperiments at very low permeable membrane velocities; so low that thesuspension experiences uniform compaction. We demonstrate this with ascaling exercise, considering the magnitudes of terms in our dimensionlessgoverning equation∂φ∂t=∂∂z(γD(φ)∂φ∂z−  φK(φ) ∂∂z(φ2∂u∂z)). (3.12)When dewatering is very slow, γ  1, and both ∂φ∂t and ∂u∂z are small, thusO(1). For the equation to then balance, ∂φ∂z is O(1/γ). With this conclusion,we can approximate our solid phase continuity definition Equation 2.1 indimensionless variables as193.2. Methodology: Py(φ)∂φ∂t= − ∂∂z[uφ] = −φ∂u∂z− u∂φ∂z∂φ∂t≈ −φ∂u∂z(3.13)which leads toφ =φ0hand u = − zh. (3.14)Thus at sufficiently slow dewatering rates, solidity within the suspension isuniform. The compressive yield stress can be found from either models’ loadboundary condition (Equation 2.17 or 2.24) asPy(φ(hˆ(tˆ), tˆ)) ≈ σ(tˆ) (3.15)where σ(tˆ) is the load provided by the permeable membrane. Solidity canbe defined from the solid phase mass ms and the height hˆ(tˆ) asφ(hˆ(tˆ), tˆ) =msρsAhˆ(tˆ)(3.16)where ρs is the density of the solid phase, and A is the cross-sectional areaof the suspension. The appropriate dewatering rate is found by successivelyslower dewatering experiments, until the trends collapse onto one another.The second technique found compressive yield stress experimentally fromthe permeation data collected for determining the suspension’s permeability.The details of this technique are left to Section 4.2. This technique was notadopted as the main method of data collection due to the desire of havingthe compressive yield stress determined by the same experimental equipmentthat collected the dewatering experimental data. This reduced error, havingthe same experimental system for both, and ensured the desirable effect ofdecreasing dewatering rate trends converging towards the compressive yieldstress curve. The first technique also allowed a larger range of solidity to bemeasured.The functional form we use is the same as Pettersson et al. [25]Py(φ) =aφb(1− φ)c (3.17)with a, b, and c being empirical fitting constants.203.3. Device Description: Py(φ)Permeable PistonSuspension ChamberLoad CellLoad Cell PlatformFigure 3.2: MTS 858 Table Top System modified for compressive yieldstress data collection.3.3 Device Description: Py(φ)An experimental system was necessary to provide compressive yield stressresults from a low, constant dewatering rate experiment. The system re-quired a controllable, constant rate permeable membrane movement, and amethod of measuring the membrane’s height and load provided. We modi-fied a pre-existing experimental system in the lab for this application. Ourdewatering experiments are also collected with this system.The pre-existing system in the lab was originally developed by MTS Sys-tems Corporation (www.mts.com). The system had been previously used forpressure filtration, thus only minor modifications were required. A modelof the MTS 858 Table Top System, along with the required components forcollecting Py(φ) data are shown in Figure 3.2. Modifications to the systemincluded a redesigned suspension chamber, and the design and constructionof a conical platform that attached to the load transducer, providing a sur-face for the suspension chamber to rest upon. The load transducer platformthreads directly into the load transducer which is part of the MTS system.The load transducer has a measurable range up to 2.2 MPa of compressiveload for our particular sized suspension chamber. The suspension chamber213.3. Device Description: Py(φ)Top CollarRubber GasketBase PlateRemovable Side WallFine MeshCoarse MeshPermeable PistonFigure 3.3: Details of the suspension chamber (left) and the permeablepiston (right) of the compressive yield stress experimental system.consists of a clear 76.2 mm ID PVC pipe sandwiched between the base plateand top collar. Four fasteners and a rubber gasket are used to compress theassembly together, providing a sealed base for containing the suspension. Achamfered inner lip at the top of the chamber’s side wall helps with aligningthe permeable piston. The suspension chamber can be seen in Figure 3.2,with details shown in Figure 3.3.A pre-existing permeable piston was used as the moving permeable mem-brane, which is constructed out of a 76.2 mm diameter, 19.05 mm tallsolid cylinder of stainless steel. Eight 12.7 mm holes were drilled verticallythrough the cylinder and an O-ring groove was milled around the perimeterof the cylinder to provide a seal for the piston. A tapped hole in the centerprovides the attachment location for the MTS hydraulic actuator rod. Acoarse weave wire mesh is attached to the bottom face of the cylinder to en-courage spreading of the flow through the piston. A fine plastic mesh withhole sizes of 0.33 mm was attached to the coarse weave mesh to prevent thesolid phase from passing through. The permeable piston’s assembly can beseen in Figure 3.3.The movement and compressive load of the permeable piston is providedby the hydraulic actuator of the MTS 858 Table Top System. The MTS 858Table Top System stand-alone controller unit is used to locally control thepiston position and define its rate. Rates can be set for any value between0.001 mm/s to 83.33 mm/s. The unit uses a linear variable differentialtransformer (LVDT) to detect the hydraulic actuator rod’s position. Themaximum range of the piston movement is 100 mm. The overall system canbe seen in Figure 3.4.223.4. Experimental Protocol: Py(φ)Figure 3.4: Complete compressive yield stress experimental system withall components shown and identified.The stand-alone controller can also be operated remotely through thedesktop computer at the work station. A LabVIEW interface has beendeveloped for remotely communicating with the stand-alone controller, aswell as collecting data inputs using a National Instruments 6009 USB DAQ(www.nationalinstruments.com). Inputs for the 6009 USB DAQ are ana-log outputs from the stand-alone controller sending signals from the LVDT(height) and load transducer.3.4 Experimental Protocol: Py(φ)A detailed manual for the equipment is shown in Appendix A. The followingis a brief description of the experimental protocol.A compressive yield stress trial began with filling the suspension chamberwith 250 g of 0.03-0.04 (wt/wt) consistency suspension. The piston wasthen manually lowered to the top of the suspension to record the initialheight (h0). Following initial height determination, the piston was raisedapproximately 20 mm above the suspension. Automation of the trial beganat this point. First the piston moved downwards at a rate of 0.5 mm/sto a height equivalent to a solidity of 0.04 (v/v). Once the piston reachedthis location, it remained paused for several seconds, and then proceededto move downwards at the rate defined for the compressive yield stress trial233.5. Data Processing and Fitting: Py(φ)(usually 0.001 mm/s). The initial movement at 0.5 mm/s is performed toreduce the overall trial time. No detectable load is achieved up to 0.04 (v/v)solidity, and any gradients achieved due to the higher rate are assumed tobe negligible. The piston continued moving at the defined velocity until thecompressive load exceeded 1.3 MPa. Once the load had been exceeded, thepiston reversed direction and moved away from the compressed suspensionand the LabVIEW interface saved the data collection. Height measurementsare compensated for compliance of the system.The sample is then remixed back into a uniform suspension, collected,filtered, dried, and weighed to obtain the solid’s dry mass. This is a moreaccurate method of determining solidity than from the initial suspension’sconsistency. At least four compressive yield stress trials were performed fora given suspension (fresh samples for each trial) to average experimentalvariations.3.5 Data Processing and Fitting: Py(φ)Experimental trial data files from the MTS LabVIEW interface are a 3-column “.txt” format file. The columns of data are height (in mm), com-pressive load (in Pa), and time (in s). Using Equation 3.16, we can determinesolidity values from the height values and the dried solid mass, and with ourboundary load condition shown in Equation 3.15 we see our compressiveload values are simply our Py values. As mentioned previously, we per-form at least four trials to account for experimental variations. We find thePy(φ) trend for each trial, and then average them to get a single trend forparameter estimation.With our averaged experimental trend, we fit our functional form ofcompressive yield stress (Equation 3.17) by linearizing the expressionln [Py(φ)] = ln [a] + b ln [φ]− c ln [1− φ] (3.18)and using linear regression to find our empirical constants a, b, and c.3.6 MaterialsVarious suspensions were investigated in this project to fulfill our objectivesof validating the base and extended models, and for cataloging dewateringbehaviors. Table 3.2 lists the series of suspensions investigated.Series 1 investigated the dewatering behaviour of a northern bleachedsoftwood Kraft pulp (NBSK), and provided the base pulp for Series 2, 3,243.7. Results and Discussion: Py(φ)Table 3.2: Series of suspensions investigated. Symbol indicates identifierused in the coming results.Series Symbol Fibre Refined Energy Chemical Treatment[kWh/t]1 M NBSKa 0 -2 O NBSK 0 0.1 (wt/wt%) EKA FIX 41 additive3 / NBSK 0 0.1 (wt/wt%) EKA PL 1510 additive4 . NBSK 0 0.1b(wt/wt%) EKA PL 1510 andEKA NP 320 additives5  TMPc 0 -6 ♦ TMP 55.8 -7 © TMP 111.8 -8 • TMP 229.1 -9 × BHKd 0 -10 + Nylon 0 -a Northern Bleached Softwood Kraft Pulp (NBSK)b Total chemical concentration, equal parts EKA PL 1510 and EKA NP 320c Thermo-Mechanical Pulp (TMP)d Bleached Hardwood Kraft Pulp (BHK)and 4, investigating the impact of dewatering chemical additives. Series 5provided a comparison of a different pulping process: thermo-mechanicalpulp (TMP). Series 6, 7, and 8 compared the effects of increased low con-sistency refining on TMP. With Series 9, we investigated the difference seenbetween a soft and hardwood fibre with a bleached hardwood Kraft pulp(BHK). Finally, Series 10 provided an ideal suspension of nylon fibres withuniform shape and no internal porosity.Background, preparation details, and physical parameters obtained throughFibre Quality Analyzer (FQA) and Canadian Standard Freeness (CSF) ex-periments are provided for the various suspensions in Appendix D.3.7 Results and Discussion: Py(φ)To begin, we investigated the validity of the results obtained experimentally.Shown in Figure 3.5 are the Py(φ) results of Series 1 obtained by bothtechniques, outlined in the methodology, compared to select values from theliterature, introduced in Figure 3.1.A comparison of the results, from the two techniques, shows good agree-ment. Comparing the collected Series 1 results to the results of Pettersson253.7. Results and Discussion: Py(φ)0 0.2 0.4 0.610−2100102104φPy(φ)[kPa]Figure 3.5: Series 1 Py(φ) values (denoted as M) compared to select valuesfrom the literature. The results from our secondary technique (from per-meation data) are highlighted with green filled circles. Softwood chemicalpulp from Pettersson et al. [25] and Vomhoff et al. [27] are shown as ⊕ and⊗ symbols respectively. Suspensions of zirconia [23] (©), alumina [28] (),water treatment sludge [29] (N), and coal-mining tailing [5] (♦) are shownfor comparison.263.7. Results and Discussion: Py(φ)Table 3.3: Empirical constants for compressive yield stress functional form,fit quality (R2), and range of solidity for the various suspensions. Functionalform is shown in Equation 3.17.Series Fitted Line Parameters R2 φmin φmaxa [kPa] b c1 — 6.0E+02 1.8 3.1 0.999 0.05 0.482 - - - 3.1E+03 2.7 1.4 0.991 0.05 0.483 · · · 9.6E+02 2.2 2.7 0.999 0.06 0.494 -·- 7.4E+02 2.0 3.0 0.999 0.06 0.495 — 5.5E+03 2.3 0.7 0.996 0.04 0.446 - - - 6.7E+03 2.5 0.4 0.995 0.05 0.467 · · · 4.9E+03 2.4 0.8 0.997 0.05 0.458 -·- 4.1E+03 2.4 0.9 0.997 0.05 0.469 — 2.6E+03 2.6 1.4 0.998 0.05 0.5010 — 7.3E+03 2.9 2.4 0.999 0.03 0.37et al. highlights a discrepancy. At equivalent solidities, Pettersson et al.experimental results suggest a higher value of Py(φ) than what we collected.Potentially, this difference could be due to errors in height calibration orcompliance of either ours or their apparatus. At high solidities, the heightof the suspension becomes very small, increasing the demand for a very ac-curate height determination. Multiple height calibrations and compliancechecks were made to ensure our measurements were accurate, however fur-ther scrutiny may be called for to determine the discrepancy. Comparison toVomhoff et al. experimental results is limited due to the small range of so-lidity provided. At low solidity, Vomhoff et al. measured a lower Py(φ) thanwe collected experimentally, however our apparatus is not accurate withinthis low range of loads, which most likely is the source of the discrepancy.Carrying forward, only compressive yield stress results collected by ourprimary technique of low dewatering rate experiments will be discussed. Wemove on now to discuss our collected experimental results in detail. Fittedempirical constants for the compressive yield stress functional form for thevarious suspensions are shown in Table 3.3.To begin our detailed comparison, we first compare the compressive yieldstress from Series 1, 5, 9 and 10, seen in Figure 3.6. Background used forthe following discussions between the various suspensions can be found in273.7. Results and Discussion: Py(φ)0 0.1 0.2 0.3 0.4 0.5050010001500φPy(φ)[kPa]Figure 3.6: Compressive yield stress determined for Series 1 (M), Series 5(), Series 9 (×), and Series 10 (+). Data points represent the average offour trials, with 2 standard deviations shown with the error bars. Variouslines show the empirical fits of the data (line legend shown in Table 3.3).Appendix D.Several expected observations can be discussed. First, we see that thechemical pulped suspensions (Series 1 and 9) reach higher solidities for agiven load when compared to thermo-mechanical pulp (Series 5). This couldbe explained by the higher flexibility and compliance chemical pulp fibres areknown for. An equivalent to this trend would be a denser sheet formed withthe chemical pulped suspensions which has been seen in the literature (eg.Figure 12 in McDonald et al. [36]). The reduced slope of the Series 5 trend athigher solidities, when compared to Series 1, could be due to the wider rangeof fibre sizes (higher fraction of fines, which are small cellulose particles)thus compaction of the TMP at this solidity may still be rearrangement ofparticles rather than a closely packed network in which individual fibres arenow being deformed.When comparing the two chemically pulped suspensions (Series 1 and 9),we see a shallower trend in the BHK (Series 9) results as well. This couldbe due to the smaller hardwood fibres, allowing closer compaction, thusreaching higher solidities. It also may be related to the thinner fibre walls,resulting in easier compaction of the individual fibres. This seems plausibledue to hardwood fibres generally having higher collapsibility compared to283.7. Results and Discussion: Py(φ)0 0.1 0.2 0.3 0.4 0.5050010001500φPy(φ)[kPa]Figure 3.7: Compressive yield stress of Series 2 (O), Series 3 (/), and Series4 (.) compared to Series 1 (4). Data points represent the average of fourtrials, with 2 standard deviations shown with the error bars. Various linesshow the empirical fits of the data (line legend shown in Table 3.3).softwood fibres, as discussed in Section D.1.1.The nylon fibres (Series 10) have a steep trend, most likely due to the uni-formly sized particles which cannot fill the small voids during compaction.Also, being a solid, stiff fibre (not porous), the networked suspension be-comes very stiff during increased contact points between individual fibres.Next, we consider the impact on the compressive yield stress of NBSKwith several chemical additives (Series 2, 3 and 4). Details of the additivesand background for discussion can be found in Appendix D. The resultingcurves are shown in Figure 3.7.As can be seen, no variation in the compressive yield stress was detecteddue to any of the chemical additives. As discussed in Section D.1.4, theadditives modify the flocculation of the suspension. It appears from theseresults, that compressive yield stress is insensitive to flocculation state.We next look at the TMP low consistency refining investigation (Series 6,7, and 8), shown in Figure 3.8. Details of the refining study and backgroundfor discussion can be found in Appendix D.The results show with increased refining, a reduction in the compres-sive yield stress curve occurs; the network becomes easier to compress withhigher levels of refining. This is reflecting the effects of increased flexibility293.8. Conclusions: Py(φ)0 0.1 0.2 0.3 0.4 0.5050010001500φPy(φ)[kPa]Figure 3.8: Compressive yield stress of Series 6 (♦), Series 7 (©), andSeries 8 (•) compared to Series 5 (). Data points represent the average offour trials, with 2 standard deviations shown with the error bars. Variouslines show the empirical fits of the data (line legend shown in Table 3.3).and collapsibility with increased refining as is discussed in Section D.1.3.Another contributing factor may be the increasing fines count, which mayallow the suspension to pack tighter at a given compressive load due to alarger variation in particle sizes.3.8 Conclusions: Py(φ)Equipment and an experimental protocol have been developed for collectingcompressive yield stress values of cellulose fibre suspensions. Two techniqueshave been implemented that show good agreement.Results for the various suspensions investigated were presented and spec-ulative discussions on the reasoning behind the various trends’ behaviourswas provided. Without a larger data set, its not possible to make any con-clusive remarks about the differences seen between the various suspensions,however the results provide a start to a cataloging of various cellulose fi-bre suspensions’ compressive yield stress values, which provide insight intodewatering behaviour.30Chapter 4Permeability k(φ)Permeability, as introduced in Section 2.1, is a material parameter thatquantifies the resistance fluid flow experiences through a porous suspension.It is an input into both the base and the extended models, requiring experi-mental determination for the various suspensions that are to be investigatedin this project. It can also provide insight into how a suspension dewa-ters, particularly when combined into diffusivity, which will be discussed inChapter 7.Throughout this chapter, we present the work done in developing theequipment and protocol for collecting permeability. We begin with a liter-ature section that reviews functional forms and several experimental tech-niques of collecting permeability. We next introduce this project’s method-ology for collecting results and our chosen functional forms. Following this,sections including a detailed description of the experimental device, an ex-perimental protocol outlining the procedure, and a brief description of pro-cessing and fitting of experimental data, are provided. Results collected arethen provided, followed by concluding remarks.4.1 Literature: k(φ)Permeability is a material parameter that is a measure of the ease at whichfluid can pass through a suspension. A high permeability value correspondsto a porous structure that fluid can readily pass through. The generalform of permeability is k(φ) → ∞ as φ → 0 and k(φ) → 0 as φ → 1.As the solidity increases, the flow passages become increasingly restricted,limiting the flowing fluid’s ability to permeate the suspension. Select resultsof permeability from the literature are shown in Figure 4.1. Cellulose fibresare highlighted in blue in the figure.A term often used in the literature for quantifying the resistance a flow-ing fluid experiences through a porous suspension is the hindered settling314.1. Literature: k(φ)0 0.2 0.4 0.6 0.810−2010−1510−10φk(φ)[m2]Figure 4.1: Select k(φ) values from the literature. Softwood chemical pulpresults from Pettersson et al.[1], Vomhoff [37], and Lindsay et al. [38] areshown as ⊕, ⊗, and  symbols respectively. Nylon fibres ( (Ingmanson etal.) and  (Labrecque)), glass fibres ( (Ingmanson et al.)), and acrylamidepolymer gel (4 (White)) compiled by Jackson et al. [39] are shown forcomparison. Theoretical Kozeny-Carman (thick black line, Equation 4.4)and results from a lattice-Boltzmann simulation of a random fibre web [40](), both for a fibre width of 20 µm, are also shown.324.1. Literature: k(φ)function, R(φ). Its relation to permeability isλVpR(φ) = R(φ) = µ (1− φ)φk(φ)(4.1)where λ is the Stokes settling coefficient and Vp is the volume of the particle.The functional form of R(φ) then is proportional to the inverse of k(φ).The hindered settling function provides the deviation from Stokes settlingbehaviour due to the interactions between particles as the concentrationincreases. The settling velocity uˆ(φ) is defined as [23]uˆ(φ) = uˆ0(1− φ)2R(φ) (4.2)where uˆ0 is the Stokes settling velocity. In concentrations above the gelpoint, R(φ) can be thought of as the resistance experienced by fluid flowthrough the network, inversely proportional to permeability [21]. Often inindustrial applications the specific volume (Vp) of the particle is difficult tomeasure and define. Thus, the hindered settling function is usually definedas R(φ), as seen in Equation 4.1 [24, 34].Various functional forms have been suggested for permeability, or thehindered settling function. A functional form that fits the low solidity limitis the following simple power lawR(φ) = C(1− φ)n (4.3)which has been used, or suggested, by various authors for fitting (eg. [18,33, 41]). Theoretically derived permeability-solidity expressions exist aswell. One of the most notable is the Kozeny-Carman, which, when definedfor flow in circular channels, results in [37]k(φ) =r24(1− φ)3cφ2(4.4)where c has been found to be 5.55 for fibre suspensions [42] and r is a radiusof the fibre.Simulations of fluid flow through fibre networks can also be used forfinding theoretical permeability expressions. An example includes the workof Koponen et al. [40] in simulating the permeability at varying solidities ofa three-dimensional random fibre web with the lattice-Boltzmann method.A fitting functional form of the results is as followsln(k(φ)/r2) = A+B(1− φ) (4.5)334.1. Literature: k(φ)Table 4.1: Empirical constants for k(φ) functional forms for cellulose fibresuspensions found in the literature.Reference Details Functional Form ConstantsVomhoff [37] In-plane, 60 SBK, k(φ) = bm(1−φ) b = 1.0 · 10−23 m22 mm ring m = 2.8 · 1013Lindsay [43] In-plane, liner- k(φ) = bm(1−φ) b = 1.4 · 10−22 m2board handsheets m = 1.3 · 1011Lindsay [43] Through-plane, liner- k(φ) = bm(1−φ) b = 3.2 · 10−24 m2board handsheets m = 9.0 · 1012Pettersson et al. SBBSK k(φ) =[C1 S20 φ3/2(1 + C2 φ3)]−1C1 = 2.3 · 102[1] C2 = 3.4 · 103S0 = 1.5 · 105 m2where A and B are empirical constants, found to be -8.53 and 10.4 respec-tively.Turning back to the cellulose fibre literature results (shown in Figure4.1), Vomhoff [37] experimentally collected in-plane permeability data forcellulose fibre webs and found that the data was well represented byk(φ) = bm(1−φ) (4.6)where b and m are fitting constants. This functional form has a limited rangeof usability, not approaching the expected permeability behaviour at low orhigh solidities. This same functional form was used by Lindsay for in-planeand through-plane permeability of cellulose fibres (eg. [43]). Pettersson etal. [1] used the following modified Kozeny-Carman expression for capturingthe through-plane permeability of cellulose fibres in liquidk(φ) =[C1 S20 φ3/2(1 + C2 φ3)]−1(4.7)where C1, C2, and S0 are two empirical fitting constants and the specificsurface respectively.Examples of Vomhoff, Lindsay, and Pettersson et al. fitted coefficientscan be found in Table 4.1.Various techniques have been developed for experimentally determiningthe permeability k(φ), or equivalently the hindered settling function R(φ),of a flocculated suspension. Like compressive yield stress, comparisons of344.1. Literature: k(φ)the results obtained with various techniques have found that permeabilityvalues are independent of the technique used, providing evidence that it isa true material parameter [21, 23].The first technique finds the hindered settling function from the initialsettling rate of the suspension. This technique is appropriate for soliditiesbelow or above the gel point, however is not applicable for high solidityvalues. Howells et al. [44] found the hindered settling function can bedetermined for the initial settling rate of the test by the following expressionR(φ0) =[1− Py(φ0)∆ρgφ0h0]∆ρg(1− φ0)2dh/dt(4.8)for small times of sedimentation, where dh/dt is the initial rate of changeof the sediment height, φ0 is the initial solidity, and h0 is the initial height.This expression includes the compressive yield stress, so if testing above thegel point is done, the functional form of Py(φ) is also needed. If below thegel point, Py(φ0) = 0, simplifying the expression back down to the definitionof the hindered settling function [23]. This technique is rather extensive anddoesn’t provide a very large range of solidities that can be tested. The rangeof this process can be increased if the sedimentations are centrifuged. Thistechnique has been used by various authors in the literature (eg. [45]).Another technique readily used in the determination of permeability isa constant pressure permeation of liquid through the suspension [23]. Per-meability can be found directly from Darcy’s law, which states thatk(φ0) =µQˆA[∆pˆhˆ]−1(4.9)where Q, A, ∆pˆ, and hˆ are the flow rate through the suspension, area ofthe suspension, pressure drop, and thickness of the suspension, respectively.This technique is generally used for determining permeability at higher so-lidities. Various examples can be found implementing this technique (eg.[46]), however, a couple challenges exist. When the pressure drop becomeshigh, the flow may induce compaction in the suspension [1]. Also, air entrap-ment within the suspension can provide large errors in permeability values[23].Finally, the hindered settling function can be determined using a tech-nique that implements a series of constant pressure experiments. A coupletechniques exist for capturing the R(φ) from the experimental data, butboth are interested in the linear region of a plot of t versus V 2 where t andV are the time of filtration and volume of filtrate per unit area of the filter,354.2. Methodology: k(φ)respectively [23]. The approach of Landman et al. [47] defines the linearslope region of a t versus V 2 plot as 1/β2. Constant pressure experimentsare performed for varying constant pressure values (∆P ) from which a trendof β2 versus ∆P can be found. The hindered settling function then can befound for each experiment completed from the following expression [23]R(φ∞) =2dβ2d∆P[1φ0− 1φ∞](1− φ∞)2 (4.10)where φ∞ is the equilibrium solidity. This technique is the most readily usedtechnique for determining the hindered settling function [23]. Similarly tothe constant pressure technique for determination of Py(φ), a “stepped pro-cess” of increasing the pressure once stability has been obtained (linearityin the t versus V 2 plot) can be implemented that allows multiple determina-tions of hindered settling function from a single sample. This allows muchquicker collection of experimental data and has been shown to provide com-parable results to single pressure filtration tests [24, 34]. Either the singlepressure or stepped pressure has been used, or suggested, by many in theliterature (eg. [24, 33]).Turning now to examples of cellulose fibre suspension techniques, Vomhoff[37] implemented the permeation technique and Darcy’s law for determiningthe in-plane permeability of a compressed cellulose fibre network. Petters-son et al. [1, 48] also used a permeation technique for the measurementof permeability of cellulose fibres, with both liquid and air. The liquid tri-als looked at permeability in the through-plane direction, and the air trialslooked at both through and in-plane directions. Kugge et al. [35, 49] usedthe proposed multi-step pressure filtration technique discussed above andfound the hindered settling function for cellulose fibres. Finally, Lindsay etal. [38, 43, 50] also used a permeation technique for determining permeabil-ity in both the through-plane and in-plane directions.4.2 Methodology: k(φ)The technique we implemented in this project follows the permeation exper-iments seen in the literature (eg. [1, 48]). As discussed, there are a coupleconcerns with collecting permeability measurements using this technique.Air entrapment concerns can be easily satisfied by deaerating the water us-ing a vacuum. The concern of bed compaction due to the pressure drop ofthe flowing fluid has merit in our experiments. Two approaches to deal withthis concern have been made.364.2. Methodology: k(φ)𝝈 𝒛 =  𝒉 𝒛 = 𝟎 𝑸 𝑸Suspension∆ 𝒑Figure 4.2: Permeability model.The first approach involves an expansion of the governing equations,and finding the inherent error present in determining the permeability val-ues from the permeation experimental results at the center elevation of thesuspension, neglecting the solidity gradients. This approach is repeated inHewitt et al. [12].The model of the permeation experiment is shown in Figure 4.2. Theexperimental method involves flowing a volumentric flow rate Qˆ through asuspension of area A compressed by a mechanical load σ between a perme-able piston at zˆ = hˆ and a permeable top boundary at zˆ = 0 while measuringthe pressure drop ∆pˆ. The average solidity within the suspension is definedasφ¯ =1hˆ∫ hˆ0φdzˆ. (4.11)We reintroduce our fluid phase continuity, Darcian expression, and con-servation of total compressive stress originally shown in Equations 2.2, 2.3,and 2.4. The expressions are simplified due to the solid phase being station-ary, and the problem being steady state. Thus, we have∂∂zˆ[(1− φ)uˆf ] = 0 (4.12)374.2. Methodology: k(φ)(1− φ)uˆf = −k(φ)µ∂pˆ∂zˆ(4.13)∂Pˆ∂zˆ= 0. (4.14)We begin with integrating Equation 4.12, using the condition that uˆf =− QˆA if φ = 0 to determine the constant. This expression, along with ourexpanded Equation 4.14, are substituted into Equation 4.13. With the solidphase velocity (us) equal to zero, the two rheology expressions (Equations2.9 and 2.20) are equivalent asP = Py(φ). (4.15)Thus we arrive at our governing equation ofk(φ)∂Py(φ)∂zˆ= −QˆµA. (4.16)We next determine our boundary conditions from Equation 4.14. Integrat-ing, and using the condition at zˆ = hˆ, P = σ and pˆ = (pˆzˆ=hˆ − pˆzˆ=0) = ∆pˆ ,we can find the constant, giving the expressionP + pˆ = σ + ∆pˆ. (4.17)With Equations 4.15 and 4.17, the boundary conditions can be found asPy(φ) = σ + ∆pˆ, zˆ = 0Py(φ) = σ, zˆ = hˆ(4.18)Since∂Py(φ)∂zˆ = P′y∂φ∂zˆ , a pressure scaling of P′y(φ) is introduced along withthe following dimensionless parameters,z =zˆhˆ, K =kA∆pˆQˆµhˆ, P =Py − σP ′y(φ¯), δ =∆pˆP ′y(φ¯)(4.19)which when substituted into our governing equation and the boundary con-ditions giveK∂P∂z= −δ (4.20)P = δ, z = 0P = 0, z = 1.(4.21)384.2. Methodology: k(φ)If δ  1, then ∂φ∂z  1, which is the desired limit. We next expand asφ(z) = φ¯+ δφ1(z) + δ2φ2(z) +O(δ3)K = K0(φ) + δK1(φ) + δ2K2(φ) +O(δ3)P = P0(φ) + δP1(φ) + δ2P2(φ) +O(δ3)(4.22)whereφ¯ =∫ 10φdz (4.23)∫ 10φi dz = 0 for all i ≥ 1. (4.24)The resulting leading order balance and its boundary conditions can befound to beK0(φ¯)∂P0(φ¯)∂z= 0 (4.25)P0(φ¯) = 0, z = 0P0(φ¯) = 0, z = 1(4.26)which when solved givesP0(φ¯) = 0. (4.27)We next determine the O(δ) balance and its boundary conditions asK0(φ¯)∂∂z[φ1P′0(φ¯) + P1(φ¯)]= −1 (4.28)φ1P′0(φ¯) + P1(φ¯) = 1, z = 0φ1P′0(φ¯) + P1(φ¯) = 0, z = 1(4.29)with prime indicating partial derivatives with respect to φ, thus P ′0(φ¯) =∂P0(φ¯)∂φ . The results of Equation 4.28 with the boundary conditions shown inEquation 4.29 areK0(φ¯) = 1 (4.30)P1(φ¯) =12(4.31)φ1 =1P ′0(φ¯)[12− z]. (4.32)Finally, we turn to the O(δ2) balance and its boundary conditions[φ1K′0(φ¯) +K1(φ¯)]=∂∂z[φ2P′0(φ¯) + φ21P ′′0 (φ¯)2+ φ1P′1(φ¯) + P2(φ¯)](4.33)394.2. Methodology: k(φ)φ2P′0(φ¯) + φ21P ′′0 (φ¯)2+ φ1P′1(φ¯) + P2(φ¯) = 0, z = 0φ2P′0(φ¯) + φ21P ′′0 (φ¯)2+ φ1P′1(φ¯) + P2(φ¯) = 0, z = 1(4.34)which give the resultK1(φ¯) = 0. (4.35)Inserting these solutions, and reintroducing the dimensional variables, wearrive at the following expressionφ(zˆ) = φ¯+∆pˆP ′y(φ¯)[12− zˆhˆ]+O(δ2) (4.36)given that P ′0(φ¯) = P ′(φ¯) +O(δ) = 1 +O(δ) from our definition of P shownin Equation 4.19. Finally expressions for the compressive yield stress andthe permeability are found asPy =∆pˆ2+ σ + P ′y(φ¯)[(φ− φ¯) +O(δ2)] (4.37)k =QˆµhˆA∆pˆ[1 + (φ− φ¯)K ′0(φ¯) +O(δ2)]. (4.38)We now consider the expression for k and φ(zˆ) that have been found. Ifwe evaluate these expressions for zˆ = hˆ/2, we haveφ = φ¯+O(δ2)k(φ¯) =QˆµhˆA∆pˆ+O(δ2). (4.39)This analysis suggests that evaluating at zˆ = hˆ/2, we can neglect the impactof flow induced compaction by taking our leading order term of permeabilityas an approximation with error O(δ2). This approximate method is ourmain approach in determining permeability measurements. Experimentally,a compressive load σ is imposed on the suspension which defines the heightof the suspension hˆ from which the average solidity can be determined asφ¯ =msρsAhˆ. (4.40)Experimental values of flow rate Qˆ, suspension area A, fluid viscosity µ, andpressure drop ∆pˆ are determined for various values of σ. Accuracy of this404.2. Methodology: k(φ)approach involves keeping the error term low. Experimentally, we were ableto keep the ratioδ =∆pˆP ′y(φ¯)< 0.05 (4.41)resulting in a small error in this approach.We notice a similar expression for Py(φ¯) exists, which allows an approx-imate method of determining compressive yield stress from the permeationexperiments as well. If we evaluate Equation 4.37 at zˆ = hˆ/2, we arrive atPy(φ¯) =∆pˆ2+ σ + P ′y(φ¯)[O(δ2)]. (4.42)This analysis suggests that if evaluated at the middle elevation of the sus-pension, we can neglect the impact of flow induced compaction by takingour leading order term as an approximation with error O(δ2). This providesa second technique for determining compressive yield stress. Technically,seeing the definition of δ, it may be safer to present the error as O(δ), sincethe O(δ2) is multiplied by P ′y(φ¯), however experimentally δ < 0.05, resultingin still a fairly low error with this approximate technique.A second approach has been developed for determining permeabilityshould the error ratio (δ) become too large, making the approximate so-lution above inaccurate. The approach involves expanding Equation 4.16with the chain rule and rearranging, resulting in∂φ∂zˆ= − µQˆAk(φ)[∂Py(φ)∂φ]−1. (4.43)We choose a functional form for permeability and substitute it into Equa-tion 4.43. Knowing the boundary conditions, shown in Equation 4.18, wecan solve the eigenvalue problem for the empirical constants within the per-meability functional form, fitting the experimental data. This approachaccounts for solidity gradients in the suspension, and is a robust alternative,should the experimentally collected results have large values of δ. It does,however, require the experimentally determined Py(φ) function.Due to the second approach’s limitation in requiring a functional form ofpermeability, our experimental results having an acceptably low ∆pˆ/P ′y(φ¯)ratio, and its more tedious procedure, it was not implemented in deter-mining the permeability results. It is developed for potential future use ifnecessary. Preliminary results did show similar results as found with ourprimary approach.The methodology adopted is to simply collect the various experimentalvalues, and directly determine our permeability versus average solidity trend414.3. Device Description: k(φ)using our approximate approach. A permeability experiment involved asingle suspension getting compressed to various loads (various decreasingbed thicknesses) to collect multiple permeability measurements for a singlesuspension trial.The primary functional form used in this project is a newly defined formk(φ) = d [ln(1/φ)/φ] e−fφ (4.44)where d and f are empirical fitting constants. The form of this equation isused due to it capturing the desired behavior at both limits of φ, capturingthe low concentration limit which should be based on flow around a singlecylinder such that k → ln(1/φ)/φ as φ→ 0 [12, 39].This functional form did not capture the permeability behavior of theTMP, which used an alternative expressionk(φ) =g (1− φ)hφk(4.45)where g, h, and k are empirical fitting constants. Both functional forms canbe used with the second approach of determining our permeability trenddiscussed, should future trials results in higher than acceptable values of theerror term, δ.4.3 Device Description: k(φ)Permeability data collection is performed on a unique experimental appara-tus. The setup consists of a suspension chamber capable of compressing thesuspension to varying loads, and a flow loop that permeates water throughthe compressed suspension. Flow diagrams of the permeability experimentalsystem can be seen in Figures B.1 and B.2 in Appendix B.The suspension chamber is constructed out of a 305 mm long, 101.6mm ID plain steel cylinder. A stainless steel pipe flange is welded to eitherend. The cylinder is oriented vertically and is bolted to a support frame.A modified pipe flange cap is used as the base of the assembly. Individualflow and pressure ports have been drilled through the flange cap, as well asa hole to allow the hydraulic linear actuator’s shaft to pass through. Insidethe cylinder resides the moveable, permeable piston that is responsible forcompressing the suspension. A section view of the suspension chamber canbe seen in Figure 4.3.The permeable piston has a range of movement of 160 mm, and can pro-vide a compressive load up to 1 MPa. The piston is milled from aluminum424.3. Device Description: k(φ)Flange CapFlangeScreen SpacerFlangeFlange CapSuspension ChamberPermeablePistonHydraulic Actuator Pressure/FlowPortsPressure/Flow PortsFlange CapWashers & Square Ring SealWashers & Square Ring SealScreen SpacerFigure 4.3: Section and exploded view of the permeability experimentalsystem.434.3. Device Description: k(φ)Fine MeshFine Mesh Support DiscPermeablePistonFine MeshScreen SpacerFine Mesh Support DiscFigure 4.4: Permeable piston and screen spacer of the permeability exper-imental system.and uses PTFE seals around its perimeter in two locations for proper align-ment inside the suspension chamber. The permeable piston has 12 throughholes of various sizes that allow water to flow vertically to a flow distribu-tion plateau. The plateau has square shaped posts that hold the fine meshsupport disc which aids in flow distribution. A fine mesh, with 0.28 mmhole size, is attached to the support disc to prevent the solid phase frompassing through. The screen spacer has a similar flow construction as thepermeable piston; a distribution network of flow ports that spreads the flowequally across the bed, encouraging distributed flow. The screen spacer andthe permeable piston can be seen in Figure 4.4.The assembly of the top of the suspension chamber is shown in Figure 4.3.The top acts as the lid of the assembly to add and remove the suspension. Toclose the suspension chamber, first a square profile ring seal is placed in thegroove on the flange followed by the screen spacer that holds the suspensionchamber’s top mesh. On top of the screen spacer, a flange cap is placed thathas a flow and pressure port drilled through. Specialty washers are placedbetween the components as we assemble the top of the suspension chamberto ensure a stiff assembly. The top assembly is then fastened together to95 N·m using eight bolts and nuts.Water is permeated through the compressed suspension by a 0.56 kW,12 stage Flint and Walling booster pump (www.acklandsgrainger.com), con-trolled by a Eaton M-Max (www.mcmaster.com) variable frequency drive(VFD). The flow loop is cooled using a plate heat exchanger to control tem-444.4. Experimental Protocol: k(φ)perature, and is maintained in a vacuum of 0.95 MPa for the duration of thetrial to control dissolved oxygen content of the water, which reduces con-cerns of air entrapment within the suspension. The fluid temperature anddissolved oxygen content is monitored by a Eutech Instruments DO 500 dis-solved oxygen meter (www.coleparmer.ca). Movement and compressive loadof the permeable piston is provided by a hydraulic linear actuator, poweredby a 1.5 kW Monarch Hydraulics Inc. power supply (www.mcmaster.com),set to a maximum pressure of 6.89 MPa.The permeating fluid pressure drop is measured using an OMEGA1.03 MPa (www.omega.ca) differential pressure transducer. Suspension bedheight is measured by an OMEGA 0.305 m (www.omega.ca) stoke linearpotentiometer. The compressive load imposed on the suspension is mea-sured by an OMEGA 13.79 MPa (www.omega.ca) pressure transducer onthe hydraulic fluid pressure powering the linear actuator.Analog signals from the various sensors are transmitted down coaxiallines. The signals are first filtered using analog low pass filters. The sig-nals are then transmitted a short distance to a National Instruments 6009USB DAQ (www.nationalinstruments.com) using sets of twisted pairs. ALabVIEW program used for collecting data then digitally filters the signals.The program stores data from the various sensors in buffers that representan hour of data collection. The program has a “slope criteria” feature, whichnumerically differentiates the signals and determines when the signals havestabilized within a certain acceptable region. Once a signal has stabilized,entry cells in the LabVIEW interface are enabled to input flow rate andtemperature information before collecting a data point. The data from eachindividual point is stored in a matrix and is output to a “.txt” file when thesave data button is pressed.4.4 Experimental Protocol: k(φ)A detailed manual for the equipment is shown in Appendix B. The followingis a brief description of the experimental protocol.A permeability experimental trial begins with filling the suspension cham-ber. Varying masses of suspension were added depending on what solidityranges were to be tested. Usually, either 500 or 1000 g of 0.03-0.04 (wt/wt)consistency suspensions were used. The assembly was then closed, and theflow loop turned on, permeating a low flow rate through the uncompressedsuspension. Approximately one hour was allowed to pass in order to stabilizethe temperature and dissolved oxygen content of the fluid. Stabilized dis-454.5. Data Processing and Fitting: k(φ)solved oxygen content values were below 3 ppm. Once ready, the permeablepiston was moved to a defined height (or load). The flow rate was controlledto prevent the fluid pressure from exceeding 20 % of the compressive bedload which corresponded to an acceptably low δ value. Once the pressuremeasurements stabilized, a flow rate was collected in the standpipe witha timer. Fluid temperature was determined for this sample to define thecorrect viscosity of the permeating flow via a look up table. The flow rateand temperature values were entered into the LabVIEW interface. Clickingthe save button stores the permeability data point values of flow rate, tem-perature (viscosity), permeating fluid pressure drop, compressive load, andsuspension height. Compliance of the experimental assembly from the com-pressive load is compensated for at this point by correcting the measuredheight. Once a permeability measurement has been collected, the permeablepiston was moved to a new, decreased height (or equivalently, an increasedload) and the process was repeated. The maximum bed loading the systemprovided was limited to 1 MPa.Once the various permeability values had been determined for the sus-pension, the piston was moved downward, the assembly was opened andthe compressed suspension was collected, dried, and weighed to obtain thedry solid mass for the determination of the average solidity of the variousheights collected. At least four permeability trials were performed for a givensuspension (fresh samples for each trial) to average experimental variations.4.5 Data Processing and Fitting: k(φ)Experimental trial data files from the LabVIEW interface have columns ofmechanical load or compaction load (in Pa), fluid pressure (in Pa), suspen-sion height (in mm), flow rate (in m3/s), and viscosity of the fluid (in Pa·s).Using Equation 4.40, we can determine solidity values from the height val-ues and the dried solid mass, and with our permeability expression shownin Equation 4.39 we can determine our corresponding permeability valuesfrom the experimental data.We fit our functional form of permeability (Equation 4.44) by linearizingthe expressionln(k(φ¯))− ln (ln(1/φ¯)/φ¯) = ln (d)− fφ¯ (4.46)and using linear regression to find our empirical constants d and f . Thisprocess can be repeated for the second functional form shown in Equation4.45.464.6. Results and Discussion: k(φ)0 0.2 0.4 0.610−1510−10φ¯k(φ¯)[m2]Figure 4.5: Series 1 k(φ) values (denoted as M) compared to select valuesfrom the literature. Softwood chemical pulp results from Pettersson et al.[1],Vomhoff [37], and Lindsay et al. [38] are shown as ⊕, ⊗, and  symbolsrespectively. Nylon fibres ( (Ingmanson et al.) and  (Labrecque)), andglass fibres ( (Ingmanson et al.)) compiled by Jackson et al. [39] are shownfor comparison. Theoretical Kozeny-Carman (thick black line, Equation 4.4)and results from a lattice-Boltzmann simulation of a random fibre web [40](), both for a fibre width of 20 µm, are also shown.4.6 Results and Discussion: k(φ)To begin, we investigate the validity of the results obtained experimen-tally. Shown in Figure 4.5 and 4.6 are k(φ¯) and k(φ¯)/r2 results of Series 1and Series 10 found by the approximate solution approach outlined in themethodology which are compared to select values introduced in Figure 4.1.We see Series 1 k(φ¯) and k(φ¯)/r2 values are aligned with previously col-lected softwood Kraft pulps found in the literature. Interestingly, we seein Figure 4.6 that the various materials (cellulose fibres withstanding) fallonto the line predicted by the theoretical approaches when scaled by theradius of the particles. Jackson et al. [39] showed this trend as well. Cel-lulose fibre results fall substantially below this grouping though. Series 10,consisting of nylon fibres, also falls into the grouping around the theoreti-474.6. Results and Discussion: k(φ)0 0.2 0.4 0.610−5100φ¯k(φ¯)/r2Figure 4.6: Series 1 (denoted as M) and Series 10 (denoted as +) k(φ¯)/r2values compared to select values from the literature, where r is the radius ofthe fibre. Softwood chemical pulp results from Pettersson et al.[1] are shownas ⊕ symbols. Nylon fibres ( (Ingmanson et al.) and  (Labrecque)),glass fibres ( (Ingmanson et al.)), and acrylamide polymer gel (4 (White))compiled by Jackson et al. [39] are shown for comparison. TheoreticalKozeny-Carman (thick black line, Equation 4.4) and results from a lattice-Boltzmann simulation of a random fibre web [40] () are also shown.484.6. Results and Discussion: k(φ)Table 4.2: Empirical constants for permeability functional forms, fit quality(R2), and range of solidity for the various suspensions. Functional forms areshown in Equations 4.44 and 4.45.Series Line Parameters R2 φmin φmaxd [m2] f g [m2] h k1 — 8.3E-13 18.5 - - - 0.985 0.03 0.382 - - - 4.3E-13 14.2 - - - 0.894 0.09 0.403 · · · 8.6E-13 13.7 - - - 0.908 0.11 0.404 -·- 1.2E-12 14.3 - - - 0.954 0.11 0.395 — - - 1.8E-19 -3.3 5.3 0.947 0.04 0.316 - - - - - 1.3E-16 5.6 2.9 0.940 0.05 0.337 · · · - - 7.7E-17 8.0 3.4 0.840 0.05 0.348 -·- - - 9.3E-18 4.2 3.8 0.697 0.05 0.349 — 6.4E-13 14.1 - - - 0.883 0.05 0.4010 — 1.6E-11 5.4 - - - 0.997 0.15 0.33cal approaches. We have confidence in the experimental assembly based onthese comparisons.We move on now to discuss our collected experimental results in de-tail. Fitted empirical constants for the permeability functional forms forthe various suspensions are shown in Table 4.2.To begin our detailed comparison, we first compare the permeability fromSeries 1, 5, 9 and 10, seen in Figure 4.7. Background used for the followingdiscussions between the various suspensions can be found in Appendix D.Beginning with the highest permeable material, nylon fibre (Series 10),results were substantially above the various cellulose fibre suspensions testedand the slope of the collected values is shallower. Series 10 results fall closeto theoretically derived permeability expressions such as Kozeny-Carmanas seen in Figure 4.7. A potential source of the higher permeability valuescomes from the homogeneous fibre size distribution in this suspension andan absence of internal porous structure, which increases the surface con-tact with the fluid greatly, creating more drag and thus lower permeability.The homogeneous fibre distribution also means there is an absence of smallparticles that can block flow passages within the compressed network. Ex-planations of the lower than theoretical permeability of cellulose fibres havebeen made by other authors. Lindsay et al. suggests that reduced flowpassages occur due to some of the fluid being trapped inside or bound to494.6. Results and Discussion: k(φ)0 0.1 0.2 0.3 0.4 0.510−1610−1410−1210−10Kozeny−Carmanφ¯k(φ¯)[m2]Figure 4.7: Permeability values found for Series 1 (M), Series 5 (), Series9 (×), and Series 10 (+). Various lines show the empirical fits of the data(line legend shown in Table 4.2). Theoretically derived Kozeny-Carmanexpression shown for the radius of NF (6.79 µm).the cellulose fibres [43], thus reducing permeability. Vomhoff [37] claims thelower than theoretical permeability and steeper trend are due to the highcollapsibility and internal porosity of the cellulose fibres.We move on and compare the TMP (Series 5) to the two Kraft pulp sus-pensions (Series 1 and 9). The lower permeability is most likely due to thehigher fines content, which would block potential flow paths. A shallowerslope with increasing solidity in Series 5 can also be observed in comparisonto Series 1 and 9. This lower sensitivity to solidity was observed by Vomhoff[37] as well, however, in his case, the TMP had a higher permeability thanthe softwood chemical pulp. Returning to Vomhoff’s explanations of thesteeper trend seen in cellulose fibres when compared to ideal fibres, perhapseither the internal flow passages or collapsibility is reduced in Series 5 com-pared to the chemical pulps, resulting in the shallowing of the trend. We doknow that collapsibility is less with the TMP, as discussed in Section D.1.2,so we can speculate this is the explanation of the TMP’s lower sensitivityto solidity.Comparing the Series 1 to Series 9 results, we see that the BHK has ahigher permeability at high solidities due to a shallower slope of the experi-mental data. When considering the size of the fibres in Series 1 and 9 (shown504.6. Results and Discussion: k(φ)0 0.1 0.2 0.3 0.4 0.510−1610−1410−1210−10φ¯k(φ¯)[m2]Figure 4.8: Permeability values of Series 2 (O), Series 3 (/), and Series 4(.) compared to Series 1 (4). Various lines show the empirical fits of thedata (line legend shown in Table 4.2).in Table D.2), this result may be surprising. With Series 9 fibres being boththinner and shorter, we may have expected to see that the hardwood fibreswould compact tighter resulting in more restrictive fluid passages, however,this is not what is seen experimentally. The shallower trend of hardwoodpulp was also seen by Pettersson et al. [1]. Like Series 5, perhaps theslope difference is due to a collapsibility or internal porosity difference. Asdiscussed in Section D.1.1, hardwood fibres are expected to have higher col-lapsibility, so perhaps a more limited internal porosity is counteracting this,or perhaps a difference in flocculation level or surface charge of the fibre isthe explanation.Next we consider the impact of the chemical additives on the permeabil-ity of NBSK. Details of the additives and background for this discussion canbe found in Appendix D. The resulting curves are shown in Figure 4.8.The results show the additive in Series 2 is less effective than Series 3 andSeries 4 at raising the permeability of the NBSK suspension. All the chemicaladditives have improved permeability compared to Series 1 by shallowingthe negative slope of permeability with solidity. Further improvements inpermeability are seen with Series 3 and 4 by a translation of the trendupwards to higher values of permeability. As discussed in Section D.1.4,the main intent of these chemical additives is to modify the suspension’s514.6. Results and Discussion: k(φ)flocculation state in some form, and so we try to consider how this mayimpact both the slope and magnitude of permeability.EKA FIX 41 (chemical additive of Series 2) increases the flocculation offines, and neutralizes the fibres surface charge. One or both of these actionsappears to change the slope of the permeability curve. Perhaps neutralizingthe surface charge has reduced the collapsibility or internal porosity of thefibres, thus increasing the slope. Potentially, retraction of microfibrils onthe fibre walls from the change in surface charge are either stiffening thefibre or closing flow passages.EKA PL 1510 (Series 3 additive) and EKA PL 1510 with EKA NP 320(Series 4 additives) both aim at flocculating the fibres together. Increasedflocculation has been shown to increase settling velocities of sediments dueto higher weight to size ratio of the aggregates (which would correspond toa lower hindered settling function and thus a higher permeability value)[8].Pulling the fibres together into flocculations would reduce the surface areaof the fibres contacting the moving fluid. This could reduce the drag as thefluid passed through the suspension, raising the permeability. Flocculation,to some extent, is similar to the permeability change seen with increasingthe particle size, which results in higher values, as was seen in various nylonfibre trials of varying size (not presented in the thesis).Finally, we turn to the TMP low consistency refiner samples, shown inFigure 4.9. Details of the refining study and background for this discussioncan be found in Appendix D. The impacts of low consistency refining on thepermeability of TMP, seems murky at best. It appears that perhaps a smallincrease in permeability is seen for Series 6, however, with further refiningit seems to move back towards the unrefined TMP. Overall, no clear trendcan be concluded from the results.The mechanisms used for discussing changes in permeability, being finescontent, collapsibility, and internal porosity, all seem to be at play with in-creased refining, so it’s somewhat surprising that permeability was unalteredin the TMP. Perhaps the mechanisms are counter acting each other. We doexpect to see higher collapsibility with increased refining, as discussed inSection D.1.3, which we may expect to result in a change in the slope of thetrend, however, perhaps internal porosity is being reduced at the same timedue to the increasing fines blocking internal passages, which would counteract the expected steeping of the trend. Finally, knowing that the fines con-tent is increasing, we would expect external flow passages to be blocked,resulting in a reduction in permeability. Perhaps an experimental error wasoccurring in the permeability measurements from the fines being flushedthrough the permeable membranes as the flow was circulated through the524.7. Conclusions: k(φ)0 0.1 0.2 0.3 0.4 0.510−1610−1410−1210−10φ¯k(φ¯)[m2]Figure 4.9: Permeability of Series 6 (♦), Series 7 (©), and Series 8 (•)compared to Series 5 (). Various lines show the empirical fits of the data(line legend shown in Table 4.2).compacted suspension. Due to the system being a closed loop, potentiallythe recirculation can reduce this error, however, perhaps not all of the finesmade it back to the suspension, and instead, end up settling on the reservoirbase.Results from previous studies for chemical pulps have suggested andshown that beating decreased the permeability [38, 51], and Carlsson et al.[51] showed that groundwood (mechanical pulp) with lower CSF values (im-plying varying levels of beating had occurred) resulted in lower permeability.However, it is unclear if fines removal was attempted by Carlsson et al.. Re-tention challenges and unclear results support further permeability work toclarify the results seen for thermo-mechanical pulp with varying levels ofrefining.4.7 Conclusions: k(φ)Equipment and an experimental protocol have been developed for collect-ing permeability values of cellulose fibre suspensions. Two approaches fordetermining permeability values from permeation experiments have beendeveloped; approach one provides an approximate solution neglecting flowinduced compaction, and approach two provides a robust method for fitting534.7. Conclusions: k(φ)a functional form of permeability that accounts for flow induced compaction.Results collected are in line with values found in the literature, validatingthe equipment.Results for the various suspensions investigated were presented alongwith speculative discussions of the various trends’ behaviours. Due to thesmall data set, its not possible to make any conclusive remarks about thedifferences seen between the various suspensions. The results however pro-vide a start to a catalog of various cellulose fibre suspensions’ permeabilityvalues, which provide insight into dewatering behaviour.54Chapter 5Dewatering Experiments andModel ComparisonsAs discussed in Chapter 2, we have formalized two theoretical models tocapture the dewatering behavior of cellulose fibre suspensions. The suitabil-ity of these two models is investigated in this chapter. The one dimensionaldewatering model of interest is re-shown in Figure 5.1.The base model, developed from the established compressive rheologymodeling approach in the literature, is a well accepted modeling approachfor capturing the dewatering behavior of flocculated suspensions. Limitedvalidation of the model’s ability in capturing dynamic dewatering is seenin the literature. We wish to validate this modeling approach. Despite itspopularity, it’s questionable if the base model will capture the dewateringdynamics of cellulose fibre suspensions due to the internal porosity of the in-dividual fibres. This concern has been raised in the past by Pettersson et al.[25]. The extended model attempts to capture this second scale of dewater-ing by a functional form of the dynamic compressibility that is proportionalto the cellulose fibre wall permeability (λ(φ) = Cφ−1). This functional formresults in one free parameter (C) within the dynamic compressibility func-tion, which is used for fitting the extended model to the experimental data.The governing equation of the extended model (Equation 2.22), and the loadcondition at the permeable membrane (Equation 2.24) are re-shown below.We recall that to revert to the base model, we simply set λ(φ) =∞.∂φ∂tˆ=∂∂zˆ(φk(φ)µ[P ′y(φ)∂φ∂zˆ− ∂∂zˆ(φλ(φ)∂uˆs∂zˆ)])(2.22 re-shown)σ(tˆ) = Py(φ(hˆ(tˆ), tˆ))− φ(hˆ(tˆ), tˆ)λ(φ(hˆ(tˆ), tˆ))∂uˆs∂zˆ∣∣∣∣zˆ=hˆ(tˆ)(2.24 re-shown).Throughout this chapter, we will present our dewatering experimentalwork and its comparisons to the base and extended model. We start with our555.1. Methodology and Experimental Protocol: Dewatering 𝒛𝝈( 𝒕) 𝒛 =  𝒉( 𝒕)Suspension 𝒛 = 𝟎Figure 5.1: One dimensional, constant dewatering rate model (re-shown).methodology of collecting dewatering experimental data, along with a briefdescription of the experimental protocol. Following this, a quick descriptionof how we process the experimental data and fit the extended model to thedata is presented. The experimentally collected dewatering results for thevarious suspensions are then presented and discussed. We next present ourbase model results in comparison to our hard particle suspension consistingof nylon fibres (Series 10). Attempts to validate the base model are madewith this comparison. Following this, we present the base and extendedmodel results in comparison to our various cellulose fibre suspensions dewa-tering data. Attempts are made to validate both models’ ability to capturethe dewatering behavior of cellulose fibre. Finally, concluding remarks onthe experimental data and the validation efforts are made.5.1 Methodology and Experimental Protocol:DewateringTo collect our various constant rate dewatering data, we will simply usethe experimental setup that was used for our compressive yield stress de-termination, that was described in Section 3.3. The difference will be usingpiston velocities greater than the value used for determining Py(φ). In thecase of the cellulose fibre trials, the Py(φ) velocity was 0.001 mm/s, and thenylon fibre trial was 0.02 mm/s. We are interested in collecting load versussolidity curves for various dewatering rates. Solidity will be found from the565.2. Experimental Results and Discussion: Dewatering0 5 10 15012345670.01 mm/s0.1 mm/s0.25 mm/s0.5 mm/s1.0 mm/s1.5 mm/s2.0 mm/s3.0 mm/s4.0 mm/s5.0 mm/s10.0 mm/sPy(φ)Figure 5.2: Colors of trend lines used to define various rates in the dewa-tering graphs.experimental data the same way as it was done for compressive yield stress,with the expressionφ¯(hˆ(tˆ, tˆ)) =msρsAhˆ(tˆ)(5.1)however in the dewatering experiments, this represents an average solid-ity within the suspension due to gradients in the concentration at higherdewatering rates.The experimental protocol is identical to that outlined for the compres-sive yield stress in Section 3.4, except the experimental starting conditions.In the dewatering experiments, data collection at the defined velocity beginsat the initial height of the suspension. Due to drastically quicker exper-iments, the distance the piston has to travel is no longer a concern. Thisslight change and a few other trivial differences in the procedure are outlinedin Appendix A. The maximum dewatering rate was limited to 10 mm/s.The base and extended models are solved using code written in MAT-LAB. In the case of the extended model, C values are varied manually to fitthe model curves to the experimental results by eye.5.2 Experimental Results and Discussion:DewateringDewatering experiments were conducted at various rates. Throughout Chap-ters 5 - 7, dewatering rates are indicated by the color of the trend line used.This allows easy comparison between suspensions. The various colors andtheir corresponding rates are outlined in Figure 5.2.We start our discussion of the dewatering results by first looking at theexperimental results of Series 1 and 9, the Kraft pulp suspensions, shown inFigure 5.3 a and b.575.2. Experimental Results and Discussion: DewateringWith both suspensions, we see a similar behavior with increasing de-watering rates, which is a scaling of the curves to the left, away from thecompressive yield stress curve. Thus, to reach an equivalent average solidityfor an increased dewatering rate, a larger load imposed on the suspension isrequired.Closely comparing the materials, we see that for a given load and givendewatering rate, Series 9 will end up at a higher average solidity. This canbe seen clearly in Figure 5.3 e. The superior dewatering behavior of Series 9is most likely due to the shallower permeability trend as seen in Figure 4.7and the shallower compressive yield stress trend as seen in Figure 3.6.Next, we turn to the experimental results of Series 5 that are shown inFigure 5.3 c.Series 5 results look similar to the previous two cellulose fibre results.Comparing Series 5 results to Series 1 and 9, we see Series 5 was moredifficult to dewater, as can be seen in Figure 5.3 f.Series 5 results indicated a higher difficulty in dewatering when comparedto Series 1 and 9, however upon inspection of the material parameters inFigures 3.6 and 4.7, we may have expected to see a larger deviation indewatering difficulty. The absence of this larger deviation is attributed toan experimental error in the data collection. It was concluded, after theexperimental results were collected, that an issue with retention occurredduring increased dewatering rates. Cloudy water was observed for highrates of dewatering, indicating that some of the solid phase had passedthrough the permeable membrane. Retention is know to be a challengewith TMP, due to the fines. This is a similar concern mentioned for thepermeability results of TMP at varying levels of refining, however in this caseno recirculation of the escaping fluid is present to try and return the finesinto the suspension. Due to this, the trends quantitatively are questionable,meaning comparison to other pulps provides limited insight. Comparison ofa lower dewatering rate was used in Figure 5.3 f then compared to Figure 5.3e, assuming the retention concerns would be reduced with lower flow rates.This was supported experimentally as observing reduced cloudiness of thewater above the permeable membrane at reduced dewatering rates.Turning now to the nylon fibre results (Series 10), shown in Figure 5.3d, we notice they look quite different when compared to the cellulose fibresuspensions results. The changed shape of the load versus solidity curvecomes from the building of a high solidity boundary layer under the movingpermeable membrane. This occurs due to a combination of the lack ofinternal porosity within the solid phase particles, allowing faster solid phaserearrangement, and the difference in its material parameters. The building585.2. Experimental Results and Discussion: Dewatering0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]e)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]f)Student Version of MATLABFigure 5.3: Experimentally collected dewatering trends at various rates fora) Series 1, b) Series 9, c) Series 5, and d) Series 10. Select experimentaltrends for e) Series 1 and 9, and f) Series 1, 5 and 9. Data points repre-sent the average of four trials, with 2 standard deviations shown with theerror bars. Black dashed lines represent compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).595.2. Experimental Results and Discussion: Dewatering0 10 2002040tˆ [s]hˆ[mm]a)0 10 20050010001500tˆ [s]σ[kPa]b)0 0.2 0.4050010001500φ¯σ[kPa]c)Figure 5.4: Select data file of Series 10 dewatering at 2 mm/s, to illustratethe linear load growth with time due to a thickening boundary layer under-neath the permeable membrane. a) shows the height versus time, b) showsthe load versus time, and c) shows the load versus average solidity trend forthis particular data file.boundary layer causes a low-permeable region under the moving membrane,increasing the required compressive load in a linear trend with time. Thelinear growth of load can be seen in Figure 5.4 b.As consolidation continues, the building boundary layer reaches the baseof the suspension chamber and further compression of this layer occurs. Thisis when the load versus time trend, seen in Figure 5.4 b, changes from alinear to exponential trend. We also notice that with increasing averagesolidity, the dewatering curves trend back towards the compressive yieldstress curve. Discussion on this point is presented in Chapter 7 when weaddress the diffusivity of our nylon fibre suspension.5.2.1 Chemical AdditivesNext, the impact of the chemical additives to the NBSK dewatering will beinvestigated. The various dewatering trends for NBSK (Series 1) and NBSKwith the three chemical additives (Series 2, 3 and 4) are shown in Figure5.5.As was seen in Sections 3.7 and 4.6, the chemical additives had no visibleimpact on the compressive yield stress, however, they raised the permeabilityeither by shallowing the slope of the permeability curve or by shallowing andtranslating the curve. This change in permeability has resulted in shiftingthe dewatering curves to the right with the additives; dewatering at a specificrate to a specific load will result in a higher average solidity with the NBSK605.2. Experimental Results and Discussion: Dewatering0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.5: Experimentally collected dewatering trends at various rates forNBSK with varying chemical additives. a) shows Series 1 for comparison,b) shows Series 2, c) shows Series 3 and d) shows Series 4. Data pointsrepresent the average of four trials, with 2 standard deviations shown withthe error bars. Black dashed lines represent compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).615.2. Experimental Results and Discussion: Dewatering0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]Figure 5.6: Select experimental dewatering results of Series 1 (4), Series2 (O), Series 3 (/), and Series 4 (.) for comparison. Data points representthe average of four trials, with 2 standard deviations shown with the errorbars. Colors correspond to particular dewatering rates (see Figure 5.2).treated with the additives when compared to NBSK. This improvement indewaterability can clearly be seen in Figure 5.6 with several select dewateringrates highlighted.The conclusion from Figure 5.6 is that the additives are effective at re-ducing the required load for dewatering to a specific average solidity. It’snot clear from these results, however, which mechanism of increasing per-meability is more effective. From the perspective of AkzoNobel and thepulp and paper industry, these results are promising in that potential forhigher production rates, due to the easier dewatering characteristics of thepulp with these additives, could be achieved. An exciting observation isseeing the effect of the additives become more apparent with increasing de-watering rates. Since dewatering in industrial operations are on the order often times faster than we can achieve in these experiments, potentially evenhigher dewatering improvements can be realized in industrial operations.5.2.2 Low Consistency RefiningThe various refined TMP suspensions (Series 6, 7, and 8), compared to theunrefined TMP (Series 5) are shown in Figure 5.7.625.2. Experimental Results and Discussion: Dewatering0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.7: Experimentally collected dewatering trends at various rates forTMP with varying levels of low consistency refining. a) shows Series 5 forcomparison, b) shows Series 6, c) shows Series 7, and d) shows Series 8.Data points represent the average of four trials, with 2 standard deviationsshown with the error bars. Black dashed lines represent compressive yieldstress. Colors correspond to particular dewatering rates (see Figure 5.2).635.2. Experimental Results and Discussion: Dewatering0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]Figure 5.8: Select experimental dewatering results of Series 5 (), Series6 (♦), Series 7 (©), and Series 8 (•) for comparison. Data points representthe average of four trials, with 2 standard deviations shown with the errorbars. Colors correspond to particular dewatering rates (see Figure 5.2).Despite the modest change in compressive yield stress and no visiblechange in permeability with varying levels of refining, drastic changes in thedewatering curves are seen. A given dewatering rate curve changes muchmore due to a change in refining energy than they had between specieschange, pulping process, or chemical additives. This drastic change dueto increased refining can be seen in Figure 5.8. The results show a wider“spread” in varying dewatering rate curves with increased refining energy.This suggests that a change in the dewatering rate dependent effect is occur-ring to account for the large change seen between varying levels of refining.We consider the source of the rate dependency effect in cellulose fibresuspensions: the fluid expelling from the interior of the fibre, which corre-sponds to a non-zero dewatering timescale for the individual fibres (a finitesolid phase rearrangement rate constant λ(φ)). We have discussed in Sec-tion D.1.3 that higher levels of refining result in more flexible and collapsiblefibres through various mechanisms in the refining process. Several of thesemechanisms likely impact the fibre wall permeability as well, thus shortenthe dewatering timescale of the individual fibres. The mechanisms includecracking of the fibre wall, breaking off regions of the fibre walls producing645.3. Base Model Results: Dewatering of Hard Particle Suspensionfines, and external and internal fibre wall fibrillation. Through these mech-anisms, either the fibre wall thicknesses would be reduced, shortening theflow paths of escaping fluid, or larger pores would be produced, allowingfluid to escape easier. Thus, it seems reasonable that the drastic changesin the dewatering curves seen for varying levels of refining, can at least bepartially attributed to an increasing fibre wall permeability from the mech-anisms present in refining.5.3 Base Model Results: Dewatering of HardParticle SuspensionThe suitability of the base model posed in Chapter 2 will now be investi-gated. As discussed, the base model’s validity is still questionable due tolimited comparisons to experimentally collected results found in the litera-ture. We aim to test the suitability of the base model with a hard particlesuspension (nylon fibres, Series 10) that is more likely to represent the sim-pler rheological expression discussed in Section 2.1 and shown in Equation2.9. An indication of the goodness of fit between the model curves andthe experimentally collected trends will be represented with the followingparameterθ2 =1φb − φa∫ φbφa[σexp(φ)− σmodel(φ)]2dφ (5.2)with θ representing the area discrepancy between the curves, divided bythe span of solidity between φa to φb. Smaller values of θ represent a bettercorrelation between the experimental and model curves.Select dewatering experimental curves of Series 10 are compared to the-oretical curves of the base model, shown in Figure 5.9. Since all parametersare defined in the base model, the model trends are purely predictive.Comparing the experimental and model curves, we see a close corre-lation. The shape of the trends is captured by the model, and, in mostinstances, falls within the error bars of the experimental trends representingtwo standard deviations found from the averaging of repeated experiments.Considering Figure 5.10, we see the fit is deteriorating slowly with increas-ing dewatering rates (θ is increasing), however, overall the fit is quite goodbetween the model and experiments. The particular values of θ are not ofinterest, however the magnitude will be used as a representation of a “good”fit.655.3. Base Model Results: Dewatering of Hard Particle Suspension0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.9: Series 10 select dewatering results (colored lines) compared tobase model trends (colored dashed lines). Experimental curves are averaged,with 2 standard deviations shown with the error bars. Black dashed linesshow compressive yield stress. Colors correspond to particular dewateringrates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.10: θ values from the base model (dashed line) for the dewateringrates collected for Series 10.665.4. Base/Extended Model Results: Dewatering of Cellulose Fibre SuspensionsIn summary, the predictive trends of the base model represent the ex-perimental data well for the nylon fibres. Consideration to the experimentalchallenges of suspensions prepared in glycerin should be made, which couldaccount for some of the discrepancy. High percentage glycerin has severeviscosity sensitivities to both moisture content and temperature. Slight vari-ations in either results in a drastic change in viscosity. It was observed thatthe viscosity was dropping through the experimental process, resulting inlower load curves when experiments were repeated later on. The viscosityused in the model equations is thus an averaged value, and does not accu-rately reflect the viscosity of certain dewatering rate curves. Improvementsto experimental data could be made by controlling temperature and mois-ture content of the sample during experiments, however, this is not a trivialtask and not pursued at this time.The results show the base model can represent the dynamics of a dewa-tering event of a suspension consisting of solid particles well.5.4 Base/Extended Model Results: Dewateringof Cellulose Fibre SuspensionsValidity of the base and extended models, introduced in Chapter 2, forrepresenting the dewatering of cellulose fibre suspensions at various rates isinvestigated. As discussed, the extended model has a free parameter. Thisparameter is the constant within the dynamic compressibility term λ(φ),being C. As discussed in the Section 5.1, we do not aim to optimize thisvalue, rather it is varied manually by changing  (see Equation 2.29) to fit theextended model dewatering curves to the experimental trends. The chosenvalues of  and the resulting C values for the coming comparison figures areshown in Table 5.1.Select dewatering experimental curves of the various suspensions arecompared to both the base and extended model curves, followed by a fig-ure representing the fit of the two models for all of the dewatering ratestested. We will first introduce the comparisons of Series 1 through 4, and 9.Discussion of these suspensions will follow after the results are presented.675.4. Base/Extended Model Results: Dewatering of Cellulose Fibre SuspensionsTable 5.1: Values of  and the resulting C from the manual fitting of theextended model curves to the experimentally collected dewatering trends.Series  C[Pa·s]−11 7.4 8.0E-082 2.8 1.3E-073 2.9 2.6E-074 1.9 5.0E-075 3.7 4.4E-096 2.3 8.1E-097 3.9 8.3E-098 3.0 4.7E-099 4.2 1.4E-07685.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.11: Series 1 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.12: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 1.695.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.13: Series 2 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.14: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 2.705.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.15: Series 3 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.16: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 3.715.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.17: Series 4 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.18: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 4.725.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.19: Series 9 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.20: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 9.735.4. Base/Extended Model Results: Dewatering of Cellulose Fibre SuspensionsGenerally speaking, the base model for the cellulose fibre suspensionspresented thus far provides a reasonable prediction of the low dewateringrates collected experimentally, however, the prediction deteriorates severelyas the dewatering rate increases. This is somewhat expected behaviour,knowing our model converges to the compressive yield stress curve at lowdewatering rates and realizing the dewatering rate dependent effect, fromfluid escaping the hollow, porous fibres, would become more pronounced thehigher the dewatering rate becomes. The diverging prediction quality of thebase model is shown in the various fit figures, as θ increases dramaticallyfor higher dewatering rates.The extended model, when fitted, has improved representation of theexperimental data at high dewatering rates and equivalent representation atlower rates. The dewatering rate dependent effect, represented by the morecomplex rheological expression, seems effective in preventing divergence athigher dewatering rates, providing confidence in the functional form of λ(φ)chosen. From the fitted parameter C, we also have gained a parameterproportional to the cellulose fibre wall permeability. Perhaps with a morecomplex form of λ(φ), even better agreement could be made, however, thisis not investigated at this time.In the coming pages we introduce the TMP (Series 5), and various refinedTMP (Series 6, 7, and 8) model comparisons.745.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.21: Series 5 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.22: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 5.755.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.23: Series 6 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.24: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 6.765.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.25: Series 7 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.26: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 7.775.4. Base/Extended Model Results: Dewatering of Cellulose Fibre Suspensions0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]a)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]b)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]c)0 0.1 0.2 0.3 0.4 0.5050010001500φ¯σ[kPa]d)Student Version of MATLABFigure 5.27: Series 8 select dewatering results (colored lines) compared tobase (colored dashed lines) and extended model trends (colored dotted lines).Experimental curves are averaged, with 2 standard deviations shown withthe error bars. Black dashed lines show compressive yield stress. Colorscorrespond to particular dewatering rates (see Figure 5.2).10−3 10−2 10−1 100 101102104106U [mm/s]θ[kPa]Student Version of MATLABFigure 5.28: θ values from the base (dashed line) and extended models(dotted line) for the dewatering rates collected for Series 8.785.4. Base/Extended Model Results: Dewatering of Cellulose Fibre SuspensionsOverall, the base model provided poor representation of the various TMPexperiments (Series 5 - 8), even at low dewatering rates. The base modelhad a very steep increase in load, appearing almost vertical, even at the lowdewatering rates. The extended model does not represent the data very welleither, however, the more complex rheological expression pulls the curves inthe correct direction. We speculate that the discrepancy mainly comes fromretention experimental errors.Despite the lower quality of representation provided by the various modeltrends, we wish to pick up the discussion on the refining process’ impact onthe fibre wall permeability. The discussion at the end of Section 5.2.2 specu-lated that the drastic changes in the dewatering curves for increased refiningcould be partially attributed to an increasing fibre wall permeability. Severalmechanisms of the refining process aimed at increasing fibre flexibility andcollapsibility seem reasonable to increase the fibre wall permeability as well.In terms of our extended model, fibre wall permeability is proportional to C,thus is proportional to λ(φ). Should this speculation hold true, we shouldobserve increasing values of C for increasing levels of refining. Observingthe values in Table 5.1, we do in fact see this for Series 5, Series 6, andSeries 7. The increasing trend does not continue with Series 8. However,upon investigation of the experimental data of Series 8 (Figure 5.27) we seethat there is very little experimental data representing the two highest de-watering rates. Not having a sufficient trend for comparison at the higherdewatering rates could have resulted in an incorrect value of  that favoredthe low dewatering rate trends. This may have resulted in a smaller valueof C being determined. We also should consider that the fit between themodel curves and the experimental trends is poorer for the various TMPtrials when compared to the previous cellulose fibre suspensions. Less cer-tainty is had, then, in the values of C for the Series 5, 6, 7, and 8, however,they do somewhat show the expected trend based on our theory of the fi-bre wall permeability increasing with increasing refining. Further supportcomes from observing how the base model curves (which correspond to aninfinite fibre wall permeability) for the various suspensions are steeper anddiverge at lower values of solidity than the extended model curves (whichcorrespond to a finite wall permeability). Qualitatively, it can be seen thatthe trends are becoming steeper, and diverging at lower values of solidity forincreasing levels of refining as well, suggesting that fibre wall permeabilityis increasing.Despite the challenges in the TMP model results, overall the extendedmodel appears to provide improved representation of the experimental datafor cellulose fibre suspensions over the base model, particularly at higher795.5. Conclusions: Dewatering Experiments and Model Comparisonsdewatering rates.5.5 Conclusions: Dewatering Experiments andModel ComparisonsImplementation of the experimental system used for determining compres-sive yield stress has allowed collection of dewatering experiment data atvarious rates. A catalog of various cellulose fibre suspensions’ dewateringbehaviours has begun. Due to the small data set however, no conclusiveremarks about the differences seen between the various suspensions can bemade, and thus the discussions provided are speculative.Efforts were made to determine the suitability of the base and extendedmodels in capturing the load versus solidity dewatering behavior of variouscellulose fibre suspensions. The base model was found to perform poorlyfor increasing dewatering rates of cellulose fibre suspensions. This supportsPettersson et al.’s findings [25]. The extended model, with its free parameterfit by eye, had drastic improvements in capturing the dewatering behavior.The chosen functional form of λ(φ) has provided good representation of thedewatering behaviour of cellulose fibres.Efforts to validate the base model were done through comparing thepredictive load versus solidity trends to the experimentally determined de-watering results for our nylon fibre suspension. The comparison showed thebase model captured the dewatering behavior of the nylon fibre well de-spite the experimental challenges of suspensions prepared in glycerin. Theresults confirmed the suitability of compressive rheology in modeling thedewatering behavior of flocculated suspensions of hard particles, and showsthe assumption of λ(φ) =∞ is reasonable for this type of suspension.80Chapter 6Model Validation ThroughPTV AnalysisAs was seen in Sections 5.3 and 5.4, the base model effectively representedthe dewatering trends of a hard particle suspension (Series 10) and theextended model had great improvements over the base model in capturingthe dewatering experimental trends of cellulose fibre suspensions. To furtherinvestigate the representative behaviours of both models, we wish to comparethe models’ solid phase movement to that which is seen experimentally. Thiswould improve our confidence further for both models. A Particle TrackingVelocimetry (PTV) analysis was conducted on a select few of the dewateringtrials to determine experimentally the movement of the solid phase. Series1 and Series 10 experiments were collected and velocity profiles of the solidphase were found. These were then compared to velocity profiles from thetwo models.Throughout this chapter, we will present the model validation work donethrough the PTV analysis. We start with a quick description of the method-ology and experimental protocol used in the analysis. Next, the experimen-tally collected results are shown, discussed, and compared to the models’results. Following this, a conclusion of the work is presented.6.1 Methodology and Experimental Protocol:PTV AnalysisExperimentally, dewatering trials were collected, as normally done and de-scribed in Section 5.1. Black tracer particles were mixed within the sus-pension to track the solid phase movement. Alternative to traditional PTVexperiments, the tracer particles in these experiments are meant to movewith the solid phase and not the liquid. The concentration of tracer parti-cles used was approximately 0.003 (weight of particles/weight of solution).The tracer particles were approximately 1-2 mm in size. A Vision ResearchPhantom V611 (www.highspeedcameras.com) high speed camera was used816.2. Results and Discussion: PTV Analysistˆ/tˆtotalzˆ/hˆ(tˆ)  0.2 0.4 0.6 0.8 100.20.40.60.81|uˆs/U|00.20.40.60.81Figure 6.1: Contour plot of Series 10 low dewatering rate trials (0.25 mm/s)showing velocity of the solid phase scaled by permeable membrane velocityas color, as a function of scaled height and scaled time of experiment. Resultsare averaged from five trials.along with flood lights with a frame rate fixing apparent speeds to less than0.01 mm/frame, and the field of view set by the initial height of the suspen-sion.Multiple trials were performed for a given dewatering rate to accountfor experimental variations and to increase the number of tracked particles.The frames of the various trials were analyzed to determine streamlines ofthe particles. The multiple trials’ streamlines were combined, and aver-age velocity was determined as functions of time and elevation. A detaileddescription of the PTV analysis developed can be found in Appendix C.6.2 Results and Discussion: PTV AnalysisFirst, we consider Series 10 (nylon fibre) dewatering and how well the basemodel captures the behavior seen experimentally. Contour plots represent-ing low and high dewatering rate events are shown in Figures 6.1 and 6.2respectively. Velocity of the solid phase is scaled by the permeable mem-brane velocity and is represented as color.We first consider the low dewatering rate Series 10 contour, seen in Fig-ure 6.1. We see a slightly evolving velocity profile development at lower826.2. Results and Discussion: PTV Analysistˆ/tˆtotalzˆ/hˆ(tˆ)  0.2 0.4 0.6 0.8 100.20.40.60.81|uˆs/U|00.20.40.60.81Figure 6.2: Contour plot of Series 10 high dewatering rate trials (3.0 mm/s)showing velocity of the solid phase scaled by permeable membrane velocityas color, as a function of scaled height and scaled time of experiment. Resultsare averaged from five trials.elevations during the event. The velocity is somewhat linear with eleva-tion, as seen as a uniform color transition from the top to the bottom. Thehigh dewatering rate Series 10 contour, seen in Figure 6.2, looks signifi-cantly different. The high dewatering rate event does not provide as linearof a velocity distribution with elevation, rather a significant proportion ofthe elevation of the suspension is either stationary or moving quite slowly,particularly at scaled time values less than 0.7.A select velocity profile from the low and high dewatering rate contoursare compared to velocity profiles found theoretically by the base model,shown in Figure 6.3.What can be seen from this comparison is the base model velocity pro-files qualitatively look quite close to the experimental results. Significantconcentration gradients would be present in the high dewatering rate exper-iment due to the low solid phase velocity in the majority of the suspension.This is the development of the high solidity boundary layer under the mov-ing permeable membrane. This high concentration region is what causesthe linear load growth in the load versus time graph shown in Figure 5.4 bdue to a low permeable region underneath the moving membrane. Overall,the base model seems to show similar velocity profiles during dewatering836.2. Results and Discussion: PTV Analysis0 0.5 100.20.40.60.81|uˆs/U |zˆ/hˆ(tˆ)a)0 0.5 100.20.40.60.81|uˆs/U |zˆ/hˆ(tˆ)b)Figure 6.3: Select solid phase velocity profiles of Series 10 from the low(0.25 mm/s) and high (3.0 mm/s) dewatering rate experiments shown ina) with error bars representing the variance in velocities at the particularelevation. The base model solid phase velocity profiles are shown in b) forcomparison. Colors correspond to the dewatering rates, with magenta beingthe low and dark green being the high dewatering rates respectively. Allcurves are taken at tˆ/tˆtotal = 0.3. Results are averaged from five trials.when compared to the experimental results found for Series 10, furtheringour confidence in the base model representing the dewatering suspensions ofsolid particles.Next we investigate the two models’ suitability with a cellulose fibresuspension: NBSK (Series 1). We already have seen that the extendedmodel represents cellulose fibres much better with the load versus soliditycurves in Chapter 5, however, questions still remain if the improvementis through better representing the solid phase movement or is from someartificial improvement. The low and high dewatering rate events are shownin Figures 6.4 and 6.5 respectively.Unlike the two contour plots for Series 10, the differences between thecontour plots of low and high dewatering rates of Series 1, seen in Figures6.4 and 6.5, are not as apparent. Both contours provide a linear distributionof color (solid velocity). From this, we can expect to see very similar selectvelocity profiles.Select velocity profiles from the low and high contours are compared toboth the base and extended model velocity profiles, shown in Figure 6.6.What can be seen in the experimental trends is that the velocity pro-file is near linear for both dewatering rates. The base model predicts aboundary layer developing under the permeable membrane with higher de-watering rates, seen as the solid phase moving quickly at the top while the846.2. Results and Discussion: PTV Analysistˆ/tˆtotalzˆ/hˆ(tˆ)  0.2 0.4 0.6 0.8 100.20.40.60.81|uˆs/U|00.20.40.60.81Figure 6.4: Contour plot of Series 1 low dewatering rate trials (1.5 mm/s)showing velocity of the solid phase scaled by permeable membrane velocityas color, as a function of scaled height and scaled time of experiment. Resultsare averaged from two trials.tˆ/tˆtotalzˆ/hˆ(tˆ)  0.2 0.4 0.6 0.8 100.20.40.60.81|uˆs/U|00.20.40.60.81Figure 6.5: Contour plot of Series 1 high dewatering rate trials (10.0 mm/s)showing velocity of the solid phase scaled by permeable membrane velocityas color, as a function of scaled height and scaled time of experiment. Resultsare averaged from two trials.856.2. Results and Discussion: PTV Analysis0 0.5 100.20.40.60.81|uˆs/U |zˆ/hˆ(tˆ)a)0 0.5 100.20.40.60.81|uˆs/U |zˆ/hˆ(tˆ)b)0 0.5 100.20.40.60.81|uˆs/U |zˆ/hˆ(tˆ)c)Figure 6.6: Select solid phase velocity profiles of Series 1 from the low (1.5mm/s) and high (10.0 mm/s) dewatering rate experiments shown in a) witherror bars representing the variance in velocities at the particular elevation.The base and extended models solid phase velocity profiles are shown in b)and c) respectively for comparison. Colors correspond to the dewateringrates, with green being the low and red being the high dewatering ratesrespectively. All curves are taken at tˆ/tˆtotal = 0.3. Results are averagedfrom two trials.remaining suspension is stagnant. This is clearly not seen experimentally.This thickening region underneath the permeable membrane, predicted bythe base model, would be the source of the load diverging significantly fromthe experimental dewatering trends for cellulose fibre suspensions, seen inSection 5.4. The high solidity formation under the membrane reduces thepermeability in this region considerably, making it difficult for the liquidphase to squeeze through.The extended model provides a closer representation of what’s seen ex-perimentally: an almost linear velocity profile for the low and high dewater-ing rates. The extended model does not predict the boundary layer underthe moving membrane. Solidity gradients would be expected to be low dueto the near linear velocity. As expected, the extended model is providingmore uniform compaction, meaning a reduction in solidity gradients from anon-infinite λ(φ), thus a non-zero dewatering time constant for the individ-ual fibres.866.3. Conclusions: Model Validation Through PTV Analysis6.3 Conclusions: Model Validation ThroughPTV AnalysisImplementation of our dewatering experimental setup in conjunction witha high speed camera and developed analysis procedure has allowed us todetermine the velocity profiles of the solid phase of a suspension duringdewatering. With this technique, we can compare experimentally collectedvelocity profiles with the profiles developed from either the base or extendedmodels. This has been used to further investigate both models’ abilities incapturing dewatering behavior.The base model was further validated for representing dewatering ofhard particle suspensions through this investigation. The velocity profilesfor our hard particle, nylon fibre suspension, found experimentally, agreedquite closely with the predicted velocity curves from the base model. Theextended model also gained further validation by representing the solid phasevelocity of a cellulose fibre suspension, found experimentally, quite well. Thisalso provided further confidence in the chosen functional form of dynamiccompressibility λ(φ).87Chapter 7Diffusivity Dˆ(φ) andQuantifying DewateringAbilityDiffusivity, as introduced in the background, is a third material parameteroften discussed in the literature of dewatering. It is a dependent combinationof compressive yield stress and permeability, and can be thought of as asolid phase diffusion coefficient. It has been used as a comparison toolbetween suspensions to show relative dewatering difficulty: a high diffusivitycorresponds to a suspension that dewaters easily [21, 23, 24].Having a parameter that quantifies a suspension’s dewatering abilitycould be valuable to industrial pulp operations. Knowing a value of howwell a suspension dewaters may help predict operating parameters such asmaximum throughput or running speed, given the equipment’s maximumload ratings. A dewatering parameter also may correlate to final productparameters, similar to Canadian Standard Freeness (CSF) measurements,providing a method of predicting final product performance during produc-tion.Throughout this chapter, we present our diffusivity work and our at-tempts at quantifying a suspension’s dewatering ability. We start with pre-senting and discussing the diffusivity results. Following this, we considerdiffusivity as a method of quantifying dewatering ability. Considerationthen is given to an empirically determined parameter, CSF, and its abilityto quantify dewatering. Finally, concluding remarks are made.7.1 Results and Discussion: Dˆ(φ)To give an indication where the dynamics of suspensions tested in thisproject fit in with various other dewatering related industries, we have de-termined our experimental values of diffusivity and plotted them along withothers found in the literature, shown in Figure 7.1.887.1. Results and Discussion: Dˆ(φ)0 0.1 0.2 0.3 0.410−610−4φDˆ(φ)[m2/s]a)0 0.2 0.4 0.610−1010−5Dˆ(φ)[m2/s]φb)Student Version of MATLABFigure 7.1: Diffusivity determined from experimental results for varioussuspensions. a) shows our experimental results (symbol legend shown inTable 3.2) with their corresponding fits (line legend shown in Table 3.3),and b) compares our results to minerals presented in Stickland et al. [21]and de Kretser et al. [24] as  and  respectively along with Stickland etal. results for starches and waste water sludge shown as  and .We first focus on our collected values of diffusivity. We notice the generaltrend of the nylon fibres (Series 10) is increasing with solidity, while the var-ious cellulose fibres are decreasing. Diffusivity is a trend that has competingcomponents as solidity increases: the stiffening of the matrix and the drop-ping permeability. The slope of diffusivity is dependent on which trend ismore aggressive. With Series 10, the network stiffened quicker than the flowpassages closed up. This is somewhat expected due to the hard particles andthe substantial increase in compressive yield stress slope with increasing so-lidity as the contact sites of the fibres increases. The fact that permeabilityis a couple magnitudes higher for Series 10 compared to the cellulose fibresuspensions also contributes to an increasing trend in diffusivity.The increasing trend in diffusivity also is part of the explanation of thedifference in dewatering trend shape of nylon fibres at high dewatering rateswhen compared to the cellulose fibres, which can be seen in Figure 5.3.With Series 10, since the diffusivity starts at a low value, the suspension isunable to propagate the concentration gradient that forms under the movingpermeable membrane, resulting in a building boundary layer. This boundarylayer was seen as the high solid velocity region at high elevations for the high897.2. Quantifying Dewatering Ability: Dˆ(φ)0.31 0.39050010001500φAvg φPyσφ¯σ[kPa]Figure 7.2: Schematically showing φAvg(σ, U) and φPy(σ) for Series 1 withU = 1.5 mm/s and σ = 500 kPa.dewatering rate trend, shown in Figure 6.3. As the concentration increases,the diffusivity also increases, resulting in increased dewatering ability. Thiscan be seen as the dewatering curves in Figure 5.3 d converge towards thecompressive yield stress curve at higher solidities.The trend of the diffusivity curves for the cellulose fibres follows thenegative slope of waste water sludge shown by Stickland. This implies thatthe decreasing permeability is the dominant factor to the diffusivity termwith cellulose fibres, which, when considering the intricate flow path, seemsreasonable. Negatively sloped diffusivity data with increasing solidities is acommon trend with organic solid phase suspensions [29].7.2 Quantifying Dewatering Ability: Dˆ(φ)To investigate diffusivity and its appropriateness to quantify a cellulose sus-pension’s ability to dewater, we start with introducing a dewatering metric,Φ. This metric is defined asΦ =φAvg(σ, U)φPy(σ)(7.1)where φAvg(σ, U) is defined as the average solidity for a particular load σ ata particular dewatering rate U , and φPy(σ) is the solidity that correspondsto the particular load σ on the Py(φ) curve. φAvg(σ, U) and φPy(σ) canbe seen schematically in Figure 7.2. Φ then represents a percentage ofideal, or uniform dewatering, achieved at a rate higher than that of the907.2. Quantifying Dewatering Ability: Dˆ(φ)0.4 0.5 0.6 0.7 0.8 0.910−810−710−610−5ΦDˆ(φPy)[m2/s]Figure 7.3: Diffusivity values calculated at various cellulose fibre suspen-sions φPy values versus our defined dewatering metric Φ, with U = 1.5 mm/sand σ = 500 kPa. Symbol legend is shown in Table 3.2.the compressive yield stress. This method eliminates the bias of differentmaterials having varied Py(φ) curves that would occur should we simplyconsider what suspension reached highest solidity.To compare the dewatering performance of the various cellulose suspen-sions in this project, σ is defined as 500 kPa, and U is chosen as 1.5 mm/s.Similar trends are seen with varying U and σ. This dewatering rate is cho-sen since it is shared between all the cellulose materials tested, and it’s slowenough that retention issues are minimized in the TMP trials (Series 5, 6,7, and 8), allowing them to be included in this discussion. The load valueis chosen as an intermediate value where the MTS 858 Table Top Systemsstand-alone controller can still maintain the defined dewatering rate.A solidity needs to be chosen at which the suspensions’ characteristicdiffusivity will be defined. Due to diffusivity being a negatively sloped trendwith increasing solidity, and speculating that the dewatering is governed bythe lowest diffusivity within the suspension, we choose to define diffusivityat φPy as this is the upper bound of solidity that will be within the sus-pension. This can be shown from examining the load boundary conditionshown in Equation 2.24. Comparison of the determined diffusivities versusthe dewatering metrics of the various cellulose fibre suspensions is shown inFigure 7.3.Diffusivity is seen to have a strong power law relationship for increasingvalues of Φ. Diffusivity seems like a promising trend to represent the easeat which a cellulose suspension can dewater, however, it still poses some917.3. Quantifying Dewatering Ability: CSFproblems. First, the experimental data results initially have a rather flattrend, meaning very small differences in diffusivity represent a large rangeof the dewatering metric (seen as the near flat trend of data from Φ = 0.35up to 0.7). Very little difference in diffusivity is seen for the Series 5, 6, 7,and 8, despite very different dewatering metric values and thus dewateringperformance. The little difference in diffusivity comes from the somewhatconstant permeability for varying refining levels and only a slight change inthe compressive yield stress. Experimental retention concerns were discussedas a potential source of the rather stagnant permeability values for increasedrefining in Section 5.2.2. If these concerns were found to be true, improvedexperimental results would lead to a more significant change in diffusivitydue to a changing permeability as well. This reduces the initial concern,and thus increases the appeal of diffusivity as a parameter representative ofa suspension’s ability to dewater.Following the sharp corner in the data, a very steep trend occurs wherea large range of diffusivities are responsible for very little differences in thedewatering metric. Considering how similar the dewatering ability of thechemical pulps was (based on Φ values and upon inspection of the dewateringgraphs in Chapter 5), it would have been more satisfying to see less spreadfor their diffusivities.Neither of these issues are ideal behavior, however, it is promising tohave a monotonic trend and the severity of these issues may be exaggerateddue to the small number of suspensions investigated. Due to the diffusiv-ity’s theoretical basis, it would be wise to continue investigating its abilityin quantifying dewatering ability by conducting trials on many more sus-pensions.7.3 Quantifying Dewatering Ability: CSFFor comparison, we turn to investigating the effectiveness of our CanadianStandard Freeness (CSF) values in quantifying a cellulose suspension’s abil-ity to dewater, shown in Table D.2. As discussed in Section D.3, CSF isan empirically based experiment used for quantifying the drainability of acellulose fibre suspension, which is proportional to its dewatering. This isone of the industry’s standardized parameter for quantifying drainage, soit will be interesting to see how it correlates. The determined CSF valuesversus our dewatering metric for the various suspensions are shown in Fig-ure 7.4. Increasing Φ values should correspond to more easily dewateringsuspensions. We see that at first, our CSF values are following this trend,927.3. Quantifying Dewatering Ability: CSF0.4 0.5 0.6 0.7 0.8 0.9400600800ΦCSF[mL]Figure 7.4: CSF values found for the various cellulose fibre suspensionsversus our defined dewatering metric Φ, with U = 1.5 mm/s and σ = 500kPa. Symbol legend is shown in Table 3.2.with increasing freenesses as we move through our TMP suspensions frommost refined (Series 8) to least (Series 5). This is an expected trend, as wasseen by Carlsson et al. [51]. This is favorable behavior if CSF is to quantifya suspension’s ability to dewater, however confusion starts when we beginobserving the various NBSK (Series 1, 2, 3, and 4) and BHK (Series 9)suspensions. Both the NBSK and BHK suspensions had what we wouldconsider easier dewatering characteristics, represented as higher values of Φ.Despite this, very similar or even lower CSF values were determined com-pared to the TMP trials which very obviously didn’t dewater as well due tothe much lower dewatering metric Φ.We plot the materials’ diffusivity values versus their CSF results to seeif any relation can be seen in Figure 7.5.Somewhat as expected, we do not see any sort of correlation betweendiffusivity and CSF of the materials tested. This is not a concern limited tothe cellulose suspension of this project. Lindsay et al. [38] showed how anorder magnitude difference in transverse permeability was seen between twounbleached, softwood pulps at the same CSF values. Although permeabilityis not equal to diffusivity, we have discussed that its the dominant proportionin cellulose fibres’ diffusivity due to its trend following the negative slopingof the permeability parameter. Thus it’s conservative to say Lindsay et al.results would also result in substantial differences in diffusivity for the samefreeness, which is what we have seen here.937.4. Conclusions: Dˆ(φ) and Quantifying Dewatering Ability300 400 500 600 700 800 90010−810−710−610−5CSF [ml]Dˆ(φPy)[m2/s]Figure 7.5: Diffusivity values calculated at various cellulose fibre suspen-sions φPy values versus our CSF values. Diffusivity values of the materialsdefined at φ values corresponding to Py = 500 kPa. Symbol legend is shownin Table 3.2.7.4 Conclusions: Dˆ(φ) and QuantifyingDewatering AbilityDiffusivity, being a third material parameter that is dependent on com-pressive yield stress and permeability, provides an ability to compare sus-pensions’ dewatering performance. Collected values of permeability andcompressive yield stress were used to find the diffusivity trends for our vari-ous suspensions. Diffusivity has provided a monotonic trend for quantifyingthe various suspensions’ dewatering ability, however, possess some concernsas well, which may be related to the small number of suspensions investi-gated. Concerns with CSF representation of dewatering ability were alsoseen. Given diffusivity’s theoretical basis, it would be wise to continue in-vestigating its suitability in quantifying a suspensions’ dewatering ability.94Chapter 8Summary and Future Work8.1 SummaryEquipment and experimental protocol have been developed for capturingone dimensional dewatering results and the material parameters’ compres-sive yield stress Py(φ) and permeability k(φ) for cellulose fibre suspensions.Two techniques have been implemented for collecting compressive yieldstress results, which show good agreement. Two approaches for determin-ing permeability values from permeation experiments have been developed:approach one provided an approximate solution that neglected flow inducedcompaction, and approach two provided a robust method for fitting a func-tional form of permeability that accounted for flow induced compaction.Comparing results to values found in the literature validated the experi-mental apparatus.The base and extended models were tested for their suitability in captur-ing the dewatering behaviour of cellulose fibre suspensions. The base modelwas found to perform poorly in representing load versus solidity curves forincreasing dewatering rates of cellulose fibre suspensions. This supportedPettersson et al.’s findings [25]. The extended model, with its fitted param-eter C within λ(φ), had drastic improvements in capturing the dewateringbehavior. The chosen functional form of λ(φ) has provided good represen-tation of the dewatering behaviour of cellulose fibres.Efforts to validate the base model were completed through comparingthe predictive load versus solidity trends to the experimentally determineddewatering results for our nylon fibre suspension. The comparison showedthe base model captured the dewatering behavior of the nylon fibre suspen-sions well despite the experimental challenges of suspensions prepared inglycerin. The results confirmed the suitability of compressive rheology inmodeling the dewatering behavior of flocculated suspensions of hard parti-cles, and shows the assumption of λ(φ) = ∞ is reasonable for this type ofsuspension.Further validation of the two models’ representation of dewatering be-haviour was investigated in terms of how well the base and extended models958.2. Future Workrepresented the solid phase movement of suspensions during consolidation.Implementation of the dewatering experimental setup in conjunction with ahigh speed camera and developed analysis procedure allowed us to determinethe velocity profiles of the solid phase of a suspension during dewatering.Nylon and cellulose fibre suspensions were investigated to determine the suit-ability of the base and extended models respectively. The base model wasfurther validated for representing dewatering of hard particle suspensionsthrough this investigation by providing close representation of the veloc-ity profiles found experimentally. The extended model also gained furthervalidation for representing dewatering of cellulose fibre suspensions. Theextended model’s velocity profiles agreed closely with experimentally de-termined profiles, whereas the base model’s velocity profiles looked quitedifferent. This also provided further confidence in our chosen functionalform of the dynamic compressibility λ(φ).Finally, we began a catalog of various cellulose fibres’ dewatering be-haviours. Compressive yield stress, permeability, and dewatering results atvarious dewatering rates were collected for a series of suspensions. Whencompressive yield stress and permeability are combined, we also can deter-mine the third, dependent material parameter, diffusivity, which has pro-vided promise for a parameter that represents a suspension’s ability to de-water. The various suspensions were selected to investigate the impact ondewatering behaviour seen with changes to a few select factors in the pro-duction of pulp. Investigations included the difference between softwood andhardwood fibres, difference seen between two pulping processes, the impactof low consistency refining, and the impact of chemical additives. Conclusiveremarks regarding the investigations cannot be made due to the small dataset, however, we have started the catalog of various suspensions’ dewateringbehaviours.8.2 Future WorkBased on the results of this project, several future work topics are suggested.Further validation of the experimental system used for compressive yieldstress results should be pursued. Uncomfortable comparisons of our exper-imental results to cellulose fibre results found in the literature potentiallypoints to a calibration or compliance error. Although this has been checkedseveral times, further investigation should be conducted into the discrep-ancy.An experimental modification is needed before any more TMP trials can968.2. Future Workbe completed due to retention concerns. Once improvements to the pro-tocol or experimental setups have been completed, repeated TMP refiningtrials would be desirable to see if our speculations about C increasing withincreased levels of refining held true and if the constant permeability withincreased levels of refining remains.Further investigation into the cellulose fibre suspension behavior duringpermeability experiments under gradual temperature changes should be in-vestigated. Unexpected, and currently unexplained, behavior during perme-ability experiments occurred in the form of gradually increasing compressiveload measurements, despite the hydraulic actuator being de-energized. Afterextensive troubleshooting, it was found that small temperature changes inthe permeating fluid (3-5◦C) throughout the course of several hours resultedin substantial compressive load increases that made stable data collectiondifficult. The mechanism of the network “swelling” due to small temperaturechanges that was seen and can be replicated should be investigated.With the promising comparisons seen between the base and extendedmodels with the various suspensions, further validation must continue. First,it should be investigated if the model is able to capture dewatering trendsat higher dewatering rates, and for varied dewatering rate functions. Ratesseen in the industrial setting of a twin roll press are an order of magnitudehigher than what we have been able to achieve, and the dewatering ratefunction is not a constant through the nip point. Ensuring the model holdsto its fitting abilities at these higher and varied rates is critical. Furtherscrutiny should be had on the form of λ(φ) as well, particularity as thedewatering rate increases. Should the functional form of λ(φ) maintain itssuitability, a rigorous technique for fitting the experimental data to deter-mine the optimized value of C should be developed.Further, cellulose fibre suspensions should be tested to confirm our re-sults discussed throughout Chapters 3, 4, 5, and 7, and to continue to catalogvarious cellulose fibre suspensions’ dewatering behaviors. Examples of fur-ther trials may include never-dried suspensions, Kraft suspensions at varyinglevels of refining, and further work into the effectiveness of chemical addi-tives at improving the dewatering performance of cellulose fibre suspensions.From the increased cataloging, further investigation into diffusivity as a de-watering parameter can occur. In particular, diffusivities determined forsuspensions with lower Φ values are needed to validate an increasing trendthat is seen between diffusivity and the dewatering performance metric Φ.A final direction of future work suggested is investigating whether a pa-rameter that is some functional form of both the suspension’s diffusivityand its dynamic compressibility function λ(φ) exists that better quantifies978.2. Future Worka suspension’s dewatering ability. As discussed in Chapter 7, having a pa-rameter that quantifies dewatering ability of a suspension may prove usefulfor industrial operations. The ability of diffusivity to quantify a suspen-sion’s dewatering ability was investigated, however diffusivity only capturesthe material parameters of the base model, and does not have any repre-sentation of the dynamic of fluid flow out of the hollow, porous fibres (thefoundation of the extended model). With the success seen with the extendedmodel, it would seem reasonable for dynamic compressibility to be includedin some parameter defining a cellulose fibre suspension’s ability to dewaterpoorly or effectively.98Bibliography[1] P. Pettersson, T. Wikstrom, and T.S. Lundstrom. Method for measur-ing permeability of pulp suspension at high basis weights. Journal ofPulp and Paper Science, 34:191–197, 2008.[2] A.D. Fitt, P.D. Howell, J.R. King, C.P. Please, and D.W. Schwende-man. Multiphase flow in a roll press nip. European Journal of AppliedMathematics, 13:225–259, 2002.[3] R. Buscall and L.R. White. The consolidation of concentrated suspen-sions. part 1. the theory of sedimentation. Journal of the Chemical Soci-ety, Faraday Transactions 1: Physical Chemistry in Condensed Phases,83:873–891, 1987.[4] K.A. Landman, C. Sirakoff, and L.R. White. Dewatering of flocculatedsuspensions by pressure filtration. Physics of Fluids A: Fluid Dynamics(1989-1993), 3:1495–1509, 1991.[5] R.G. de Kretser, P.J. Scales, and D.V. Boger. Improving clay-basedtailings disposal: case study on coal tailings. AIChE Journal, 43:1894–1903, 1997.[6] D.M Audet and A.C. Fowler. A mathematical model for compactionin sedimentary basins. Geophysical Journal International, 110:577–590,1992.[7] R.J Wakeman. Separation technologies for sludge dewatering. Journalof Hazardous Materials, 144:614–619, 2007.[8] K.A. Landman and L.R. White. Solid/liquid separation of flocculatedsuspensions. Advances in Colloid and Interface Science, 51:175–246,1994.[9] A. Swerin. Rheological properties of cellulosic fibre suspensions floccu-lated by cationic polyacrylamides. Colloids and Surfaces A: Physico-chemical and Engineering Aspects, 133:279–294, 1998.99Bibliography[10] I.M.L. Chew, D.C.Y. Foo, J.C. Bonhivers, P. Stuart, A. Alva-Argaez,and L.E. Savulescu. A model-based approach for simultaneous waterand energy reduction in a pulp and paper mill. Applied Thermal Engi-neering, 51:393–400, 2013.[11] G.A. Smook. Handbook for Pulp and Paper Technologists. Angus WildePublications Inc., 2 edition, 1997.[12] D.R. Hewitt, D.T. Paterson, N.J Balmforth, and D.M. Martinez. De-watering of fibre suspensions by pressure filtration. Physics of Fluids,Submitted 2016.[13] R. Buscall, I.J. McGowan, Stewart R.F. Mills, P.D.A, D. Sutton, L.R.White, and G.E Yates. The rheology of strongly-flocculated suspen-sions. Journal of non-newtonian fluid mechanics, 24:183–202, 1987.[14] R. Buscall, P.D.A. Mills, and G.E. Yates. Viscoelastic properties ofstrongly flocculated polystyrene latex dispersions. Colloids and Sur-faces, 18:341–358, 1986.[15] R. Buscall, P.D.A. Mills, J.W. Goodwin, and D.W. Lawson. Scalingbehaviour of the rheology of aggregate networks formed from colloidalparticles. J. Chem. Soc., Faraday Trans. 1, 84:4249–4260, 1988.[16] R. Buscall, J.I. McGowan, and A.J. Morton-Jones. The rheology ofconcentrated dispersions of weakly attracting colloidal particles withand without wall slip. Journal of Rheology, 37(4):621–641, 1993.[17] R. Buscall. The elastic properties of structured dispersions: A simplecentrifuge method of examination. Colloids and Surfaces, 5:269–283,1982.[18] K.A. Landman, L.R. White, and M. Eberl. Pressure filtration of floccu-lated suspensions. American Institute of Chemical Engineers Journal,41:1687–1700, 1995.[19] F.M. Tiller and W.F. Leu. Basic data fitting in filtration. Journal ofthe Chinese Institute of Chemical Engineers, 11:61–70, 1980.[20] F.M. Tiller and Z. Khatib. The theory of sediment volumes of compress-ible, particulate structures. Journal of Colloid and Interface Science,100:55–67, 1984.100Bibliography[21] A.D. Stickland and R. Buscall. Whither compressional rheology? Jour-nal of Non-Newtonian Fluid Mechanics, 157:151–157, 2009.[22] R. Burger, F. Concha, and K.H. Karlsen. Phenomenological modelof filtration processes: 1. cake formation and expression. ChemicalEngineering Science, 56:4537–4553, 2001.[23] R.G. de Kretser, D.V. Boger, and P.J. Scales. Compressive rheology:an overview. Rheology Reviews, pages 125–166, 2003.[24] R.G. de Kretser, S.P. Usher, P.J. Scales, and D.V. Boger. Rapid filtra-tion measurement of dewatering design and optimization parameters.American Institute of Chemical Engineers Journal, 47:1758–1769, 2001.[25] P. Pettersson, K. Lindgren, T.S. Lindstrom, and T. Wikstrom. De-velopment of material models for dewatering of pulp suspensions. The19th International Symposium on Transport Phenomena, 17-20 August,2008, 2008.[26] A.J. Panshin and C. de Zeeuw. Textbook of Wood Technology. McGrawHill, 4 edition, 1980.[27] H. Vomhoff and A. Schmidt. The steady-state compressibility of sat-urated fibre webs at low pressures. Nordic Pulp and Paper ResearchJournal, 12, 1997.[28] G.M. Channell and C.F. Zukoski. Shear and compressive rheology ofaggregated alumina suspensions. American Institute of Chemical En-gineers Journal, 43:1700–1708, 1997.[29] K.A. Northcott, I. Snape, P.J Scales, and G.W. Stevens. Dewater-ing behaviour of water treatment sludges associated with contaminatedsite remediation in antarctica. Chemical Engineering Science, 60:6835–6843, 2005.[30] M.D. Green. Charaterisation of suspensions in settling and compres-sion, PhD Thesis. Dept. of Chemical Engineering, University of Mel-bourne, Parkville, Victoria, Australia, 1997.[31] M.D. Green, M. Eberl, and K.A. Landman. Compressive yield stressof flocculated suspensions: Determined via experiment. American In-stitute of Chemical Engineers Journal, 42:2308–2318, 1996.101Bibliography[32] M.D. Green and D.V. Boger. Yielding of suspensions in compression.Ind. Eng. Chem. Research, 36:4984–4992, 1997.[33] M.D. Green, K.A. Landman, R.G. de Krester, and D.V. Boger. Pres-sure filtration technique for complete characterization of consolidatingsuspensions. Ind. Eng. Chem. Research, 37:4152–4156, 1998.[34] S.P. Usher, R.G. de Kretser, and P.J. Scales. Validation of a new filtra-tion technique for dewaterability characterization. American Instituteof Chemical Engineers Journal, 47:1561–1570, 2001.[35] C. Kugge, H. Bellander, and J. Daicic. Pressure filtration of cellulosefibres. Journal of Pulp and Paper Science, 31:95–100, 2005.[36] D. McDonald, K. Miles, and R. Amiri. The nature of the mechanicalpulping process. Pulp and Paper Canada, 105(8):27–32, 2004.[37] H. Vomhoff. On the in-plane permeability of water-saturated fibre webs.Nordic Pulp and Paper Research Journal, 15:200–210, 2000.[38] J.D. Lindsay and P.H. Brady. Studies of anisotropic permeability withapplications to water removal in fibrous webs - part 1. Tappi Journal,76(9):119–127, 1993.[39] G.W. Jackson and D.F. James. The permeability of fibrous porousmedia. The Canadian Journal of Chemical Engineering, 64:364–374,1986.[40] A. Koponen, D. Kandhai, E. Hellen, M. Alava, A. Hoekstra, M. Kataja,K. Niskanen, P. Sloot, and J. Timonen. Permeability of three-dimensional random fibre webs. Physical Review Letters, 80(4):716–719,1998.[41] Eberl,M and Landman,K.A. and Scales,P.J. Scale-up procedures andtest methods in filtration: a test case on kaolin plant data. Colloidsand Surfaces, 103:1–10, 1995.[42] J.L. Fowler and K.L. Hertel. Flow of gas through porous media. Journalof Applied Physics, 11:496–502, 1940.[43] J.D. Lindsay. The anisotropic permeability of paper. Tappi Journal,73(5):223–229, 1990.102[44] I. Howells, K.A. Landman, A. Panjkov, C. Sirakoff, and L.R. White.Time-dependent batch settling of flocculated suspensions. Appl. Math.Modelling, 14:77–86, 1990.[45] F.M. Auzerais, R. Jackson, W.B. Russel, and W.F. Murphy. The tran-sient settling of stable and flocculated dispersions. J. Fluid Mech.,221:613–639, 1990.[46] S.K. Teoh, Reginald B.H. Tan, and C. Tien. Correlation of c-p cell andfiltration test data using a new test cell. Separation and PurificationTechnology, 29:131–139, 2002.[47] K.A Landman, J.M. Stankovich, and L.R. White. Measurement of thefiltration diffusivity of a flocculated suspension. American Institute ofChemical Engineers Journal, 45(9):1875–1882, 1999.[48] P. Pettersson, T.S. Lundstrom, and T. Wikstrom. A method to measurethe permeability of dry fiber mats. Wood and Fiber Science, 38:417–426,2006.[49] C. Kugge. Consolidation and Structure of Paper Coating and FibreSystems, PhD Thesis. YKI, Ytkemiska Institutet AB, Institute forSurface Chemistry, Stockholm, Sweden, 2003.[50] J.D. Lindsay and P.H. Brady. Studies of anisotropic permeability withapplications to water removal in fibrous webs - part 2. Tappi Journal,76(11):167–174, 1993.[51] G. Carlsson, T. Lindstrom, and T. Floren. Permeability to water ofcompressed pulp fiber mats. Svensk Papperstidning, 86(12):R128–R134,1983.[52] S. Gharehkhani, E. Sadeghinezhad, S.N. Kazi, H. Yarmand,A. Badarudin, M.R. Safaei, and M.N.M. Zubir. Basic effects of pulprefining on fiber properties-a review. Carbohydrate Polymers, 115:785–803, 2015.[53] H.F. Jang, R. Amiri, R.S. Seth, and A. Karnis. Fiber characterizationusing confocal microscopy- collapse behaviour of mechanical pulp fibers.Tappi Journal, 79(4):203–210, 1996.103Appendix ACompressive Yield Stressand DewateringExperiments: Operator’sManualThe following procedure has been developed for collecting compressive yieldstress and dewatering experimental results using the experimental setupdescribed in Section 3.3 and 5.1. Following these steps carefully can ensurerepeatable data and safe operation of the equipment.The experimental equipment can be a dangerous apparatus.Care needs to be taken to prevent injury or damage to the equip-ment.A.1 Start-Up Procedure1. Open cooling water to the hydraulic pump by turning the valves onthe wall behind the system.2. Turn on the hydraulic pump to low pressure, the MTS controller, andthe PC. After 1 minute, turn the hydraulic pump from low to highpressure.3. On the MTS Controller, switch the interlock settings to Enabled toallow operation of the system. Set Communication to Local in order tocontrol the position of the permeable piston using the MTS Controller.4. On the MTS Controller, change the hydraulic pressure from Off toLow, then to High sequentially.5. Leave the MTS system running for 2-3 hours to allow the system toheat up. If trials are done before the system has properly heated104A.2. Experimental Procedureup, discrepancies in the data occur due to thermal expansion in thesystem.A.2 Experimental Procedure1. Open the LabVIEW Dynamic Dewatering Interface Version 2 pro-gram.2. Press the Run button.3. With the MTS controller Communications set to Local, use the Func-tion Generator Set Point to raise the piston to its highest elevation.The Sine functional form is best for this.4. Remove and fill the suspension chamber with the sample to be tested.A suspension of approximately 250 g and 0.03-0.04 (wt/wt) consis-tency works best.5. Place the suspension chamber back onto the load transducer platform,centering it as best as you can.6. In the LabVIEW program, enter the Initial Suspension Mass, InitialConsistency, and Piston Velocity values of the particular trial intothe corresponding cells. If conducting a compressive yield stress ex-periment, Piston Velocity values for various suspensions are found inSection A.3. If conducting a dewatering experiment, various piston ve-locities for the suspensions that have been done previously are found inSection A.4. Next, select the solid material of the suspension from thedrop down menu, cup size from the drop down menu, and define thetest’s initial condition using the slider (Top Surface or Set Solidity).Generally, to save time, we select the Set Solidity initial condition forcompressive yield stress experiments, which will move the piston toa height equivalent to approximately 0.04 (v/v) solidity before start-ing the defined rate. For dewatering experiments, we select the TopSurface initial condition. Finally, we fill in the remaining cells (EndSolidity, Max Force, Sample Frequency, Sample Number, and TimeOut) with the values found in Section A.3 or A.4, depending on if itsa compressive yield stress experiment or a dewatering experiment.7. Next we determine the initial height of the suspension. Using theMTS Controller in Local communication, carefully move the permeablepiston down.105A.3. Compressive Yield Stress: Specific Material Trial DetailsCAUTION: Take care as the piston is inserted into the suspensionchamber, watching for pinch points. Also, try to prevent binding thatcould occur due to unnecessary misalignment between the suspensionchamber and the permeable piston.Move the permeable piston downwards to slightly compress the sus-pension. Continue as the water flows through the permeable pistonuntil the floating nylon washer lies flush against the nut on the MTShydraulic actuator rod. Press the Collect button on the LabVIEWinterface to record the initial height of the suspension.8. Move the piston to its highest elevation. Hold the base of the sus-pension chamber as the permeable piston moves upwards to preventit from lifting.9. In the LabVIEW interface, press the Run button.10. As prompted, change the MTS controller communication to Remote.Press OK on the LabVIEW message box.11. Once the trial has completed, save the file, appending the extension.txt to save as a “.txt” file.12. As prompted, change the MTS controller communication to Local.This completes running an experimental trial.13. Remove the suspension chamber, and break up the compacted suspen-sion. Collect the suspension and filter it to obtain the dry mass of thesolid phase of the suspension (ms).A.3 Compressive Yield Stress: Specific MaterialTrial DetailsFrom experience, the following values are presented for collecting data for thevarious materials tested. The values in the tables provide guidelines, whichcan be changed with the discretion of the operator. Suspension preparationof 0.03-0.04 (wt/wt) consistency, and suspension masses of approximately250 g are preferred. For nylon glycerin trials, a mass of 7.5 g of nylon fibresis mixed into glycerin to obtain a 250 g suspension. The nylon fibres have ahigh moisture content, so a lower initial consistency will be determined oncethe solid phase mass has been filtered and weighed.CAUTION: Nylon fibres should only be handled with gloves, since theyare fine enough to enter the body through your skin.106A.4. Dewatering: Specific Material Trial DetailsTable A.1: Material specific values to be entered into the LabVIEW inter-face for compressive yield stress experiments.Suspension Piston Velocity End Solidity Max Force Frequency Sample Number Time Out[mm/s] [kN] [Hz] [s]Cellulose Fibres 0.001 0.9 6 1 2 60and WaterNylon and 0.02 0.9 6 1 2 60GlycerinTable A.2: Material specific values to be entered into the LabVIEW inter-face for dewatering experiments of cellulose fibre suspensions.Dewatering Rate End Solidity Max Force Frequency Sample Number Time Out[mm/s] [kN] [Hz] [s]0.005 0.9 6 10 2 600.01 0.9 6 10 2 600.1 0.9 6 100 10 150.25 0.7 6 100 10 150.5 0.7 6 100 10 151.5 0.7 6 100 10 155.0 0.7 6 100 10 1510.0 0.35 6 1000 50 2A.4 Dewatering: Specific Material Trial DetailsFrom experience, the following values are presented for collecting data for thevarious materials tested. The values in the tables provide guidelines, whichcan be changed with the discretion of the operator. Suspension preparationof 0.03-0.04 (wt/wt) consistency, and suspension masses of approximately250 g are preferred to provide reasonable and predictable behavior. Fornylon glycerin trials, a mass of 7.5 g of nylon fibres is mixed into glycerin toobtain a 250 g suspension. The nylon fibres have a high moisture content,so a lower initial consistency will be determined once the solid phase masshas been filtered and weighed.CAUTION: Nylon fibres should only be handled with gloves, since theyare fine enough to enter the body through your skin.107A.4. Dewatering: Specific Material Trial DetailsTable A.3: Material specific values to be entered into the LabVIEW inter-face for dewatering experiments of nylon glycerin suspensions.Dewatering Rate End Solidity Max Force Frequency Sample Number Time Out[mm/s] [kN] [Hz] [s]0.1 0.9 6 10 5 601.0 0.9 6 100 10 152.0 0.7 6 100 10 153.0 0.7 6 100 10 154.0 0.7 6 100 10 155.0 0.7 6 100 10 15108Appendix BPermeability Experiments:Operator’s ManualThe following procedure has been developed for collecting permeability ex-perimental results using the experimental setup described in Section 4.3.Following these steps carefully can ensure repeatable data and safe opera-tion of the equipment.The experimental equipment can be a dangerous apparatus.Care needs to be taken to prevent injury or damage to the equip-ment.NOTE: The following procedures use identifiers for the components ofthe setup, which can be found in the flow charts shown in Figure B.1 andFigure B.2. For example, valve 6 is indicated as V6 on the water flowdiagram in Figure B.1 and in the following procedures.B.1 Start-Up and Flush ProcedureThe following start up procedure assumes the system is empty of water,and all power and water supplies are turned off. The air vent line to thereservoir (V19), and the two low point drains (V4 and V5) are open. V20should be closed. The screen spacer and flange cap should be off, exposingthe suspension chamber.1. Open the non-potable water supply at the wall by turning the twovalves directing water to the system.2. Turn on the power bar on the left side of the back board.3. Turn on the power to the VFD. Navigate the menus of the VFD dis-play to reach the set point feature. See VFD Operation Procedure inSection B.4.4. Open V6 and fill the reservoir with non-potable water and close V1.Once the reservoir is full, close V6.109B.2. Experimental Procedure5. Set the VFD frequency to 20 Hz and press the green start button.Water will begin flowing out the low point drain V4. We run waterdirectly to the drain for a short time (5-10 seconds) to flush the pump’simpeller housing. Once the water is running clear to the drain, closeV4. Water should start circulating to the reservoir through the returnline. Fill the reservoir back up to the top with non-potable water byopening V6.6. The next step is a method of flushing the suspension chamber. Usinga small length of flexible 1/2” PVC tubing, we siphon water out of thechamber as it’s pumped in from the flow loop. The process requireshaving a bucket, or a mop bucket cart, for collecting the flush water.Insert one end of the flexible tubing through one of the flange holesand into the suspension chamber, allowing the other end of the tubeto hang down the side of the assembly. Close V5. With the pumpstill running, slowly open V1 to allow water to begin flowing towardsthe suspension chamber. Continue filling the suspension chamber untilthe water level is visible above the permeable piston. With the tubesubmerged in the rising liquid, siphon the water into the bucket. Oncethe flexible tube is successfully flowing water to the bucket, adjustV1 accordingly to stabilize the water level in the suspension chamber.Continue flowing water out of the system until it flows clear and thesuspension chamber is clean. It may require adding more non-potablewater to continue flushing the system.7. Open V4 and V5 to drain any remaining water in the system. Pressthe red stop button on the VFD once the flow stops circulating in thesystem.B.2 Experimental ProcedureThe following experimental procedure assumes the system has completed itsstart-up and flush procedure, and the system is in the state of the completionof this procedure.1. Close V1, V4, and V5.2. Open the union between V17 and V18. Using a small funnel, fill thewater reservoir to approximately 3/4 full with reverse osmosis (RO)water. Once filled, close the union.110B.2. Experimental Procedure3. Start the water pump by pressing the green button on the VFD.4. Open V1 temporarily until the RO water rises up to the surface of thepermeable piston. Close V1.5. Pour the sample into the suspension chamber. Stir the sample tohomogenize the suspension. Slowly open V1, diluting the suspensionto raise the level until near the top of the chamber.6. Place four of the specialty washers on the flange surface concentricto the flange holes with the filed notch facing inwards (thus the flagspointing outwards). The washers should be on alternating holes. En-sure the square rubber seal is present in the groove of the flange.7. Place the screen spacer on top of the flange. Place the remainingspecialty washers on the surface of the screen spacer concentric tothe fastener holes that were not given a washer on the flange surfacewith the filed notch facing inwards (thus the flags pointing outwards).Ensure the square rubber seal is present in the groove of the screenspacer.8. Place the 150 PSI flange cap on top of the screen spacer and insertthe eight 5/8”-13 fasteners through the holes. Ensure a washer ison the top and bottom of the flange joint, and thread on the nuts.Using a socket wrench and spanner, tighten the fasteners in the orderlabeled on the flange cap (a crossing pattern). Once all fasteners aretight, use the torque wrench to set the fasteners to 70 ft·lbs. Followthe tightening order on the flange cap. Tighten each fastener to 70ft·lbs. twice by repeating the tightening order to ensure all fastenersare torqued correctly.NOTE: Its important to set the torque wrench to 0 ft·lbs. once fin-ished using to not damage the tool.9. Attach the two brass hose connectors with the pressure port line onthe left male fitting and the flow port line in the center male fitting.Close V15, V9, and V14. Ensure V16 is directed towards the flow ratestand pipe and that V17 and V18 are open.10. Open V1 and slowly open V15 until water is trickling down the standpipe. Low flow rates are desired so aim on the conservative side.11. Close V19 and turn on the vacuum pump. Open V20.111B.2. Experimental Procedure12. As the vacuum develops in the system, the water will degas, loweringthe pump’s performance. Also with the decreasing inlet pressure tothe pump, the output pressure will follow. We wish to keep the waterin the flow loop at or above atmospheric pressure to reduce air leakageinto the system and damage to our dissolved oxygen sensor (electrolytesolution will get sucked from the probe in a vacuum). To do this, weneed to compensate with incrementally increasing the frequency on theVFD during degassing. A frequency of 41 Hz is usually appropriate tomaintain outlet pressure close to atmospheric during the lowest effi-ciency point during degassing. As the gas is removed from the water,the efficiency of the pump increases, resulting in a higher outlet pres-sure. Lower the frequency on the VFD incrementally as the efficiencyincreases. Continue lowering the frequency until you reach 20 Hz andthe outlet pressure is close to atmospheric.13. Once the water pump frequency reaches 20 Hz, open the Permeabil-ity Testing Apparatus LabVIEW interface. Press the run button tostart the program, which begins filling the data buffers. Run the sys-tem uninterrupted for 1 hour to fill the data buffer and to allow theexperimental system to stabilize its dissolved oxygen content and tem-perature of the fluid.14. Open V7, V11, V12, V8, and V13.15. Open V9 and V14 simultaneously and continue flushing water throughthe pressure transducer piping network until no bubbles are seen leav-ing V9 and V14 (this should take no longer than 10 seconds). Close V7and V12. Close V8 and V13. Collect a pressure transducer calibrationdata point using an artificial mass, temperature, and time entry.NOTE: The time entry determines how long the LabVIEW interfacetakes in an average calculation, so allow the system to stabilize for thetime you will be entering. For example, if 60 seconds is selected, letthe system sit undisturbed for this duration. This is a trial specificcalibration that ensures we have a correct pressure datum.16. Close V11. Next, open V7 and V12 simultaneously.17. Remove the prop bar from the 4-way control valve. Turn on the hy-draulic fluid pump by pressing the green button. Wait for the pressureto build in the system (5-20 seconds depending on what mechanicalload is currently set on the bed).112B.2. Experimental Procedure18. Open HV2, and slowly move the control valve forward to move thepermeable piston upwards to the desired height (or bed load).NOTE: If a long transition is required, an appropriate speed is 1 mmper 5 seconds. This piston velocity allows a controllable mechanicalload rise as the bed compresses, and prevents dangerous overloadingof the system.19. Once the desired load is obtained, release the control valve and closeHV2.20. Stop the hydraulic pump by pressing the red button.21. Place the prop bar against the 4-way control valve fixing it in a forwardposition.22. Once the “slope criteria” has been satisfied, close V17 and start atimer. Ensure V22 is open to prevent pressurization of the stand pipe.Close V18. Once a sufficient mass of water has been collected, stopthe timer and direct the three way valve, V16, directly to the tank.Close V22.23. Open the union between V17 and V18. Crack open V17 slowly topressurize the stand pipe back to atmospheric pressure. Empty thecollected water into a torn beaker and weigh the sample. Enter themass of the sample, duration of collection, and temperature of thesample into the corresponding boxes in the LabVIEW interface.24. Press the Collect button to store the data point.25. Reassemble the union. Slowly crack open V22 to depressurize the flowrate stand pipe. Open V22 fully once depressurization is complete.Open V18 and redirect flow through V16 to the flow rate stand pipe.26. A data point collection is complete. To collect the next data point,return to Step 17. Repeat until the desired number of data pointshave been collected.27. Once the desired number of data points have been collected, save thetrial’s data points by pressing the Save button in the LabVIEW inter-face. Append .txt to the file name to save as a “.txt” file.113B.3. Fibre Collection, Flush, and Shutdown ProcedureB.3 Fibre Collection, Flush, and ShutdownProcedureThe following procedure assumes you have just completed step 25 of theexperimental procedure.1. Shut off the vacuum pump and close V20.2. Slowly crack open V19 to return the pressure of the reservoir to atmo-spheric pressure.3. Remove the prop bar from the control valve. Open HV2. Pull backon the control valve with the hydraulic pump NOT running. Thisunloads the compressed suspension.4. Open V4, V5, and V11 to drain the system.5. Once the return line from the pump to the reservoir stops flowing, stopthe water pump by pressing the red button on the VFD.6. Inspect the outlet tube from suspension chamber for a water column.If water is still residing on top of the suspension, pump the hydrauliccontrol valve, with the hydraulic pump NOT running, downwardsto unload the bed, allowing the fluid to pass through, or open V15slightly.7. Disconnect the pressure port line and flow port line from the 150 PSIflange cap. Loosen the fasteners incrementally and in the tighteningorder on the flange cap to not overload the remaining fasteners holdingthe joint. Remove the flange cap. Collect the washers on top of thescreen spacer.8. If water is present in the passages of the screen spacer, siphon thewater out into a bucket using the flexible 1/8” PVC tube provided.Lift off the screen spacer exposing the compressed suspension.9. Collect the compact suspension for mass determination. Best practicefor this is to re-dilute and filter the suspension. Be sure to clean the topscreen on the screen spacer and the walls of the suspension chamberto obtain all fibres of the trial.10. Turn on the hydraulic pump. Move the permeable piston to the bot-tom of its stroke. Turn off the hydraulic pump.114B.4. VFD Operation Procedure11. Close V4, V5, and V1, and refill the reservoir with non-potable water.Start the water pump by pressing the green button on the VFD. Slowlyopen V1, allowing flow towards the suspension chamber. Flush thesuspension chamber again to remove any remaining fibres by siphoningwater into a bucket, or mop bucket cart. Once the reservoir is emptied,open V4 and V5, and stop the water pump by pressing the red buttonon the VFD. Using a towel, hand dry the interior of the suspensionchamber to reduce rusting.12. Turn off the water pump by switching the breaker on the VFD enclo-sure. Turn off the sensors power supplies by turning off the power baron the left vertical support. Close the two water valves on the supplyline on the wall above the MTS computer.B.4 VFD Operation ProcedureThe following procedure guides in how to arrive at the VFD menu that isresponsible for setting the frequency at which the pump will operate. It isassumed that the VFD was initially off.1. Turn on the VFD by switching the breaker to on.2. Press the Back/Reset button. A small arrow on the screen next toMON will begin to flash.3. Use the up arrow to move the flashing arrow to REF.4. Press the OK button5. The current frequency the pump is set to will be displayed.6. Press the OK button and the hundredth digit will begin flashing. Usethe up and down arrows to change the value. Use the left and rightarrows to change the digit to be modified. The VFD will automaticallyadjust for the newly selected frequency.7. Press the OK button to confirm the frequency.115B.4.VFDOperationProcedurePTo DrainTo DrainV1V2V3V4V5V6V8V9 V14V13V10V11Water PumpWater Reservoir SuspensionDOFlow Rate Stand PipeNon-Potable  Water SupplyVacuum Pump PDO- Water Line- Non-Potable Water Line- Vacuum Line- Pressure Gauge (0-200 psig)- Dissolved Oxygen Sensor- Union- Valve- 3-Way Valve- Needle Valve- Differential Pressure Transducer (0-5 psid)- Differential Pressure Transducer (0-150 psid)V7 V12V15V16V17V18V19V20To DrainHeat ExchangerV21V22Figure B.1: Permeability experimental system’s water flow diagram.116B.4.VFDOperationProcedure- Hydraulic  Line- Needle Valve- Pressure Gauge (0-3000 psig)Hydraulic Pump PHydraulic Cylinder4 Way Control ValveHV1HV2HV3P- Gauge Pressure Transducer (0-2000 psig)- Pressure Relief (1000 psig)SuspensionFigure B.2: Permeability experimental system’s hydraulic fluid flow diagram.117Appendix CPTV AnalysisA set of MATLAB scripts has been developed for stepping through a devel-oped algorithm for obtaining the velocity profiles of the solid phase duringdewatering from frames captured during the experiment. The major stepsare outlined in the flow diagram shown in Figure C.1.We will now further expand upon this by proceeding through the stepshighlighted. Inputted into the analysis are the Dewatering LabVIEW in-terface file that was outputted and saved for the dewatering event and theframes of the event. From the LabVIEW file, we can extract the height ver-sus time trend (hˆ(tˆ) versus tˆ) of the permeable piston. From this we can alsodetermine the initial height of the suspension (h0) in mm. From the film, wefirst extract the individual frames, filter, digitize, and invert (change blackto white) them. Next, we identify the piston within the first frame of thefootage. This is done by identifying the pixel in which the tracer marker onthe piston is located. This marker on the piston is then followed from frameto frame to track the piston position for the event. We can find the initialframe (F0) upon which the piston begins moving (since the footage is nottriggered by the piston movement automatically). With the initial framefound, and the position of the piston known, we next manually identify thelocation within the frame where the base of the suspension is located. Fromthe base pixel and the piston pixel, we can now define the original heightof the suspension (h0) in pixels. Taking our two h0 values, we can find aconversion coefficient between mm and pixels.As was mentioned above, we manually had to identify the base of thesuspension in the first frame (F0). Instead of doing this manually for all theframes of the dewatering event, we used our hˆ(tˆ) versus tˆ trend, along withour tracked piston location and conversion coefficient to calculate the pixellocation of the bottom of the suspension for the successive frames. At thispoint we know the location of the piston and the location of the base for theduration of the dewatering. This provides us our physical search area fortracer particles to be tracked. From our initial frame and from the durationof the MTS data, we also have the frame bounds (the region in which wecan analyze the movement).118Appendix C. PTV AnalysisDewatering LabVIEW Interface Output FileFilm of Dewatering Event 𝐡 (  𝐭) 𝐯𝐬.  𝐭Find & Track PistonFind h0 [mm]Coefficient [mm/pixel]Find Initial Frame, F0Find h0 [pixel]Locate BasePhysical BoundsFrame Boundsn = 1Extract FramesFrame n  (A) Frame n+1  (B)Identify Particles Identify ParticlesPair ParticlesCatalog Particlesn = n + 1Particle StreamlinesParticle VelocitiesAveraged VelocityFigure C.1: PTV Analysis Flow Diagram.119Appendix C. PTV AnalysisAt this point we enter our particle tracking loop. The process involvescomparison of particle positions within two successive frames. We start withour first frame (F0) as our Frame A. We take the second frame as Frame B. Inboth frames we identify the tracer particles which correspond to bright whitedots in the digitized images. We locate the centroid of the particles (x and ycoordinates), as well as their pixel area. The next step is to pair the particlesfrom Frame A to Frame B. This is necessary to see where the particle movedto. A searching criteria that compares particle centroids and particle sizesfrom Frame A to Frame B is implemented that pairs the particles. Equatingcentroid values between frames is done within a certain tolerance, because, ofcourse, the particles have moved, thus changing the centroid values, however,the significant frame rate allows very small changes in centroids to occurbetween frames. We then catalog the positions of particles in a matrixwith rows corresponding to a unique particle and columns representing theframes of the event. The entries are then the particles’ vertical positionsin each frame (a similar matrix is developed for the horizontal positions,but since the dewatering happens in one dimension, this matrix is of littleuse). With the particles’ movements tracked and cataloged for the first setof Frames A and B, the loop advances to the next pair of frames (Frame Bfrom the first loop becomes Frame A, and the third frame becomes FrameB). This looping continues until all the frames have been analyzed. At thispoint, we will have a matrix of unique particle positions within the framesof the dewatering event. Not all particles may be present throughout all theframes (particle moving out of sight) and some particles may appear partway through the analysis (particle coming into sight).At this point we can develop streamlines of the particle movements dur-ing the dewatering, from which we can determine their velocities. We com-bine streamline plots from multiple trials (at the same dewatering rate) toaccount for experimental variation and increase the number of particles wehave tracked. Combining the streamline plots is done by phasing the vari-ous streamlines such that the hˆ(tˆ) versus tˆ plots are aligned for the variousexperiments.From the final streamline plot, we can find average velocities of the par-ticles within a range of elevations for a given frame. Once this has been donefor the entire set of frames analyzed, we have arrived at our averaged velocityas a function of height and time. These experimentally determined velocityprofiles then can be plotted as contours, or compared to profiles developedby the base and extended models to validate the dewatering models.120Appendix DInformation on SuspensionsIn an attempt to validate the base and extended model, and to begin cata-loging dewatering behaviours of different cellulose fibre suspensions, varioussuspensions were investigated in this project. The series of experimentalsuspensions can be found in Table 3.2. In this Appendix, background onthe series of suspensions is provided, along with preparation steps, and phys-ical parameter results obtained through both Fibre Quality Analyzer (FQA)trials and Canadian Standard Freeness (CSF) experiments.D.1 Background on Cellulose Fibre SuspensionsGenerally speaking, cellulose fibres are hollow tubelike particles with lowpermeable walls. However, many variables present in the pulp manufactur-ing operations can impact the suspension’s fibres. Size, distribution, andmechanical properties are just a few examples of variables that can be sub-stantially different between various pulp suspensions.We wish to begin cataloging various cellulose fibre suspensions to dis-cover how the factors in the production of pulp impact dewatering perfor-mance. A small number of investigations are pursued in this project. Theyinclude:• Softwood versus Hardwood Fibres (Series 1 compared to 9)• Difference in Pulping Process (Series 1 and 9 compared to 5)• Impact of Low Consistency Refining (Series 6, 7, and 8 compared to5)• Impact of Chemical Additives (Series 2, 3, and 4 compared to 1)Following are discussions of the select factors in the manufacturing ofpulp that are investigated for dewatering behaviour differences.121D.1. Background on Cellulose Fibre SuspensionsD.1.1 Softwood versus Hardwood Fibres (Series 1Compared to 9)Species of trees fall into one of two categories: conifers (softwoods) or broad-leafed (hardwoods). Softwoods include such species as pine, spruce andhemlock, which have leaves that are either needle-like, linear, awl-shaped,or scale-like. Softwoods are often referred to as evergreens. Hardwoodsinclude such species as oak, elm, and poplar, and have broad leaves thatcome in various shapes [26]. These trees can often be identified as thosewhose leaves change colors and drop in autumn. Both categories of trees areused in the pulp and paper industry, and there are several general differencesseen between the two groups that may impact the dewatering of suspensionsmade from each group of fibres.Generally speaking, softwoods (Series 1) provide longer and wider fi-bres than hardwoods (Series 9). This promotes strength in sheets of soft-wood pulp, and limits hardwood pulps to applications where strength andtear properties are not as vital. Hardwoods, thus, are generally used asfiller pulps [36]. Softwood fibres, however, tend to have thicker fibre wallthickness when compared to hardwood, meaning softwoods have poorer col-lapsibility. This promotes hardwoods’ application of filler pulp due to theirability to brighten and raise opacity of a sheet, which are properties of ahighly collapsible fibre wall.A northern bleached softwood Kraft pulp (NBSK) is used for Series 1,and a bleached hardwood Kraft pulp (BHK) is used for Series 9.D.1.2 Difference in Pulping Process (Series 1 and 9Compared to 5)Two major processes are used in the pulp industry for extracting fibresfrom the raw wood material. The methodologies behind both are the same:to separate the fibres from the lignin fibre matrix of the wood structure.This can be achieved by mechanical, thermal, or chemical means [11]. Twocommon processes, which will be discussed, are Kraft pulping (a chemicalpulping technique) and thermo-mechanical pulping (a mechanical pulpingtechnique).The methodology behind chemical pulping is to dissolve the lignin matrixthat surrounds the fibres, leaving them behind and intact. Two chemicalmethods are used in industry: using an alkaline (Kraft process) or using anacid (sulfite process) [11]. The Kraft process (Series 1 and 9) involves cook-ing the wood chips in a solution of sodium hydroxide and sodium sulphide.122D.1. Background on Cellulose Fibre SuspensionsThe process results in strong, long, and flexible fibres with good strengthproperties, and is readily used with both soft and hardwood species [11].The mechanical pulping methodology is to crack or break apart the fibrelignin matrix. The process does not separate the fibres from the matrix ascleanly as chemical pulping, leaving lignin on the fibres’ surfaces. Less flexi-ble, shorter fibres are produced with mechanical pulping along with a higherfraction of fines (small cellulose particles) [36]. Although not as ideal of fibre,the yield is substantially higher. Several methods exist in mechanical pulp-ing. The oldest and simplest technique is the groundwood technique whichinvolves pressing a block of wood lengthwise against a grinding stone. A sec-ond, more recent technique, involves mechanically shredding and defiberingchips of wood between rotating discs with metal bars on the surfaces creat-ing grooves. This technique is referred to as refiner mechanical pulping [11].Refiner mechanical pulping results in longer fibres compared to groundwood.A branch of refiner pulping, where wood chips are exposed to high temper-ature steam to soften the lignin fibre matrix, is thermo-mechanical pulping(TMP), Series 5. The softening of the wood chips, from the high tempera-tures, results in higher energy costs, but results in longer fibre lengths whichcan increase strength and density of the sheet [36]. All forms of mechani-cal pulping are generally limited to softwood due to the process requiringwood chips with relatively long fibres. This is because an inherent productof mechanical pulping is cutting of the fibres, therefore, sufficient length ofinitial fibres are needed to provide sufficient bonding, forming, and strengthproperties of the final pulp.D.1.3 Impact of Low Consistency Refining (Series 6, 7, and8 Compared to 5)Low consistency refining is a process that is used in both chemical andmechanical pulping processes. In both processes, the goal of refining isto develop, or modify, the fibres in order to optimize the final product.Refining of TMP (Series 6, 7, and 8) is of particular interest due to itsimportance in developing the less ideal fibres, which improves formationand printability properties by increasing flexibility and collapsibility of thefibres [36]. Ideally, this would be done without loosing length since lengthof the fibres correlates to the strength of the formed sheet.Collapsibility and flexibility of the the fibre is improved through variouseffects of the refining process, including internal and external fibrillation,fines formation, fibre straightening, and fracturing in the fibre wall [52, 53].Fibre shortening is also inherently an effect of refining, which is not ideal.123D.1. Background on Cellulose Fibre SuspensionsCollapsibility improves with increasing levels of refining through both meanfibre wall and fibre thickness reduction [53]. The metric used for definingthe extent of low consistency refining for this project is Specific RefiningEnergy (SRE), which is defined asSRE =Pt − PnF C[kWh/t] . (D.1)Pt, Pn, F , and C are the refiner load, idle power, flow and consistency respec-tively. This investigation will provide insight into how varying collapsibilityimpacts dewatering properties of cellulose fibre suspensions.D.1.4 Impact of Chemical Additives (Series 2, 3, and 4Compared to 1)Significant research and development into chemical additives for improvingpulp properties and machine performance have been done by various com-panies. Many of these chemicals are designed to alter the dewatering of thefibre suspension. Three chemical packages, provided by AkzoNobel, thathave been developed for modifying the flocculation state of fibre suspen-sions, will be investigated to see how they impact the dewatering behavior.The first chemical of interest is EKA FIX 41 polyamine (Series 2). Thisadditive has a low molecular weight, and a highly positive charge. Thechemical sticks to the negatively charged fibre walls, neutralizing the chargebetween fibres, which reduces flocculation strength within the suspension.This additive promotes flocculation of fines together so higher retention isachieved.The second chemical investigated is EKA PL 1510, which is a linearcationic polyacrylamide (Series 3). This is a lower positively charged, highmolecular weight ionic polymer. The additive aids in flocculating fibres,which has negative impacts on formation.The final chemical trial considered (Series 4) is a two chemical packageconsisting of EKA PL 1510 followed by EKA NP 320 colloidal silica solution.EKA NP 320 is an negatively charged microparticle. This combinationresults in stronger flocculants than EKA PL 1510 alone, however, the flocsize is reduced.This investigation will provide insight into how varying flocculation statesimpact dewatering properties of cellulose fibre suspensions.124D.2. Preparation of SuspensionsD.2 Preparation of SuspensionsD.2.1 Series 1 and 9 PreparationFibres for Series 1 (NBSK) and 9 (BHK) suspensions used in this projectcame in the form of dried pulp sheets which needed to be re-pulped. To beginthis process, we soaked large torn sections of the pulp sheet (approximately25 g) in reverse osmosis (RO) water (approximately 2 L) for a minimum of30 minutes. Once the pulp had soaked for this amount of time, we tore thelarge sections of pulp in the soaking water down to “chunks” approximately5 cm x 5 cm. The sample was next poured into a bench top re-pulper.We ran the re-pulper for 15000 revolutions to obtain our suspension. Thiswas repeated multiple times to obtain the appropriate amount of suspensionnecessary for the various trials.The re-pulping process resulted in a 0.0125 (wt/wt) consistency suspen-sion. It has been found that initial consistencies of 0.03-0.04 (wt/wt) provideacceptable fibre masses for experiments, so we must concentrate the suspen-sions before they are ready to be used in the experimental systems. Thisis done using a tap aspirator, vacuum flask with a filtration funnel, and anylon mesh screen. In order to avoid pulling fibres through the nylon mesh,we sparingly provide the vacuum and pour substantial amounts of suspen-sion onto the nylon mesh. A thick filter cake develops, which will catch thesmall particles from passing through the nylon mesh. Once prepared, thesuspension is kept in a cold room to slow degradation. Vigorous mixing ofthe suspension is performed before sampling for trials.D.2.2 Series 5, 6, 7, and 8 PreparationThe TMP used in this project came in the form of dried, shredded stock. Thefirst step involved mixing the pulp back into suspension. This was done byadding the shredded pulp to a hot bath of tap water (approximately 60◦C)and continuously mixing for an hour. Hot water is used in an attempt tobreak up the shieves. The mixing suspension consistency was 0.025 (wt/wt).This mixing was done in the repulper that is attached to the low consistencyrefiner pilot plant at the UBC Pulp and Paper Centre. A tank sample wascollected and taken as the base TMP suspension (Series 5).A refiner trial was performed with the remaining fibre suspension in therepulper. A single plate, fixed flow, fixed net power, multiple pass trialwith varying gap size was performed. Sampling of the recirculating flow wascollected immediately after the refiner. The level of refining experienced bythe samples is defined by the number of passes through the refiner (Series125D.2. Preparation of SuspensionsTable D.1: Details of the recirculating TMP low consistency refiner trial.Due to interest in the cumulative SRE values, the third pass values areincluded.Series Passes Consistency BEL RPM Flow Gap Pgross Pnet SEL SRE Sum SRE[%] [km/rev] [L/min] [mm] [kW] [kW] [J/m] [kWh/t] [kWh/t]6 1 2.98 2.74 1579 257 0.613 91.7 25.6 0.36 55.8 55.87 2 2.95 2.74 1572 256 0.675 91.3 25.5 0.35 56.0 111.8- 3 2.93 2.74 1570 253 0.702 91.3 25.7 0.36 57.9 169.78 4 2.91 2.74 1573 247 0.563 92.0 25.6 0.36 59.5 229.16, 7, and 8). The resulting low consistency refiner trial values are shown inTable D.1.Attempts were made on Series 5 through 8 to reduce the fines content.This was done by rinsing the suspensions over a mesh with 0.149 mm holesize. The suspensions were manually mixed while being sprayed. Oncesufficient rinsing was complete, the suspension was prepared to the desiredconsistency of 0.03-0.04 (wt/wt).D.2.3 Series 2, 3, and 4 PreparationNBSK suspensions were used for the investigation of the effects of chemicaladditives on dewatering. Suspensions of NBSK were first prepared usingthe procedure outlined in Section D.2.1. Once the suspension of 0.0125(wt/wt) consistency had been prepared, the suspension was diluted furtherto 0.005 (wt/wt) consistency prior to the chemicals being added. This lowconsistency is necessary to allow the chemicals to attach to the fibre surfaceseffectively.EKA FIX 41 (Series 2) and EKA PL 1510 (Series 3) chemical packageshave the same procedure for adding to the fibre suspension. Based on thedesired concentration and suspension mass, the appropriate mass of chemicalis added slowly to a stirring sample of 0.005 (wt/wt) consistency NBSK.The sample is stirred for an additional 30 seconds after the addition of thechemicals. At this point the suspension is ready to be dewatered usingthe same technique outlined above for the chemical pulps to our desiredconsistency of 0.03-0.04 (wt/wt). Loss of chemicals during this dewateringstep was not of concern since the chemicals adhere to the solid phase.EKA PL 1510 plus EKA NP 320 (Series 4) suspensions were preparedas follows. Equal amounts of each chemical were to be added. Based ondesired concentration and suspension mass, the appropriate mass of each126D.3. Physical Parameters of Suspensionschemical was measured. First, EKA PL 1510 was added to the stirringsample of 0.005 (wt/wt) consistency chemical pulp, and was stirred for anadditional 30 seconds as done for the isolated EKA PL 1510 trial. After 30seconds, with the suspension still stirring, the EKA NP 320 chemical wasadded. Again, an additional 30 seconds of mixing was allowed, followed byconcentrating of the suspension to the desired 0.03-0.04 (wt/wt) consistency.Again, if the procedure was followed correctly, the chemical additives wouldnot be lost in the concentration efforts.D.2.4 Series 10 PreparationNylon fibres (Series 10) came in the form of dry, shieves of fibres. Theywere mixed into suspension with reverse osmosis (RO) water for perme-ability measurements at our target consistency of 0.03-0.04 (wt/wt). Forcompressive yield stress determination and dewatering experimental trials,the nylon fibres were mixed into high purity glycerin at the target consis-tency of 0.03-0.04 (wt/wt), in order to exaggerate the effects of varyingdewatering rates. Care needs to be taken with glycerin suspensions due tothe fluid’s highly sensitive viscosity behavior with varying temperature andmoisture contents.D.3 Physical Parameters of SuspensionsThe reverse osmosis (RO) water used in the dewatering and compressiveyield stress experiments was assumed to be 1 mPa·s, whereas the temper-ature was collected and the viscosity was calculated for the various perme-ability trials. The fluid temperature was always within 20-25◦C, so viscositywas always around 1 mPa·s as well. The average viscosity of the glycerinused in Series 10 dewatering and compressive yield stress experiments wasfound to be 850 mPa·s.To further supplement discussions of dewatering behavior and the ma-terial parameters, select physical properties of the various suspensions weredetermined. To gain various suspension fibre properties, we use an OpTestFibre Quality Analyzer (www.optest.com). The Fibre Quality Analyzer(FQA) is a device that measures geometric properties of length, mean width,curl, kink, fines content, and can determine a value of coarseness (lineardensity). The device images a very dilute flow of fibres and statisticallydetermines these parameters. The standard 16065 test protocol was used.Another parameter of interest is each suspension’s Canadian StandardFreeness (CSF) value, which is a measure of drainability. High CSF values127D.3. Physical Parameters of SuspensionsTable D.2: Physical parameters obtained from CSF and FQA experiments.FQA experiments were not performed on chemically treated suspensions(Series 2, 3, and 4) to prevent damaging the FQA flow cell. For the Series10 trials, the length weighted value (Length LW) is simply the specifiedfibre length, and the width is a determined equivalent diameter from the 1.5denier value (a linear density, units of g/9000 m) with an assumed densityof nylon being 1.15 g/cm3.Series ρs CSF Fine Percentage LW Length LW Mean Width Coarseness[g/cm3] [ml] [%] [mm] [µm] [mg/m]1 1.5 703.4 2.95 2.57 26.67 0.1432 1.5 703.3 - - - -3 1.5 743.63 - - - -4 1.5 759.07 - - - -5 1.5 718.7 6.21 1.64 36.67 0.3666 1.5 680.77 6.45 1.63 36.63 0.3357 1.5 580.6 7.24 1.59 6.43 0.3328 1.5 389.83 9.11 1.50 35.60 0.3169 1.5 611.17 5.46 0.79 20.13 0.09710 1.15 - - 3.05 13.58 -refer to a suspension that easily drains. A detailed procedure for this testcan be found in the Technical Association of the Pulp and Paper Industry(TAPPI) Standard T 227 (www.tappi.org). CSF values were collected forall the cellulose suspensions (Series 1 through 9), however, not for Series 10.The physical parameters determined from the FQA and CSF experimentsare shown in Table D.2.As discussed in Section D.1, we can see some expected conclusions inregards to the fibre size of the various samples. As expected, we can seethat the NBSK suspension (Series 1) had longer and wider fibres comparedto the BHK (Series 9). By considering the coarseness values, a linear densityof the fibre, and the mean width of the two samples, we can see that, forsome ideal hollow cylindrical fibre, Series 9 also had a thinner average cellwall (1.08 µm) compared to Series 1 (1.19 µm). This also is expected, asdiscussed in Section D.1.1.When comparing the TMP (Series 5) and NBSK (Series 1) results, wecan see the TMP fibres were found to be shorter. This is an expected trendwhen comparing the different pulping processes. The TMP having a largerwidth may also be related to the pulping process. As discussed in SectionD.1.2, the fibre separation from the wood matrix is a much cruder process128D.3. Physical Parameters of Suspensionsthat cannot fully separate the fibres from the surrounding lignin. Potentially,this residual lignin leads to a higher mean width. As discussed in SectionD.1.2, the TMP fibres have lower flexibility than the NBSK, which can beseen in the higher coarseness value determined. The FQA results also showthat, despite efforts to remove fines from the suspension, higher levels arestill seen with the TMP. This is another expected observation as a higherlevel of fines is characteristic of TMP when compared to NBSK.As discussed in Section D.1.3, we would expect to see higher fines forhigher levels of refining of TMP. The FQA results show this as well withincreased fines with Series 6, 7, and 8. We also notice that with higherrefining, the mean width and length are both reducing. This potentially iswhere the increased fines are coming from: cutting the fibres and breakingaway the cell wall. We see from the decreasing coarseness values that fibrewall thickness is also reducing with increased refining, as expected. Allthe results from the FQA for Series 5 through 8 support higher levels offlexibility and collapsibility with increasing low consistency refining.CSF values are discussed in Chapter 7 when we look at quantifying asuspension’s ability to dewater.129

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