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Measurement of fine particle deposition from flowing suspensions Chen, Charley Y. 1993

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MEASUREMENT OF FINE PARTICLE DEPOSITION FROMFLOWING SUSPENSIONSByCHARLEY Y. CHENB Sc., MSc. South China University of TechnologyA THESIS SUBMITIEED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESCHEMICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1993© CHARLEY Y. CHEN, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department ofChemical EngineeringThe University of British ColumbiaVancouver, CanadaNov. 15, 1993DateDE-6 (2/88)ABSTRACTA large number of investigators have taken on the task of formulating themechanisms of the particle deposition process. Correspondingly little has been done,either theoretically or experimentally, on the process of particle attachment.Bowen and Epstein’s work (1, 16), a systematic investigation of particledeposition and release from and to aqueous suspensions in fi.illy developed laminarflow, was extended to turbulent flows in the present experimental study. Theexperimental investigation was carried out using uniform, spherical, silica particles(0.881 p.m diameter) and a rectangular channel (10 mm x 12 mm) constructed fromplate glass cemented to a stainless steel supporting structure. The plate glass wascoated with a plastic to achieve suitable surface conditions. The measurements ofdeposition and release of negatively charged silica spheres onto and from a positivelycharged plastic substrate was greatly facilitated by employing a direct microscopictechnique and an image analysis system.Under the conditions of the present experiments, it was found that the rate ofrelease from the channel surface was not observable. Thus, the declining rate ofaccumulation with time observed in most experimental runs could only be attributed tothe declining deposition rate.The measured initial rates of deposition were found to be in good agreementwith those predicted by theories of Bowen (1) and Epstein (10, 62) for laminar andturbulent flows, respectively. The initial deposition rate was observed to be influenced11by the suspension flow rate and the magnitude of the positive wall zeta-potential. Itwas found that the concentration of deposited particles reached an asymptotic value forthose runs which were performed long enough. The particle surface coverage neverexceeded 3.5%.111Table of ContentsABSTRACT iiList of Tables viiiList of Figures ixACKNOWLEDGMENT xi1 INTRODUCTION 12 PERTINENT PRIOR WORK 42.1 THEORY OF PARTICLE DEPOSITION 42.1.1 Particle Deposition Model Based on Particle Transport 62.1.2 Particle Attachment SurfaceForces Sticking Probability 92.1.3 Particle Deposition Models Based on Combined ParticleTransport and Attachment TurbulentFlowCase LaminarFlowCase 112.1.4 Particle Re-entrainment 142.2 EXPERIMENTAL STUDIES OF PARTICLE DEPOSITION 163 EXPERIMENT 193.1 INTRODUCTION 193.2 PARTICLES 19iv3.2.1 Materials 203.2.2 Production of Uniform Silica Spheres 213.2.3 Preparation ofDisperse Silica Sols 243.3 EXPERIMENTAL CHAMEL 263.3.1 Construction 263.3.2 Coating 283.4 MEASUREMENT OF PARTICLE DEPOSITION 313.4.1 Introduction 313.4.2 Apparatus 313.4.2.1 Test System 313.4.2.2 Instrumentation 343.4.3 Image Analyzing System 353.4.3.1 Apparatus 353.4.3.2 Algorithm for Image Analysis 443.4.4 Experimental Procedure 393.4.4.1 Accumulation Measurements 403.4.4.2 Release Measurements 433.4.4.3 Analysis of Deposition Data 443.5 MEASUREMENT OF ZETA POTENTIAL 444 RESULTS AND DISCUSSION 464.1 INTRODUCTION 46V4.2 PARTICLE RELEASE 464.3 PARTICLE DEPOSITION 514.3.1 Initial Deposition Rates 514.3.1.1 Effect ofFlow Rate on Initial Deposition Rate 544.3.1.2 Effect of Double Layer Thickness onInitial Deposition Rate 614.3.2 Deposition With Time 635 CONCLUSIONS AND RECOMMENDATIONS 72NOMENCLATURE 75REFERENCES 79A THEORETICAL CONSIDERATIONS ONPARTICLE DEPOSITION 88A. 1 LAMINAR FLOWS 88A.2 SUMMARY OF MAJOR THEORIES ON TURBULENTPARTICLE TRANSPORT 91B EXPERIMENTAL RESULTS 92B.1 CALIBRATIONS 92B. 1.1 Conductivity ofNaCl Solutions 92B.1.2 Flow Rate 92B. 1.3 Electrophoresis Apparatus 92B. 1.3.1 Interelectrode Distance 92B. 1.3.2 Eyepiece Graticule 96B.2 SAMPLE CALCULATIONS 97viB.2. 1 Double Layer Thickness, 1/ic 97B.2.2 Particle a-potential 100B.2.3 Wall a-potential 104B.2.4 Initial Deposition Rates 105B.2,4.1 LaminarFlowCase 105B.2.4.2 Turbulent Flow Case 107B.3 ERRORS 111B .3.1 Errors in Measurement 111B. 3.2 Errors in Electrophoresis Measurements 111B.3 .3. Errors in Electro-osmosis Measurement 114B.4 EXPERIMENTAL DATA 117viiList of TablesTable 2.1 Particle Deposition Studies in Vertical Flow Systems 17Table 2.2 Particle Deposition in Horizontal Flow Systems 18Table 4.1 Initial Deposition Rate 58Table A. 1 Summary of Major Theories on the Deposition ofParticles from Turbulent Flows 91Table B. 1 Interelectrode Distances 96Table B.2 E versus y0 103viiiList of Figures3.1 Reaction bottle for preparation of silica particles 223.2 Silica particles 233.3 Ultra-filtration system 253.4 Rectangular experimental channel 273.5 Plastic coating apparatus 303.6 Schematic diagram of experimental system 323.7 Algorithm for image analysis 363.8 Block diagram of frame to frame differentiation 384.1 Complete accumulation curves for Runs 11-5and 111-2 showing release measurements 484.2 Complete accumulation curves for Run IV-1showing release measurements 504.3 Experimental results. Series I 524.4 Deposition concentration versus time. Run 111-7 534.5 Initial deposition rate versus Reynolds Number 554.6 Comparison of the measured and predicted initialdeposition rate. Series II 564.7 Comparison of the measured and predicted initialdeposition rate. Series ifi 574.8 Deposition concentration versus time. Run 11-3 594.9 Effect of double layer thickness on initial deposition rate 624.10 Effect of suspension flow rate on deposition 66ix4.11 Effect of counterion concentration on deposition 674.12 Effect of counterion concentration on particleand wall a-potentials 694.13 Comparison of deposition results obtained for apositively charged substrate with those measured for anegatively charged substrate 70A. 1 A rectangular duct 88B. 1 NaC1 concentration versus measured conductivity 93B.2 Rotameter reading versus flow rate 94B.3 Deposition curve. Run 11-3 121B.4 Deposition curve. Run 11-4 122B.5 Deposition curve. Run 11-5 123B.6 Deposition curve. Run 11-7 124B.7 Deposition curve. Run 11-8 125B.8 Deposition curve. Run 11-9 126B.9 Deposition curve. Run 11-10 127B. 10 Deposition curve. Run 111-3 128B. 11 Deposition curve. Run 111-4 129B. 12 Deposition curve. Run 111-5 130B.13 Deposition curve. Run 111-8 131B.14 Deposition curve. Run 111-10 132xACKNOWLEDGMENTSI would like to express my sincere gratitude to Dr. B.D. Bowen and Dr. N.Epstein for their enthusiastic supervision throughout the course of this work and forthat I am more grateful than I can adequately express.I am indebted to Dr. F. Vasak for his excellent work in experimental setup andcomputer programming.Help of the faculty, staff and fellow students at the Department of ChemicalEngineering at the University ofBritish Columbia is appreciated.Financial support from the Natural Sciences and Engineering Research Councilof Canada and a Scholarship from T.K. Lee are gratefully acknowledged.Finally, I thank you the most, my wife Nancy, for the love and understandingthat make you the most important person in my life, and my little daughter Aanja whomissed all that time we could have spent together.xChapter]. Introduction 1CHAPTER 1INTRODUCTIONThe deposition of fine particles, suspended in a flowing fluid, onto a foreignsurface is experienced in a wide range of industrial equipment. Applications involvingdeposition in channels include the particulate fouling of heat exchangers, membraneseparators, and nuclear reactors. It is important therefore to understand thefundamental mechanisms of the deposition process and to be able to predict particledeposition rates in order to obtain significant improvements in the effective operationof such equipment.The deposition of particles from a flowing suspension onto a channel wall isgenerally a rather complex process. Although many investigations on particledeposition have been conducted, the results obtained generally represent only theoverall accumulation process which, in fact, may be the net outcome of the twocompeting processes of deposition and release.The deposition process is generally assumed to consist of two separate steps.The first step is particle transport, in which a particle in the bulk suspension istransferred to the interface region. The second step is attachment, whereby a particle inthe interface region becomes attached to the collector surface.Bowen and Epstein (1, 16) conducted a systematic investigation of particledeposition and release from and to aqueous suspensions in fully developed laminar flowChapter 1. Introduction 2using a radioactive tracer technique. In their study, the role played by surfaceinteraction forces in the attachment step of the particle deposition process wasthoroughly investigated both theoretically and experimentally.The primary objective of the present work is to extend Bowen and Epstein’sexperimental investigation to turbulent flow. The effects of a number of experimentalparameters, such as suspension flow rate and double layer thickness, on the initialparticle deposition rate in turbulent flow are therefore investigated in the present study.Particle deposition and release in fhlly developed laminar and transitional flows are alsostudied as a comparison with previous work.Vasak et al. (27) developed a direct microscopic technique in which thedeposition surface was scanned continuously by an optical microscope and the imagewas then processed by an image analysis system. The primary advantage of thistechnique is that it allowed the simultaneous measurement of the rate of particledeposition and release. The present study takes advantage of this technique and severalof the experimental features introduced by previous workers (1, 27, 30, 32), such as thepreparation of silica spheres and the plastic coating of the channel surface.This thesis is organized in the following manner:• Chapter 2 reviews the important prior theoretical and experimentalinvestigations on particle deposition and release.• Chapter 3 describes the experimental equipment and protocols used in thepresent study.Chapter 1. Introduction 3• Chapter 4 presents and discusses the results obtained from the experimentswith reference to the theories of particle deposition developed by Bowen(1) and Epstein (10), respectively.• Chapter 5 forms the conclusions of this thesis and makes recommendationsfor further work.Chapter 2. Pertinent Prior Work 4CHAPTER 2PERTINENT PRIOR WORK2.1 THEORY OF PARTICLE DEPOSITIONThe deposition of particles suspended in a fluid onto a channel surface is oneof the main modes of fouling of heat transfer surfaces. Epstein (2) has identified theprocesses which govern the rate and extent of fouling as transport of particles to theheat transfer surface, attachment of particles at the surface and re-entrainment ofparticles from the surface. Thus, the rate of transport and attachment together controlthe gross rate of deposition of particles onto a surface.A large number of investigators have taken on the task of formulating themechanisms of particle deposition processes, and their theories have been recentlysummarized in a comprehensive review paper by Papavergos and Hedley (3), andelsewhere (2, 4, 8, 9, 33-56). Several of these theories, which are pertinent to thepresent investigation, are discussed below.In studying the deposition of fine particles from a turbulent particle suspensionflow to a channel wall, most theoretical treatments, e.g. Friedlander & Johnstone (5),Lin et al. (6), Davies (7), and Beal (8), adopt the point of view of a conventionalthree-layer flow structure starting from the wall - the viscous sublayer, the bufferzone, and the turbulent core - from studies of single-phase, fhlly developed turbulentflow. In the turbulent core and the buffer zone, particles are assumed to be laterallyChapter 2. Pertinent Prior Work 5transported by eddy diffusion in the same way as scalar quantities, such as heat ordissolved species, are assumed to be transported. Particles reaching the edge of theviscous sublayer as a result of this transport are assumed to coast towards the wallacross the sublayer to form deposits.The flux of particles from a turbulent particle suspension flow towards asurface over which the stream is flowing is given by:dy y.bor in dimensionless form:[1]vCb v v dy Y=bV./Vwhere 4 is the deposition flux, DB the Brownian diffi.isivity of particles, E, the particleeddy difibsivity, C the mean local particle concentration, y the distance normal tomedian plane of channel, which is specified by y = b and y = -b; y = 0 is the medianplane, b the half-thickness of the channel, v the wall friction velocity of the fluid, Cbthe bulk particle concentration, v the kinematic viscosity of fluid, Vd thedimensionless particle deposition velocity, y = yv/v, and C CICb.The particle eddy diffusivity, es,, is often set equal to or directly proportional tothe fluid eddy diffusivity of momentum, em, in Equation [1], which represents theeffects of fluid turbulence on the transport of particles in the direction normal to thewall. Obtained mainly from empirical correlations and following the classical view ofturbulent flow, knowledge of e1,, therefore, is the basis of most of the theories ofparticle deposition.Chapter 2. Pertinent Prior Work 62.1.1 Particle Deposition Model Based on Particle TransportMost hydrodynamic theories of particle deposition, summarized in Papavergosand Hedley’s review paper (3), are really theories of particle transport (2). Table 1from (3) is reproduced as Appendix A.2 (with reference numbers and symbols fromthe original paper). In Papavergos and Hedley’s paper, these theories were dividedinto two groups, those based on classical concepts of turbulence and eddy diffusion(the first seven in Table 1) and those based on stochastic (probabilistic) approachessuch as random walk (9) or turbulent burst (50) theory (the last four in Table 1). In arecent study, Turner (95) has determined particle transport velocities from publisheddata for aqueous suspensions and compared these to predictions from several theoriesof particle transport.Berger and Hau (17) have proposed the following empirical equation forsolute mass transfer in duct flow over the range Re = 8000 - 200,000 and Sc = 1000 -6000:Sh = kmde = 0.0165 Re°86 [2]D8where Sh is the Sherwood number, km the mass transfer coefficient, de the equivalentdiameter of the duct, DB the Brownian diffusivity of particles, Re the Reynoldsnumber, and Sc the Schmidt number.Chapter 2. Pertinent Prior Work 72.1.2 Particle AttachmentFor convenience, it is usually assumed that the deposition process takes placein two separate steps (1, 2):i) Transport, in which particles in the bulk suspension are transferred tothe interface region.ii) Attachment/Adhesion, in which particles in the interface region becomeattracted to the wall surface.While theoretically at least, transport phenomena considerations can explainand predict the mechanisms in the particle transport step, they cannot determinewhether or not the particle adheres to the wall. Only a consideration of surface forcescan explain the attachment step (1, 2, 41, 93-95). Surface ForcesA ffindamental approach to the particle attachment process in a colloidalsystem is to take into account the actual surface forces that exist between a colloidalparticle and a wall. The attachment or adhesion step in the particle deposition processis controlled by the various interaction forces which arise at small distances ofseparation between the particle and the wall. The knowledge of the interactionbetween a spherical particle and a plane surface is thus of importance in predicting andcontrolling the attachment process in particle deposition onto channel walls. Thenature of these forces and their effects on particle deposition were demonstrated inChapter 2. Pertinent Prior Work 8detail in Bowens work (1) and elsewhere (2, 4, 93, 94). The three important physicalinteraction forces in aqueous suspensions are (1):i) London-van der Waals forces, which arise from the interaction offluctuating dipole moments generated by the motion of electrons around thenuclei of neutral atoms in close proximity to each other.ii) Electrical double-layer interaction forces, which arise from theelectrical charges commonly acquired by particles or surfaces immersed in anelectrolyte, and the compensating difihise layer of counter-ions in the fluidadjacent to these surfaces.iii) Hydrodynamic interaction forces, which arise from the increasedresistance to movement experienced by a particle near a foreign surface.In a single phase fluid, the London-van der Waals forces between particles andbetween a particle and a surface are usually attractive.The double layer interaction arises from the overlap of the diffuse layers ofcharge that are in the solution immediately adjacent to a charged surface. Thepotential energy arising from the overlap of the diffuse layers of charge is repulsive ifthe surface and the particle have like charges, and is attractive if they have unlikecharges. If the electrical double layer forces are attractive, there will be no energybarrier to attachment and the deposition rate will be essentially equal to the rate atwhich particles are transported to the surface. If the double layer potential is repulsiveand sufficiently large, there will result a large energy barrier which must be overcomebefore the particles can actually become attached to the wall. Many investigators havedeveloped approximate theories for analyzing the role played by surface interactions inthe particle attachment process (1, 11-16, 93, 94).Chapter 2. Pertinent Prior Work Sticking ProbabilityThe particle attachment process can be formulated statistically in terms of S,the probability that a particle which reaches the wall sticks to it, or alternatively thefraction of particles reaching the wall which actually stay there (before any reentrainment) (2). The sticking probability has been widely interpreted as a measure ofthe force of adhesion of particles to a surface (8, 63, 96), where it is assumed thatadhesion occurs through the formation of a physico-chemical bond between theparticles and the wall. Parkins (96) proposed that particles adhered to the surfacethrough the formation of chemical bonds; thus, S was postulated to have an Arrheniusdependence on the surface temperature. Other factors that were assumed to influencethe sticking probability included fluid velocity and particle size.By utilizing a more comprehensive equation to define the initial depositionrate, Watkinson and Epstein (63) applied the concept of “sticking probability”, whichwas expressed asAdhesive bond between particle & surfaceSShear stress on particle at surfaceBeal (8) has also considered the effects of sticking probability in hisinvestigation of particle transport in turbulent flow.Chapter 2. Pertinent Prior Work 102.1.3 Particle Deposition Models Based on Combined Particle Transport andAttachment2.1.3.1 Turbulent Flow CaseEpstein (10) proposed a theoretical model to explain both the observedincrease and the observed decrease of the initial rate of heat transfer surface foulingwith increasing fluid velocity. His theory took into account both the transport andsurface-attachment mechanisms of particulate fouling. In considering also chemicalreaction and corrosion fouling, Epstein gives the expression for 4, the deposition fluxof the key reactant, solute or suspended particles as[3]km krC’where Cb is the bulk concentration of key reactant, solute or suspended particles, C,the concentration of this species adjacent to the surface, km the mass transfercoefficient, and k the surface-rate, integration or attachment constant.In applying Equation [3] to particulate fouling, Epstein proposed that krepresents a sticking or surface-attachment rate constant and that, followingRuckenstein and Prieve (12), n 1 for Brownian particles.In the case of turbulent liquid flow, Epstein derived the following equations:k______v*m—11.8Sc — k1Chapter 2. Pertinent Prior Work 11krcCtsand consequentlykr=1 [5]k2vwhere v is the friction velocity, Sc the Schmidt number of suspended particles, k1 andk2 are, for fixed fluid properties and fixed T, constants defined by Equations [4] and[5], respectively, E is the activation energy, R the universal gas constant, and T, thesurface temperature. In Equation [5], the chemical kinetics of the surface reactionprocess are accounted for by the Arrhenius term, and the hydrodynamic forces areassumed to be lumped into the shear stress, t, acting on the surface. From Equations[3], [4], and [5] with n = 1, 4 is given asb [6]k1v;’ +k2vAccording to Epstein, if is the critical value of v at which 4 is amaximum at constant temperature T,, thenk= k1 [712 2(v) Laminar Flow CaseBowen (1, 11, 16) developed an approximate theory for analyzing the roleplayed by surface interactions in laminar flow particle deposition. He applied theapproximation developed by Ruckenstein and Prieve (12) and others (13, 14) forparticle filtration to the analogous problem of submicron particle deposition in aChapter 2. Pertinent Prior Work 12parallel-plate channel under laminar flow conditions. In his theory, particle depositionin the presence of London-van der Waals, electrical double-layer, and hydrodynamicinteraction forces was shown to be equivalent to convective mass transfer in the bulkof the fluid and a first-order reaction at the channel surface.According to Bowen, for a parallel-plate channel, when interaction forces areincluded, the particle concentration C is given by the equation of convective diflhsionin a potential energy field iji =1i_X-’1v =_FD+1 [8]2 b2)môx ‘L ‘ kT’jwhere x is the distance in the direction of fluid flow parallel to the channel walls, y thedistance normal to these walls measured from the center plane, b the half width of theparallel-plate channel, vm the average velocity of the fluid, D the particle diffusivity, kthe Boltzmann constant, and T the absolute temperature. Equation [8] is subject tothe boundary conditionsC(O,y)=C0, [9][3)]= C’(x,O) = 0, [10]andC(x,b)0 [11]where C0 is the homogeneous suspension concentration at the channel inlet and theprime denotes differentiation with respect to y.In order to uncouple the above problem, Bowen divided the flow channel intotwo regions:Chapter 2. Pertinent Prior Work 13i) a wall region where the convective terms can be neglected, andii) a core region where the potential energy and hydrodynamic interactionterms can be neglected.In the case of large Peclet numbers, Bowen took 0 = C/C0 as a fhnction of y,the dimensionless longitudinal distance (if Pe = 4VmbfD, is the Peclet number, y =(1/Pe)(8xJ3b), where D, is the constant particle diffusion coefficient outside the regionof hydrodynamic interaction), and of , = h/b where h = b-y. Using the conditionsdJ2b << << 1, the convective diffusion equation for the core region becomes80 o22l—=—— [12]8y 8E,2with the single-wall boundary conditions9(o,)=1, 0(y,oc)=1, [13]and0(y, 0) + (1IK)0’(y, 0) = 0 [14]where the prime now denotes differentiation with respect to E, K is the dimensionlessreaction rate constant (K = bK1 fD,), K1 the surface reaction rate constant, andKDwhere ö is the thickness of the wall region, c = DX/D is the Stokes’ law correctionfactor given by Brenner (101), and y is the overall interaction energy due to van derWaals and electrical double layer forces.Chapter 2. Pertinent Prior Work 14Bowen extended Leveque’s method to provide a general solution for Equations[12]- [14] for all K. The dimensionless particle deposition rate, 4)’, is thus given, bytransforming Equation [12] to an ordinary differential equation, as(2/9v4)’=O’(y O)= “ ‘‘ [15]f()+(lIK)(2/9y)where4)’— DCQEquation [15] has the same form as Epstein’s Equation [6], i.e.4) = driving concentration differenceresistance due to + resistance due tomass transfer from bulk attachment at the wallWhen the dimensionless reaction rate constant K = , the infinite sink wall conditionresults. The dimensionle particle deposition rate, which corresponds to mass transfercontrol, is then given by[16]f()2.1.4 Particle Re-entrainmentCompared to the attention that has been given to the formulation of depositionrate equations in recent years, fewer researchers (42, 69, 71, 72, 73, 77, 93, 94, 97-99) have attempted to speculate about the nature of the forces which remove particlesfrom a surface. Most models adopted the Kern and Seaton (97) concept where theChapter 2. Pertinent Prior Work 15shear stress due to the velocity gradient within the boundary layer was the onlyimportant quantity to cause particle re-entrainment. Epstein (98) has questionedwhether a particle would ever get deposited if it is subject to re-entrainment forces asit approaches the surface.Based on the microscopic studies of the structure of turbulent boundary layers(99), Cleaver and Yates (72,73) suggested that deposited particles could be reentrained by the up-draft generated during periods when bursts of fluid are ejectedfrom the wall region, while particle deposition occurred during the gentler sweepingprocess between bursts. Their evaluation of deposition and re-entrainment rates isbased on a tentative picture of bursting events within the sublayer.Hubbe (69, 77) has studied the mechanisms of particle re-entrainment from aflat surface exposed to flow, taking into consideration the Cleaver and Yates (73)model in which a lifting force is assumed due to stagnation-point flow in the viscoussublayer of a turbulent field. Hubbe proposed that, depending on the size and shape ofthe particles and the direction of the dominant hydrodynamic force (normal or parallelto the wall), a particle may either slide, roll or be lifted away from its initial depositionsite during re-entrainment. Hubbe’s analysis shows that the component of thehydrodynamic force acting parallel to the wall is larger than the normal forcesconsidered by Cleaver and others and that the actual detachment mechanism stronglydepends on the geometry of the system.Chapter 2. Pertinent Prior Work 16In a recent review paper (94), Visser suggested that the mechanism of reentrainment, in most cases, can be explained in terms of coiloid chemistry and fluiddynamics, and discussed both aspects in detail.2.2 EXPERIMENTAL STUDIES OF PARTICLE DEPOSITIONParticle deposition onto collectors or channel walls has been studied by manyinvestigators (1, 18-32). The first experimental data on deposition onto a collectorwith a well-defined geometry under well-defined hydrodynamic conditions werereported by Marshall and Kitchener (30) and by Hull and Kitchener (32). OnlyBowen and Epstein (16) conducted an experimental investigation of fine particledeposition in laminar flow as an explicit ftmnction of the surface interaction forces in achannel. Tables 2.1 and 2.2 summarize some of the many experimental studies onparticle deposition.In a recent study, Vasak et al. (27) made measurements of fine particledeposition and re-entrainment from and to flowing suspensions in a rectangularchannel using a microscopic technique. In their work, the microscopic image of thedeposited particles was transferred by means of a TV camera and a frame-grabbingboard to a personal computer. They developed specialized software for therecognition and processing of these images, which enabled them to obtain timedependent information about the number of particles on the wall of the channel at anyinstant, as well as their rates of deposition and re-entrainment. The details of thisimage analysis system, which is also employed in the present study, will be describedin Chapter 3, Section 3.4.Table2.1.ParticleDepositionStudiesinVerticalFlowSystemsParticleDuctI.D. orInvestigator(s)ParticleDensityDimensionsWallRe(x10)Measurementsize(inn)(kg.m3)(m)CoatingMethodForney&Spielman24.56500.0254Petroleum3.52-43.5Microscopic(18)jellySchwendiman&2-44200.00254-Siliconeoil3-20MicroscopicPostma(3)0.0138Wells&0.175-51000-0.038 1-50-Chamberlain(19)1180Watkinson&12.8-17.3-0.0087-50pressuredropEpstein(63)Fanner(3)100-260-0.0127---Liu&Agarwal(20)1.4-21-0.0127x-10,50Fluorometric1.020Govanetal.(21)110,250,26000.032-Imageanalysis550Newsonetal.(22)0.2-0.011-11RadioactiveMatsumotoetal.210-29302500, 87000.02-8Optical(23)Dabros &vande1.030.025x0.05-20-1600MicroscopicVen(31)discBowen&Epstein0.402,21800.25x0.1x2-vp/styrene;70-270Radioactive(16)0.649,0.60.085formvarTable2.2.ParticleDepositioninHorizontalFlowSystemsParticleDuctI.D.orInvestigator(s)ParticlesizeDensityDimensionsWallRe(x10)Measurement(pm)(kg.m3)(m)CoatingMethodMarshall etal.(30)0.45-2-vp/styrene-MicroscopicHull &Kitchener0.3080.22disc2-vp/styreneMicroscopic(32)Alexanderetal.(24)250.0472-77000-Pitot tubes295000Namie&Ueda(3)131-11870.06x0.01-McCoy(3)413-6170.305x-0.0254Yoder&Silvennan0.26,0.810600.02630000--(3)100000Montgomery(25)0.44-2.160.152--MicroscopicHahnetal.(26)0.041-0.2-0.0975RoughTurbulentFluorometricsurfaceVasaketal.(27)1.0521800.0lx0.0122-vpfstyrene1000-20000ImageanalysisRashidaetal.(28)88-11001000-0.2x0.15-2500-Imageanalysis25007500Shimadaetal.(29)0.01-0.04-0.006-1000-Condensation2000nucleuscounterChapter 3. Experiment 19CHAPTER 3EXPERIMENT3.1 INTRODUCTIONThere are various methods to measure the rate of particle deposition. Thesemethods are described in more detail in Bowen’s review (1) and elsewhere (18-32, 27,63-71). Bowen and Epstein (1,16) conducted an experimental study, based onpreviously developed theory (11), using a radioactive technique to investigate thedeposition and re-entrainment of micrometer-size silica spheres from and to aqueoussuspensions in laminar flow. Vasak et al. (27) developed a more direct microscopictechnique which allowed the simultaneous measurement of the rate of particledeposition and release to and from the wall of a channel containing a colloidal silicaparticle suspension. They performed some initial trial experiments which illustratedthat the image analysis system does indeed work. The objective of the present work isto extend Bowen and Epstein’s investigation to turbulent flow by employing this directimage analysis technique in order to obtain a better understanding of the deposition offine particles in turbulent flow.3.2 PARTICLESTo simplify the experimental investigation of particle deposition, a modelcolloidal suspension system of monodisperse, micrometer-size, spherical particles wasrequired. In this size range, several organic and inorganic materials can be prepared asChapter 3. Experiment 20uniform spheres (78-85, 87, 88). The colloidal system used in this study weremonodisperse, negatively-charged, silica spheres suspended in distilled water. Theamorphous silica spheres were produced, following the procedures outlined by Stöberet al. (84) and Tan et al. (78), by the chemical reaction of tetra-esters of silicic acid(tetra-alkyl silicates) with water. Because water and all alkyl silicates are immiscible,the reaction is carried out in a mutual solvent. The hydrolysis is catalyzed by acid orbase solutions. In this study, tetra-ethyl orthosilicate (TEOS) was used with npropanol as the solvent and dissolved ammonia as the catalyzing base. The reactionsequence is as follows (1):i) hydrolysis of ester to silicic acidSi(0C2H5)+ 4H20 —> Si(OH)4+ 4C2H50Hii) dehydration of silicic acid to form amorphous silica (particle or gel)Si(OH)4—* Si02 .j. +2H0In the presence of hydroxyl ion catalyst and an excess of water, both the hydrolysis anddehydration reactions are fast and complete (1).3.2.1 MaterialsN-propanol (AnalaR grade, BDH) was used as solvent. Tetraethyl orthosilicate(reagent grade, ICN - K&K Laboratories) was distilled under vacuum in thefractionating column (Penn State Column, Ace Glass Inc.) before use in theexperiments to ensure maximum sphericity and monodispersity as reported by Bowen(1). Water was distilled just prior to use. Anhydrous ammonia (99.9%, UnionCarbide) was used as the catalyst /stabilizer.Chapter 3. Experiment 213.2.2 Production of Uniform Silica SpheresSilica particles were produced by reacting tetraethyl orthosilicate with water inalcohol solutions saturated with ammonia. The procedures discussed below weresimilar to those employed by Bowen (1).For these experiments, the volume ratio of TEOS:water:alcohol was 1:5:25, aratio found by Bowen (1) to yield optimal particle sphericity and uniformity for theTEOS, water, and n-propanol system. The system was prepared by using 3 mL ofTEOS, 15 mL of distilled water, and 75 mL of n-propanol. Measured volumes of npropanol and freshly distilled water were pipetted into a 1 20-mL glass reaction bottle(Figure 3.1) with a ground glass cap and an insulated jacket. An ethylene glycol-watermixture was circulated through the jacket from an refrigerated constant temperaturebath (NESLAB Endocal RTE-9) to maintain the reaction temperature at 0.0 ± 0.1°C inorder to produce particles of about 1.0 p.m diameter (78). The contents of the reactionbottle were agitated continuously by a magnetic stirrer. After thermal equilibrium wasreached, anhydrous ammonia gas from a cylinder was bubbled into the water-alcoholmixture through a glass fit until saturation was achieved, indicated by no fi.irthervolume increase. Bowen (1) suggested that maximal particle sphericity and uniformityof size was obtained at maximum ammonia concentration. The TEOS, which had beenmaintained at the same temperature, was then pipetted into the reaction bottle and thecap was clamped down tightly to prevent the escape of ammonia.After an invisible hydrolytic reaction forming silicic acid, the mixture suddenlybecame opalescent signif’ing the onset of silica precipitation. The precipitate appearedChapter 3. Experiment 22Figure 3.1 Reaction bottle for preparation of silica particles5-10 minutes after adding the tetra-alkyl silicate. After this initial phase, the transitionto a turbid white suspension occurred within a few more minutes.According to the recommendations of Bowen (1) and others (78, 84), thereaction time was set to 3 hours in order to achieve a complete reaction. Clean glasscapillaries were used to transfer droplets of the suspension sample to carbon-coatedelectron microscope carrier grids. The samples were allowed to dry and then electronmicrographs of the particles were taken at several random locations on the grid using aHitachi S-570 scanning electronic microscope.The average size and the standard deviation of the silica particles weredetermined from the photographs, along with those of a calibration standard (54864lines/in., Ladd Research Industries), by manually measuring about 150 particles fromseveral random micrographs. From the magnification factor given on the micrographs,the true size of the particles was found to be 0.881 ± 0.023 j.tm. From Bowen’s work,the density of amorphous silica was 2.18 ± 0.04 glcm3, determined from settling ratemeasurements. An electron micrograph of the silica particles is shown in Figure 3.2.Ammonia gasinInletconstant temp.bathChapter 3. Experiment 23Figure 3.2 Silica particles.Chapter 3. Experiment 243.2.3 Preparation of Disperse Silica SolsA well-dispersed suspension of silica particles in water with little carry-over ofcontaminants from the production solution was prepared by filtration, following theprocedures developed by Bowen (1) and Tan et al. (78).An ultra-filtration system was employed in the washing process. The apparatusis shown in Figure 3.3. A 0.45 .tm membrane filter paper was positioned in the ultrafiltration device. To eliminate most of the ammonia, the particles were first removedfrom the production solution by absolute filtration and the wet filter cake resuspendedin fresh n-propanol using a magnetic stirrer and a homogenizer (#125E, Brinkmann).The contents were then transferred to the ultra-filtration unit through the top opening.Then, all the screws were tightened. The pressurized tank was first filled with propanol,and nitrogen gas from a cylinder was allowed into the tank so that a constant flow rateof propanol through the ultrafiltration device could be maintained. After all thepropanol was driven into the ultra-filtration device, and when a sufficient N2 space hadbeen created, the nitrogen pressure was relieved. Then the tank was filled with distilledwater and the distilled water was driven through the ultrafiltration device by thepressure exerted by the nitrogen gas. Once the distilled water flow had started, theconductivity of the filtrate from the ultra-filtration device was measured at half hourintervals. All contaminants on the silica particles were considered to be removed whenthe conductivity of the filtrate was about 1 jimho/cm, about the same value as distilledwater (89).Chapter 3. Experiment 25CompressuredN2 ganPressurized tankPropanol or waterinletSampling forconductivityCollectingcontainerFigure 3.3 Ultra-filtration systemAfter washing, the still wet filter cake was added to distilled water to obtain,upon dispersion, suspensions whose initial conductivities were in the range of 1-2mho/cm. Two batches of particle mother suspensions were prepared havingconcentrations of 2.3 48 xl and 3 .288x 1 particles/cm3,obtained gravimetrically bytaking the density of amorphous silica to be 2.18 g/cm3. The particle suspensions forthe different deposition runs were prepared by diluting known volumes of mothersuspension with additional distilled water. The concentrations of these final suspensionswere checked by using a gravimetric method on a small volume sample.Pressure reliefvalveUltra-filtrationdeviceChapter 3. Experiment 263.3 EXPERIMENTAL CHANNELA rectangular experimental channel, on which particle deposition is measured,was employed in this study. The deposition surface of the channel was constructedfrom plate glass in order to obtain the required smoothness and to allow microscopicexamination of the deposition process. The walls of the experimental channel werecoated on the inside with a plastic to obtain suitable double-layer potentials underconditions where the suspension remains stably dispersed. Details of the constructionof the experimental channel and the coating procedures are described below.3.3.1 ConstructionThe side wall and end supports of the experimental channel were milled from asingle piece of stainless steel. The deposition surface consisted of two 20 x 600 mmsheets of 1.8 mm thick plate glass which were cemented to the stainless steelsupporting structure with an epoxide adhesive (Araldite Gi, Industrial Formulators)(Vasak Ct al., 57). Before assembling, the plate glass sheets were first cleaned withchromic acid (conc. sulfuric acid saturated with sodium dichromate) at 50 °C, rinsedwith distilled water, thoroughly dried for 4 hours, and then the adhesive was applied.After the resin was cured for 24 hours, the channel was cleaned thoroughly to removeany contaminants which may have entered during the gluing process. When assembled,the channel was 10 mm by 12 mm in cross-section and 594 mm long (see Figure 3.4).The experimental channel was prepared for plastic coating by first cleaning it inchromic acid at 50 °C for 15 minutes. Then, to eliminate all traces of chromic acidChapter 3. Experiment 27600.9 mmr_______________________25.4 mmAlA-Amm12.0 mmTAglass plateFigure 3.4 Rectangular experimental channelChapter 3. Experiment 28remaining after the cleaning process, distilled water was used to continuously flush thechannel for 12 hours at a flush rate of 40 mL/min. According to Bowen (1), acomplete removal of all traces of contamination could be guaranteed in this way.3.3.2 CoatingThe plate glass surface will show a highly negative charge over the range of pHconditions employed in the present experiments. Thus, it is necessary to coat the glasssurface to obtain a positive double layer potential, thereby ensuring maximum rates ofparticle deposition. Based on the deposition experiments of other investigators (1, 30,32), a cationic copolymer of 80% 2-vinyl pyridine and 20% styrene (2VP/S), whichbears a slightly positive charge under neutral pH conditions, was chosen in this study.The co-polymer 2VP/S, not available commercially, was prepared by solutionpolymerization following the procedure described by Bowen (1) which is outlinedbelow.In the first step of the preparation procedure, both the 2-vinyl pyridine (97%,b.p. 79-82°C/29mm, Aldrich Chemical) and styrene (99+%, Aldrich Chemical)monomers which contained high boiling point inhibitors added to extend their shelf-life,were purified under vacuum in the distillation unit described earlier (Section 3.2.1). 4mL methanol (reagent grade, BDH), 4 mL freshly distilled styrene and 15 mL freshlydistilled 2-vinyl pyridine were injected into a 100-mL test tube. The test tube wasequipped with a sealable screw cap and was tightly wrapped with aluminum foil toexclude light. After it was deoxygenated in a pyrogallol solution (reagent grade,Fisher) and dried in a U-tube containing silica gel, nitrogen gas was bubbled throughChapter 3. Experiment 29the mixture via a glass capillary for one hour. At this juncture, 0.2 g of benzoylperoxide (reagent grade, BDH) was added to the mixture to initiate the polymerizationreaction. With a further six hours of nitrogen gas bubbling, the viscosity of the solutionhad increased to the point where it was no longer possible to pass nitrogen through it.After removing the glass capillary, the test tube was tightly sealed and stored in a darklocation for two days at room temperature.After carefully breaking away the glass test tube, the polymer mass wasdissolved in 250 mL of chloroform (AnalaR, BDH). Petroleum ether (reagent grade,BDH) was used to purifj the plastic by reprecipitating it twice. In each case, thepolymer solution was placed in a separation funnel and added dropwise to 1600 mL ofpetroleum ether in a well stirred 2000 mL beaker. A glass rod was used tocontinuously remove the white fibrous polymer precipitate as it formed. The finalprecipitate was washed in 400 mL of fresh petroleum ether and then dried undervacuum for one day.According to Bowen (1), a 2W/S solution containing 2.0% by weight of plasticshould be used in the coating process in order to obtain a plastic film of optimalthickness and having a uniformly smooth surface.A modified version of the equipment employed by Bowen (1) was used to coatthe experimental channel with plastic (see Figure 3.5). Before the coating process, thechannel was rinsed with distilled water to thoroughly remove all traces of residualchromic acid, soaked with methanol for one hour, and then dried for four hours. Thechannel was connected to a glass storage tank through a 1 mm diameter glass capillary.Chapter 3. Experiment 30A solution of plastic dissolved in chloroform was forced up into the channel bypressurizing the glass storage tank with compressed air. To ensure that the velocityprofile was fully-developed and that the particle concentration was uniform at the startof the deposition section, only the exit section of the experimental channel (starting at45 equivalent diameters downstream) was coated. The channel was filled until the levelof the solution reached the pre-marked position. Then the compressed air was valvedoff, the valve on the storage tank was opened to the atmosphere, and the plasticsolution was drained slowly back to the storage tank. After coating, the channel wasleft in situ to dry for a half hour before being used for a deposition experiment.The average thickness of the film produced in this method was about 20 nm asreported by Bowen (1).Test sectionPressurizedair Control valveCollectorFigure 3.5 Plastic coating apparatusChapter 3. Experiment 313.4 MEASUREMENT OF PARTICLE DEPOSITION3.4.1 IntroductionThis study employed a direct image analysis technique, developed by Vasak etal. (57), to simultaneously investigate the rates of particle deposition and release to andfrom the walls of a channel containing a flowing colloidal particle suspension. Theexperimental apparatus, based on the design by Vasak et al. (57), to measure bothdeposition and release rates is described in the following section.3.4.2 Apparatus3.4.2.1 Test SystemA detailed schematic of the system is shown in Figure 3.6. The experimentalsystem consists of a single closed flow ioop with a suspension storage tank, theexperimental channel, a stainless steel gear pump with variable speed motor andcontroller, and a rotameter. Teflon fittings and Teflon tubing, a material on which thesilica particles showed little tendency to deposit (1), were used to connect componentsof the system.The suspension storage tank was a round glass container, with a capacity of 1.8liters of suspension. The exit hole is located in the center of a spherical depression inC.l)C) CD C) C 0 CD CD CD CDCDQ. DC, 0 C) 0-v 0= 0 D0 C-o-UC,0o-oDOCD0Chapter 3. Experiment 33the bottom of the tank, which assured complete drainage of suspension. A port locatedin the top of the container was used to add make-up particles and chemicals required toadjust the electrolyte and pH conditions of the suspension. During a depositionexperiment, the port was closed using a 3-way stopcock.The experimental channel was connected to the ioop by Teflon fittings andtubing, and was supported by a specially designed stand. The deposition and release ofsilica particles were measured by means of a microscope focused on the lower innersurface of the glass wall 5 mm downstream from the start of the coated section (i.e.about 50 equivalent diameters downstream from the channel entrance).Loop circulation was provided by a stainless steel gear pump (PacificScientific). The pump was driven by a 1/3 h.p., 90 v.d.c. electric motor. The speed ofthe motor was controlled using a variable transformer-regulator (Penta Power). Themaximum flow rate attainable using this arrangement was 3.5 U.S. gal/mm.The additional lines shown in Figure 3.6 allowed for the draining and flushingof the channel prior to its removal at the end of an experimental run and for the fillingof a fresh channel after its installation. Their use will be discussed in more detail in theProcedure section (3.4.4). The fill solution was stored in a 2 L glass container. Theflush tank was filled with distilled water, stored in two 25 L polyethylene containerslocated at floor level. The particle suspension was drained to a 25 L drain tank.Chapter 3. Experiment 343.4.2.2 InstrumentationThe concentration of particles deposited on the wall of the experimental channelwas measured using the image analysis system developed by Vasak et at. (57). Thesystem will be described in more detail in the next section (3.4.3).A rotameter (K72-10/1, King Instrument Co.) was used to monitor thesuspension flow rate. A calibration curve for the rotameter is given in the Appendix B,Section B. 1.2.The temperature of the particle suspension was measured by thermometer#BCR (15-35 °C, 0.1 °C divisions) at the start and end of each run.The pH of the solutions was measured by an Orion Research Model 601Adigital electrometer with a Baxter combination electrode. The pH meter was frequentlycalibrated against buffer solutions of known pH (pH = 4.0 and pH = 7.0, Assurance,BDH).A YSI conductivity meter Model 35 using a YSI Model 3403 probe was usedto measure the conductivities of samples of suspension and flush water. Theconductivity meter was periodically calibrated against a KCI standard solution (TDS,Myron L Company). A calibration curve relating the concentration of NaC1 in solutionto the measured conductivity is shown in the Appendix B, Section B. 1.1. This plot canbe used to determine the NaCI content of the solutions at higher electrolyteconcentrations.Chapter 3. Experiment 35The zeta-potential of the particles was measured by electrophoresis. The zeta-potential of the experimental channel was measured by electro-osmosis. Details ofthese measurements will be discussed in Section Image Analyzing System3.4.3.1 ApparatusThe experimental channel was placed on the stage of a Nikon Diaphot-TIVIDinverted optical microscope equipped with a 40x objective. The deposition and releaseof the silica particles were observed under dark field illumination conditions. A COHUsolid state camera (Model 48 15-5000/0000) is mounted on the inverted opticalmicroscope and is coupled to a PC-vision plus frame grabber board (Model 47-H00010-01), which digitizes the image from the camera. The board, installed in a33Mhz 80386 personal computer (IPC) with a math coprocessor, can achieve aresolution of 512 x 480 pixels with 256 grey levels. A separate monitor was used todisplay the image contained in the frame grabber memory. The deposition surface areaobserved was 79.0 x 100.1 m. The total magnification of the camera plus themicroscope was 2178. Algorithmfor Image AnalysisThe image analysis program also developed by Vasak et al. (57) is describedbelow.Chapter 3. Experiment 36Figure 3.7 shows the image analysis algorithm. First, a data file for storing theinformation from each frame is opened. A set of initializing parameters is then inputtedand the image from the camera is digitized to the frame grabber memory. Manual orautomatic image enhancement followed by automatic segmentation is performed next.The image is then processed. A range of acceptable pixel dimensions for the particle isspecified interactively by the operator using the very first image. This allows theprogram to automatically eliminate from ftirther analysis extraneous dust particles orparticle clusters that are larger or smaller than the individual silica particles. Aftersetting this acceptable range, the subsequent frames are processed in an endless ioopuntil the operator manually interrupts the program. For each frame, the processingsteps include image segmentation, counting of particles within the range of acceptabledimensions, and determination of the number of particles which have been depositedand released during the time period between the present frame and the previous one.The time interval between two consecutive frames is 1.1 -1.3 seconds.INPUT DATAI IMAGE ACQUISITION IIMAGE ENHANCEMENT the first imageIMAGE SEGMENTATION SPECIFY ACCEPTABLEPROCESSING DIFFERENCEAYeSFigure 3.7 Algorithm for image analysisChapter 3. Experiment 37The processing steps, including image enhancement, image recognition and theoutline finding algorithm will now be described.Input Data and Image Acquisition The following information is asked forinteractively in order to initiate the program:a) the name of the data file,b) if all particle parameters are to be printed,c) whether the original images are positive or negative,d) if the input image is to be enhanced or not.Several low level subroutines from the Image Technology ITEX Align SoftwareLibrary were used for reading the image from the camera to the frame grabber boardmemory and for controlling the function of these two hardware items.Image Enhancement and Segmentation The camera gain and offset, as well as thepreset value of the threshold can be changed, if image enhancement is needed. Byemploying the algorithm and the contour-following approach described in (90), thenumber of particles present in the image and the co-ordinates of their center points canalso be evaluated.Frame to Frame Dfferentiation By determining the averages of the minimum andmaximum x and y values, the co-ordinates of the centerpoints of each particle areknown for any given frame. The numbers of particles deposited and re-entrainedduring that interval can thus be determined by comparing these co-ordinates betweentwo successive frames. This comparison was made in three steps (see Figure 3.8). InChapter 3. Experiment 38no. in previous frameFigure 3.8 Block diagram of frame to frame differentiationthe first step, the co-ordinates of each particle from the previous frame were comparedwith the co-ordinates of all particles in the present frame. The particles in both frameswere labelled as “unchanged” whenever agreement was achieved. In the second step,all the unlabelled particles in the present frame were compared with each unlabelledparticle from the previous frame. During this comparison, the exact distance betweentheir centerpoints as well as the minimum of these distances was determined. Inturbulent flow, especially with slightly varying light conditions, the co-ordinates of thecenters of stationary particles could fluctuate by as much as 2 pixels (the diameter ofthe particle image on the screen was normally about 8 - 12 pixels); therefore, this stepwas necessary though time consuming. The co-ordinates of the particles with theminimum distance between centers were again compared. When they differed by lessthan 3 pixels, they were both labeled as “unchanged”. In the third step, all unlabelledagreementreturnno. in present frameChapter 3. Experiment 39particles in both frames were counted. The number of unlabelled particles in theprevious frame represents the quantity of particles released, while the number in thepresent frame is the quantity deposited in the view area during the time required toprocess the two consecutive frames. Before processing the next frame, informationabout particles from the previous frame was replaced by information from the presentframe in the grabber board memory. Once the operator manually interrupts theprogram, the data file is closed and further processing stopped.The data file in which information was stored about the time of digitizing, theoverall number of particles, the number of newly attached particles and the number ofreleased particles could then be used for subsequent evaluation of the time dependentrates of particle deposition and re-entrainment.3.4.4 Experimental ProcedureFour series of deposition measurements were carried out corresponding to thetwo batches of silica particles whose preparation was described earlier (Section 3.2.3).At the start of each run, a certain volume of mother suspension (either 10 mL, 15 mLor 20 mL for the first and fourth series and 10 mL for the second and third series) wasadded to 40 mL of freshly distilled water in a wide mouth 80 mL square bottle. Thecontents of the water-cooled bottle were then dispersed by the BrinkmannHomogenizer. The progress of the dispersion process was followed by monitoring thechange with time of the cluster-size distribution using the Nikon Inverted Microscope.When an adequate degree of dispersion (>95% single spheres) had been obtained, thesuspension was added to a 2 liter glass bottle. A certain volume of distilled waterChapter 3. Experiment 40(either 1950 mL, 1945 mL or 1940 mL for the first and fourth series and 1950 mL forthe second and third series) was then added to dilute the particle suspension to thedesired concentration.The pH of the suspension was adjusted by adding either NaOH (0. iN reagentgrade, Fisher) or HC1 (0. iN, reagent grade, Fisher) to the solution by means ofsyringes. The electrolyte concentration as determined by conductivity measurements(see calibration curve, Appendix B, Section B. 1.1) was increased by adding preweighedquantities of NaC1 (reagent grade, Fisher) to the solution. The BrinkmannHomogenizer was used again to disperse the contents of the particle suspension in the 2liter glass bottle. The concentration of the diluted suspension was selected so that thedeposition process could be easily followed by the image analysis system and so that anasymptotic surface coverage could be achieved in a reasonable time. The chemicallyadjusted and well-dispersed suspension was then added to the loop suspension bottle bymeans of a glass flinnel. Accumulation MeasurementsAt the start of each run, all the measuring instruments including the imageanalysis system, the pH and conductivity meters, and the electrophoresis water bath(Section 3.6.2) were turned on to allow a sufficient warm-up before any readings weretaken. Samples of the suspension in the loop suspension bottle were withdrawn usingthe bottle sample line for temperature, conductivity, pH, and particle concentrationmeasurements. When withdrawing suspension samples, at least 20 mL was flushedChapter 3. Experiment 41through the line before the sample (about 40 mL in a 100 mL volumetric cylinder cutdown to hold 60 mL) was taken.Temperature, conductivity and pH measurements were made by placing thethermometer, the conductivity probe and the pH electrode directly into the sample.The conductivity and pH measurements were temperature corrected. Theconcentration of particles in the suspension was determined gravimetrically by filtering30 mL of the sample, using a syringe and a 0.45 jim, 13 mm membrane filter (MillexHV13, Millipore). The filter was then dried under vacuum at 55 °C for 24 hours. Asample was also collected for particle zeta-potential measurement by electrophoresis,and for wall zeta potential measurement by electro-osmosis.A newly coated and dried experimental channel was installed in the system. Allexperimental measurements were made at a position 0.5 cm downstream from the startof the coated section (i.e., at x = 0.5 cm). The entire experimental loop including thecoated experimental section was first evacuated by the vacuum pump (in order toeliminate air bubbles in the loop) and then immediately filled with the suspension asfollows:i) Valves D, ®, and ® were closed; all other valves were opened.ii) The vacuum pump was started to evacuate the loop.iii) Valves and were closed.iv) The feed valve D was opened and enough suspension was sucked byvacuum into the common section to fill the ioop.v) Valve c was closed and the vacuum pump was stopped.Chapter 3. Experiment 42vi) Valves cZ and were opened and valves ® and c were closed.At this point, the supply pump was started to circulate the suspension around the ioop.The flow rate was controlled to obtain the required Reynolds number. Once theflowrate was set, the image recognition program was initiated to process one frameevery 1.1-1.3 seconds. The program determined the number of particles which hadaccumulated on the viewing area of the wall at that instant as well as the number ofparticles which had been deposited and detached within the time between twoconsecutively digitized frames, and stored these results in a data file for further analysisand plotting. Soon after the start of the run, the electrophoresis and electro-osmosismeasurements were carried out (see Section 3.5).The duration of runs varied between two and fifteen hours. At the end of someruns, when asymptotic deposited particle accumulations appeared to have beenreached, the image analysis system was stopped, while the pump remained running. Byadjusting a knob in the microscope, which changed the position of the viewing pointwithout changing the position of the experimental channel, and starting the imageanalysis system, eight to ten additional measurements of deposited particle numberswere obtained by the image analysis system. These readings were used to determinethe average and standard deviation of the number of deposited particles at the end ofthe run. In some experiments, an attempt was made to measure particle release at theend of the deposition run (see Section If such a measurement was not carriedout, the pump was stopped and the suspension remaining in the common section wasexchanged for flush water using the following procedure:i) Valves and were opened and the remaining suspension wasdrained into the drain tank.Chapter 3. Experiment 43ii) Valves (3’ and ® were opened and the pump was started. 20 liters ofdistilled water was used to flush the ioop.iii) After flushing, the remaining distilled water was drained from thesystem.The used experimental channel was then removed from the loop. A sample of theparticle suspension was removed for final particle concentration, temperature,conductivity, and pH measurements. Release MeasurementsWhile particle deposition and release were simultaneously measured by theimage analysis system, several release measurements were undertaken after theaccumulation curve had been completed. These measurements of deposited particlerelease were carried out by changing the pump speed and thereby causing a stepincrease in suspension flow rate. All release rate measurements were made at the sameviewing point used for the deposition measurements. Analysis ofDeposition DataWhile the image analysis system automatically recorded the experimentalresults, manual recording of the actual number of particles deposited on the channelsurface was also made occasionally. Data points selected at specific times from the rawrecorded data were used for plotting and to analyze the results. In some cases, averagevalues of the raw data for a time period of about 1 minute were used in plotting.Chapter 3. Experiment 443.5 MEASUREMENT OF ZETA POTENTIALIn order to determine the double layer interaction energy between a suspendedparticle and the channel surface, knowledge of the Stern potentials (1j15) of the twosurfaces are required (1). It is, unfortunately, not possible to measure directly the Sternpotentials. However, a direct measurement of the zeta potential (Q of each surface ispossible. In the application of the DLVO theory in studies of colloid stability, it iscommonly assumed that I’3 = C (1).In the present experiments, the zeta potential of the particles and the plasticcoating on the channel wall were determined by micro-electrophoresis and electroosmosis, respectively. A Rank Brothers Mark II micro-electrophoresis apparatus wasused to determine the zeta potential of the particles from mobility measurements. Theaverage electrophoretic mobility (iimlsec)/(voltlcm) is obtained by measuring the timetaken for a number of individual particles to cover a given distance in a known potentialgradient. The mobility can then be converted into a zeta potential using Wiersema etal.’s theoretical relationship (Appendix B, Section B.2.2). The calibration of theelectrophoresis apparatus is given in Appendix B, Section Al.3.The zeta potential of the plastic lining the experimental channel was measuredin a similarly-coated rectangular electrophoresis cell. The wall and particle zetapotentials were obtained simultaneously in the coated cell. The wall C-potentials isresponsible for the electro-osmotic flow which occurs when a potential gradient isapplied along the axis of the cell. Thus, if the electro-osmotic velocity is determined atany location in the rectangular cell, the wall c-potential can be estimated from theChapter 3. Experiment 45equation in Appendix B, Section B.2.3. However, the movement of the liquid cannotbe measured directly. But, if the liquid contains suspended particles, the measurementof the apparent electrophoretic velocity at one other position besides the stationarylevel allows an estimation of the electro-osmotic velocity at this position. The center ofthe channel is chosen as the second position because the gradient of the apparentvelocity profile is zero there and hence, the measurement errors are minimal at thislocation.Chapter 4. Results and Discussion 46CHAPTER 4RESULTS AND DISCUSSION4.1 INTRODUCTIONAppendix B, Section B.4 tabulates all the experimental results. The tablescontain a listing of all parameters relevant to each experimental run including thesuspension flow rate, the suspension concentration, the counterion concentration, thesolution pH, the solution conductivity, and the various measured zeta potentials.Records of the particle accumulation and release measurements are given in the samesection as plots.In this chapter, the experimental results for the particle release andaccumulation measurements are presented and discussed in detail.4.2 PARTICLE RELEASEIn order to obtain a better understanding of the time-dependent nature of theparticle accumulation process, which, except at t = 0, involves the two competingprocesses of deposition and release, particle release measurements were simultaneouslymade in the course of deposition measurements in the present experiments. Whileparticle deposition and release were simultaneously measured by the image analysissystem, some release measurements were also undertaken after the accumulationprocess had been completed.Chapter 4. Results and Discussion 47By employing the image analysis system, particle deposition rate and releaserate were measured simultaneously throughout the experiments at all Reynoldsnumbers. The results of the various measurements of particle release, conductedsimultaneously with particle deposition, are very simple to report. In almost all casesrepresenting a variety of fluid flow rates, no measurable release of particles occurred.Figure 4.1 shows, for example, the effect of changing the Reynolds number and doublelayer thickness on particle release obtained in runs 11-6 and 111-2. The solid line isincluded to clarifj the trend of the data. After 12 and 10 hours in runs 11-6 and 111-2,respectively, a substantial amount of accumulation has been achieved at low Reynoldsnumbers, i.e. Re = 1219 and 3529 for runs 11-6 and 111-2, respectively. At these times,step increases in flow rate were obtained by quickly adjusting the pump speedcontroller and the flow of the suspension was adjusted to higher Reynolds numbers,viz. 9806 and 10203 for runs 11-6 and 111-2, respectively. With the increase of theReynolds numbers in both cases, even though the channel wall was monitored for atleast five hours, no particle release was measured even at these higher Reynoldsnumbers. As is also shown in Figure 4.1, from the simultaneously recorded particledeposition and release data, the changing of the double layer thickness from 0.14 in run11-6 to 0.012 p.m in run 111-2 did not affect the release process in these runs.The apparent absence of particle release in laminar flows was not a surprisingoutcome. In the comparable experiments conducted by Bowen (1), the same resultswere obtained. Bowen (1) suggested that, in laminar flow, particle release can onlytake place via the following three mechanisms:i) diffusion,Chapter 4. Results and Discussion 4850-Re=980640-Vdocity increaseRe=121930-Re=10203Vdodty increase20- Re=352910-00 200 400 600 800 1000 12000 RjnIl-6• Rin 111-2a Rin 11-6, releaseA Rin 111-2, releaseTime (mm)Figure 4.1 Complete accumulation curves for Runs 11-6 and 111-2 showing releasemeasurementsEC-)InxChapter 4. Results and Discussion 49ii) shear-aided difihision,iii) erosion.It is of interest to find that, under the conditions of the present study, nomeasurable particle release was recorded while deposition was occurring even withinthe turbulent flow range, except in run Tv-i, which will be discussed below. For therange of conditions investigated here, it can be concluded that release plays a negligiblerole in determining the time-dependent shape of the measured accumulation curves.Figure 4.2 illustrates the complete accumulation curve obtained for run IV- 1,where significant particle release was observed. In run TV-i, particle release wassimultaneously measured along with deposition during the initial part of the run atReynolds number of 3200 and a suspension pH of 9.5. At this pH, the electrical doublelayer surface potential became slightly negative, i.e., the wall c-potential was -1 mV,while the particle a-potential was -46 mV. After the accumulation process had beencompleted, the measurement of particles release into the flowing suspension wasundertaken by step increases in flow rate. The flow rate at which the initial particledeposition measurements were carried out was 34.8 cm3/sec, while the two increasedflow rates were 79.5 and i 88.6 cm3/sec, respectively. The particle release rates at theinstants when the flow rate was changed were determined as 758.7 and 606.9particles/cm2-sec, respectively. Even though there were still particles in suspension, therecorded instantaneous particle deposition and release data indicated that no furtherparticle deposition occurred after the flow rate of the suspension was increased. Thus,the change of the particle accumulation curve was only due to particle release from thewall of the experimental channel. It is therefore suggested that, under the conditions ofChapter 4. Results and Discussion 50151050Tniie (rrin)Figure 4.2 Complete accumulation curves for Run TV-i showing releasemeasurements0 100 200 700 800 900Chapter 4. Results and Discussion 51run Tv-i (i.e. slightly negatively charged wall surface and negatively charged particles),turbulence and the interaction forces between particles and channel wall play asignificant role in particle deposition and release at higher Reynolds numbers.Unfortunately, due to the time constraints of the present study, only one releasemeasurement under this test condition could be performed.4.3 PARTICLE DEPOSITION4.3.1 Initial Deposition Rates26 successfhl experiments to determine initial deposition rates were performed.The series I experimental runs were considered to be of a trial nature and hence onlythe effect of changing the flow rate on initial deposition rates was studied. Figure 4.3illustrates the results obtained in the series I runs. Since good reproducibility wasdemonstrated for two pairs of runs (I-i, -2 and 1-3, -4), it was felt that the experimentalresults obtained in this study could be considered fairly reliable.Figure 4.4 shows the variation of the concentration of deposited particles, Cu,,with time for Run 111-7. In Run ffl-7, the pH of the suspension was 5.7 and the zetapotential of the silica particles was -45 mV, while that of the 2VP/S-coatedexperimental channel, as determined by an electro-osmosis measurement, was + 10 mV.The experimental initial deposition rate, Pexp, determined by fitting a straight line passingthrough the origin to the first 6 points in Fig. 4.4, was found to be 2.28 x 102particles/cm2-sec.Chapter 4. Results and Discussion 526-AAA5-Rir I-i (Re=G827)Run 1-2 (Re9)EAci • Rui 1-3 (Re1341O)o Run 1-4 (Re134)U?0 AA1 runl-1A n.nI-20 runl-3z •o • runl-4C_____• 00• I ‘ I • I • I • I ‘0 10 20 30 40 50 60 70Time (mm)Figure 4.3 Experimental results. Series IChapter 4. Results and Discussion 538-6 Re=46830 20 40 60 80Time (mm)Figure 4.4 Deposition concentration versus time. Run 111-7Chapter 4. Results and Discussion 544.3.1.1 Effect ofFlow Rate on Initial Deposition RateThe effect of the Reynolds number on the measured initial particle depositionrate is illustrated in Figure 4.5. A solid line is superimposed on the data to show theoverall trend. As can be seen in Figure 4.5, the experimental results correlate quitewell with one of the experimental parameters, namely, the Reynolds number. In SeriesII and III, the average double layer thicknesses were 0.13 jim and 0.0 13 jim,respectively, while other deposition conditions remained reasonably constant. Theseresults suggest that the initial deposition rates first increase in laminar flow and thendecrease in turbulent flow with increasing suspension velocity. Other investigators havealso reported this behavior (63, 100, 103).The experimental results obtained when Re was varied from 674 to 2000 areanalyzed by Bowen’s model (1) (extended to handle a rectangular channel, seeAppendix A, Section A.2). Epstein’s model (10, 62) and Berger and Hau’s correlation(17) are employed to analyze the experimental results for Re > 2000. In applyingEpstein’s theory, the points on Figure 4.6 and Figure 4.7 corresponding to the welldefined maximum initial deposition rates were taken as the reference points for runseries II and III, respectively. The measured deposition rates are compared to thepredicted values using Bowen’s theory (for laminar flows), and Epstein’s as well asBerger and Hau’s theory (for turbulent flows) in Figure 4.6, Figure 4.7 and Table 4.1for Series II and Ill. For runs 11-i to -4 and rn-i to -3, 4m, the mass transfercontrolled initial deposition rate, is determined by Bowen’s model. For all of the otherruflS, 4mass and the initial deposition rate including surface attachment, aredetermined by Berger and Hau’s and Epstein’s models, respectively.Chapter 4. Results and Discussion 55300...200//00II./100-. 90Co. o605040 0 SeriesIl• Series III30, • • •6 810 20 40 60 80100Re(x102 )Figure 4.5 Initial deposition rate versus Reynolds numberChapter 4. Results and Discussion 56700-600-500•C)C’11400_B&Hi(17)a)C)30OCu200-,stn (10,62)0’100-I 0 o1)0-. I • I • I • I •0 2000 4000 6000 8000 10000 12000 14000 16000 18000ReFigure 4.6 Comparison of the measured and predicted initial deposition rate,Series II. Epstein model is keyed to black point, taken as maximum4’ in turbulent flow.Chapter 4. Results and Discussion 57I200Co-e400Re10000Figure 4.7 Comparison of the measured and predicted initial deposition rate,Series III. Epstein model is keyed to black point, taken as maximum4’ in turbulent flow.Chapter 4. Results and Discussion 58Table 4.1 Initial Deposition RatesRun [ Re 1/,c Cp F Cw Q V 4expt I dkiieory I 4>massI (rim) (mV) (mV) (cm3lsec) (mJsec) (particles/cm2-sec)11-1 674 0.1255 -70.36 28.99 6.62 0.055 169.41 - 126.5011-2 1026 0.1263 -71.26 30.03 10.09 0.084 170.67 - 145.5611-3 1636 0.1263 -72.33 24.89 16.09 0.134 185.84 - 170.0111-4 1989 0.1227 -72.83 30.03 19.56 0.162 221.24 - 181.4711-5 2021 0.1262 -71.88 22.48 19.87 0.166 227.56 227.56 113.1111-6 3529 0.1416 -67.41 25.55 34.69 0.289 193.43 175.65 182.6811-7 3925 0.1262 -71.26 37.61 38.86 0.324 195.95 156.80 201.3811-8 10008 0.1179 -81.13 26.36 98.41 0.820 73.70 40.22 447.7711-9 12189 0.1263 -71.26 23.58 119.86 0.999 70.16 28.82 530.5211-10 13472 0.1683 -89.84 24.93 132.47 1.104 35.40 24.29 578.2011-11 16039 0.1179 -81.25 23.54 157.71 1.314 0.00 17.99 671.74111-1 962 0.01242 -50.61 2.41 9.46 0.079 158.03 - 142.46ffl-2 1219 0.01232 -47.27 18.36 11.99 0.099 211.13 - 154.15ffl-3 1604 0.01258 -36.74 10.86 15.77 0.131 245.26 - 168.91ffl-4 2021 0.01232 -40.59 23.01 19.87 0.166 280.66 280.66 113.11111-5 2502 0.01242 -43.93 24.89 24.60 0.205 274.34 274.95 135.92111-6 3208 0.01217 -62.68 6.79 31.54 0.262 262.96 239.29 168.30111-7 4683 0.01232 -44.44 9.98 46.05 0.384 227.56 161.65 233.04111-8 5517 0.01242 -37.25 9.49 54.25 0.452 194.69 129.41 268.31111-9 7025 0.01232 -42.39 8.12 69.08 0.576 104.17 90.12 330.27111-10 8597 0.01217 -62.68 6.79 84.53 0.704 70.16 65.26 392.90111-11 9302 0.01244 -41.66 22.36 91.47 0.762 0.00 57.29 420.48According to Figure 4.6, Figure 4.7 and Table 4.1, the agreement betweenexperiment and Bowen’s theory in the laminar flow range is good. A similar conclusionwas also reached during Bowen’s work (1) studying fine particle deposition in laminarflow through parallel-plate channels, using a similar experimental system, i.e. negativesilica particles and a positive wall. This good agreement thus supports the reliability ofthe present experimental measurements.As an example, consider Figure 4.8 which shows the variation of theconcentration of deposited particles, C, with time for Run 11-3. In this run, theChapter 4. Results and Discussion 59Time (rrin)Figure 4.8 Deposition concentration versus time. Run 11-3Chapter 4. Results and Discussion 60suspension counterion concentration was 5.8 x 10 moles/L, and the zeta potential ofthe silica particles was -70 mV, while that of the 2VP/S-coated experimental channel,as determined by an electro-osmosis measurement, was +29 mV. The experimentalinitial deposition rate, 4, determined by fitting a straight line passing through theorigin to the first 6 points in Fig. 4.8, was found to be 1.69 x 102 particles/cm-sec.Wall concentrations predicted from the theoretical mass-transfer controlled depositionrate, determined by Bowen’s theory, are also plotted on Figure 4.8. The closeagreement between experiment and Bowen’s theory suggests that, at least for this case,the measured data are well represented by assuming that the deposition process ismass-transfer controlled. This also proves that, in the present experimental system, aparticle transport theoretical model, e.g. the special case of Bowen’s model, isappropriate for analysis of the experimental results in laminar flow.It can be seen from Figure 4.5 and Table 4.1 that the agreement betweenEpstein’s theory (10, 62) and the experimental results obtained from the turbulent flowrange is good, while the poor agreement between experiment and mass transfer-controlled theory (17) in the turbulent flow range, as shown in Figures 4.6 and 4.7,suggests that the measured data can not be well represented by assuming that thedeposition process is mass-transfer controlled. This also suggests that a theoreticalmodel combining both the effects of particle transport and attachment, e.g. Epstein’smodel (10, 62), is more appropriate for analyzing the results obtained in this Reynoldsnumber range.Another interesting feature of Figures 4.6 and 4.7 is that the values of kieory forthe turbulent flow range are almost always less than the experimentally determinedChapter 4. Results and Discussion 61values of4pt In other words, the surface interactions and turbulence play a weakerrole in reducing the overall deposition rates than is predicted by the theory.In a detailed study of the causes of variation in the measured initial depositionrates compared to the purely mass-transfer controlled values in a laminar flow system,Bowen (1) suggested that the primary cause of the variation is the influence of theinteraction forces. Since a similar experimental system was employed in the presentstudy, it is therefore expected that the same situation exists in the case of the laminarflow range in this study. Of secondary importance to the existing variations areexperimental errors (see Appendix B.3). Effect ofDouble Layer Thickness on Initial Deposition RateFigure 4.9 illustrates the deposition rate results obtained in Series II and III, inwhich the double layer thickness was changed in a systematic manner, viz, averagevalues of ic are 8.0 x i04 cm1 for Series II and 8.0 x iO cm1 for Series III. A decreasein double layer thickness was obtained by increasing the NaC1 concentration of thesuspension while maintaining constant pH conditions. It can be seen from Figure 4.9that, although the deposition conditions remained otherwise reasonably constant,decreasing the thickness of the double layer decreased the initial deposition rate for Re1000 or Re 6000, but increased the initial deposition rate in the range of Re 1000to 6000.Consider the contribution of electrical double layer interaction forces to particledeposition in laminar flow as discussed by Bowen (1). In the present experiments,Chapter 4. Results and Discussion 62300A0 •20000.C.)ci)C?(‘.JE 100a) 90!C)•1-’1Cu70 • 0500 Series II40 • Serieslil030• • •6 810 20 40 6080100Re(x102 )Figure 4.9 Effect of double layer thickness on initial deposition rate. Averagevalue of ic is 8.0x104cm’ for Series II and 8.Ox 10 cm’ for Series III.Chapter 4. Results and Discussion 63where negatively charged particles deposit onto a positive substrate, if one ignores theinfluence of viscous interaction as a sphere approaches a plane surface, the potentialenergy well is essentially infinitely deep such that a particle which diflh.ises to thecollector surface is irreversibly removed from the suspension. It is therefore expectedthat, as the importance of the double layer attraction is decreased (i.e. by decreasing thedouble layer thickness), the double layer attraction will be reduced and the initialdeposition rates will be decreased. Clearly, the role of the attractive van der Waalsand, in this case, attractive double layer interaction forces is to counteract the viscousinteraction, making it easier for particles to approach the collector surface. As shownin Figure 4.9, it is strongly suspected that the same situation exists in the case ofparticle deposition in a turbulent flow system. According to Figure 4.9, although theattracting force decreased due to the decrease of the double layer thickness, the initialdeposition rates still increased until Re = 6000. This suggests that there is a netattractive force to enhance particle deposition at the channel surface up to Re = 6000,beyond which the effect of shear on the attachment process is manifested as a sharpdecrease of deposition rate.4.3.2 Deposition With TimeThe effects of surface coverage, flow rate, counterion concentration, andsuspension pH on the time course of particle deposition are considered in this section.The surface coverage 8 is defined as the fractional area covered by depositedparticles of diameter d assuming that each particle occupies an area equal to d2. Theformation of a close-packed monolayer of particles having a square array thereforeChapter 4. Results and Discussion 64corresponds to complete coverage, i.e. 9 = 1. 9 is given by 9 = d2C, where C,,. is thesurface particle concentration in particles/cm2.Since the major objective of the present experimental study was to investigatethe initial particle deposition rates, only enough data were gathered in most runs toaccurately establish initial deposition rates. However, in a few runs (11-1, -6, -10, Ill-i,-2, -6, -9), deposition was allowed to continue until the rate of accumulation haddecreased almost to zero.The accumulation-time curves for those runs continued until an almost invariantwall concentration was obtained. All such runs share two rather distinctive features.First, the overall shape of the curve was almost identical in each case. This shape,which is illustrated in Figure 4.1 for runs 11-6 and 111-2, may be characterized in thefollowing manner. Initially, the accumulation of particles on the wall is linear withtime. At a certain point, there is a perceptible decline in the accumulation rate. This isfollowed by a long period during which the accumulation rate steadily decreases. Theother feature of these accumulation-time curves is that the maximum surface coveragesattained were remarkably low. The maximum coverages obtained for thoseexperiments in which the wall concentration approached an approximately asymptoticvalue fell in the range 0.0007 9 0.03 5. It must kept in mind that, for the operatingperiod selected in the present investigation (maximum 18 hrs.), a true asymptoticcondition (zero accumulation rate) might still not be reached and hence it is quiteconceivable that the wall concentrations could continue to grow well beyond thecoverages indicated above. However, the fact that the accumulation rates were soChapter 4. Results and Discussion 65much below their initial values at such low surface coverages seems somewhatremarkable.Reversible accumulation models, i.e. those involving simultaneous depositionand re-entrainment, have been widely used (22, 63, 97) to explain the asymptoticgrowth curves frequently encountered in studies of the particulate fouling of heatexchangers. In the present investigation, it has been demonstrated (Section 4.2) thatthe accumulation process is difficult to reverse. Thus, the characteristic shape of theaccumulation curves can only be explained in terms of a declining deposition rate. Intheir comparable experimental studies of particle deposition, Bowen (1) and others (22,63, 103) obtained similar accumulation-time curves.Figure 4.10 is a plot of the accumulation results obtained in runs 111-6 and -9where, under otherwise reasonably constant conditions, the flows of suspensionthrough the experimental channel were 31.54 and 69.08 cm3/sec, respectively. Aspredicted, for runs 111-6 and -9, the initial deposition rates decrease in correspondencewith the increasing flow rate (in the turbulent flow range). However, increasing theflow also appears to increase the effect of surface coverage on the reducedaccumulation rate.The accumulation results obtained when the concentration of neutral electrolyte(NaC1) was varied under constant pH conditions are shown in Figure 4.11 for runs 11-2and 111-1, in which the counterion concentration increased from 6.08x10 (H4 andNH in distilled water) to 5.96x io (Na, NaC1 was added) moles/L., respectively. Aswas discussed earlier (Section, Figure 4.11 shows that as the concentration ofChapter 4. Results and Discussion 66Run III-6(Re3208)15-E1o.ci)C)5-Run 111-9 (Re=7025)0O4y i • i • i • i •0 20 40 60 80 100 120Time (mm)Figure 4.10 Effect of suspension flow rate on deposition. Run 111-6 and -9Chapter 4. Results and Discussion 67IFigure 4.11 Effect of counterion concentration on deposition. The counterionconcentrations were 6.08x10 moles/L for Run 11-2 (II and NH indistilled water) and 5,96x l0 molesfL (Na, NaCI was added) for Run‘IT-i.Time (mm)Chapter 4. Results and Discussion 68indifferent electrolyte (NaCl) increases, the initial deposition rate decreases. Also, asthe NaCI concentration increases in this Reynolds number range, the subsequentaccumulation rate is also affected and a lower surface concentration is obtained.Figure 4.12 shows the particle and wall c-potentials measured for theexperimental conditions encountered in series II and III. According to Bowen’s theory,increasing the concentration of neutral electrolyte decreases the double layer thicknessas well as the magnitudes of both the particle and the wall a-potentials and, as a result,decreases the rate of particle deposition (as shown in Figure 4.11). Figure 4.12 doesdemonstrate the decrease of particle and wall c-potentials.When a suspension of negatively charged silica particles was made to flowthrough the experimental channel whose walls were also negatively charged, it wasfound that the initial deposition rate was less than that of the negatively chargedparticles depositing onto a positive substrate. Figure 4.13 compares the accumulationcurves obtained for runs 11-6 and IV-1. Both runs were operated under similarexperimental conditions and in both cases the experimental channels were coated withthe 2W/S copolymer. However, a slight pH shift between runs resulted in an initialwall zeta potential of +25.55 mV in run 11-5 compared to -0.94 mV in run IV-1. Theinitial deposition rate predicted from Epstein’s theory was 1.76 x 102 particles/cm-sfor both runs. The experimental values were 1.93 x 102 and 1.33 x 102 particles/cm-sec for runs 11-6 and IV-1, respectively. Thus, it is apparent that the repulsiveinteraction between the two similarly charged double layers encountered in run IV- 1led to an extra resistance to deposition at the channel walls. Unfortunately, the timeavailable did not allow an extensive investigation of particle deposition onto negativelyChapter 4. Results and Discussion 69>CU-I-’Cci)4-00(134-ci)NCounteron conc’n (moles/L)Figure 4.12 Effect of counterion concentration on particle and wall c-potentials. Theaverage counterion concentrations were 6.05x 106 moleslL for Series II (Hand NH4in distilled water) and 5. 80x 1 O moles/L (Na, NaC1 was added)for Series Ill.500-50-100.0 series II• series III0 c, series IIA c series III.00I • - I-III I III10.6 i04 i0 102 101 100Chapter 4. Results and Discussion 70Time (mm)300Figure 4.13 Comparison of deposition results obtained for a positively chargedsubstrate (Run 11-5, pH = 5.7, C = 22 mV) with those measured for anegatively charged substrate (Run TV-i, pH = 9.5, = -1 my).0 50 100 150 200 250Chapter 4. Results and Discussion 71charged channel walls. Similar results were obtained in studying colloidal particledeposition against an electrostatic barrier by other investigators (1, 30, 32).Chapter 5. Conclusions and Recommendations 72CHAPTER 5CONCLUSIONS AND RECOMMENDATIONSThe deposition and re-entrainment of micrometer-size silica spheres from and toaqueous suspensions in a rectangular channel has been investigated experimentally. Themeasurement of deposition and release of negatively charged silica spheres onto andfrom a positively charged plastic substrate was greatly facilitated by employing a directmicroscopic technique and image analysis system.Under the conditions of the present experiments, except in the case of oneexceptionally imposed state, it was found that the rate of particle release from thechannel surface was not observable. This suggests that the adhesion force acting tohold the particles on the wall was too strong to permit re-entrainment of particle fromthe surface even in the presence of extensive fluid shear in the case of high Reynoldsnumbers. Thus, the declining rate of accumulation with time observed in most runswas a result of a declining deposition rate but could not be attributed to particlerelease.In laminar and transition flows, the initial rate of deposition was found to beessentially mass-transfer controlled. In the range of turbulent flows, the initial rate ofdeposition was found to be controlled by particle transport as well as particleattachment onto the wall surface. Except for a few runs, good agreement betweenmeasured values and results predicted from Epstein’s model was obtained. Thedeviations between experimental results and predicted values could be explained byChapter 5. Conclusions and Recommendations 73consideration of the roles played by the various interaction forces, surfaceheterogeneities, experimental and data handling errors.The particle deposition rate did not maintain its initial value but insteaddecreased with time for all runs. It was found that the concentration of depositedparticles reached an asymptotic value for those runs which were performed longenough. The particle surface coverage never exceeded 3.5%.The initial deposition rate was observed to be influenced by a number ofexperimental parameters. For example, in laminar flows, higher initial deposition ratescould be obtained by increasing the suspension flow rate and increasing the magnitudeof the (positive) waIl a-potential; and higher initial rates could be attained by decreasingthe suspension flow rate and increasing the c-potential of the channel wall in turbulentflows. The surface coverage was also apparently influenced by experimentalparameters. For example, higher asymptotic surface coverages could be obtained bydecreasing the suspension flow rate in turbulent flow and increasing the magnitude ofthe wall a-potential. These findings are in line with results obtained by previousinvestigations on particle deposition onto channel walls.It is suggested that the measurements should be extended over a wider range ofparameters, such as suspension pH value and double layer thickness, to provide a morecomplete investigation of the deposition onto a positive substrate; a more thoroughexamination of the initial deposition onto negatively charged substrates; and a moreextensive search for conditions which lead to significant particle release. Improvedexperimental results using the present system could probably be obtained if theChapter 5. Conclusions and Recommendations 74measuring loop were modified to even more rigorously exclude the introduction ofcontaminants. A more precise speed controller is also suggested for use in theexperiments in order to obtain a more stable suspension flow rate.Nomenclature 75NOMENCLATUREOnly those symbols used in the main text of the thesis are defined here. The units givenbelow are those which are most frequently employed.a half-width of experimental channel (cm)A Hamaker constant (ergs)A cross-sectional area of flat cell at measuring plane (cm2)b half-thickness of experimental channel (cm)b half-thickness of flat cell at measuring plane (cm)C = C(x, y), concentration of suspended particles (particles/cm3)C0 homogeneous suspension concentration at channel inlet (particles/cm3)Cb bulk concentration of suspended particles (particles/cm3)Cs suspension concentration at channel wall (particles/cm3)C concentration of deposited particles (particles/cm2)de duct equivalent diameter (cm)d particle diameter (cm)D particle diffusion coefficient (cm2/sec)DB Brownian difihisivity of particles (cm2/sec)E activation energy (J/mole)f Fanning friction factork1 constant defined by Equation [4]k2 constant defined by Equation [5] (kg’1-sec3/m)km mass transfer coefficient (cm/see)Nomenclature 76kr attachment rate constant (cm/see)k Boltzmann constant 1.38054 x 10.16 erg K-’K = bK, /D, dimensionless surface reaction rate constantK1 surface reaction rate constant (cm/see)interelectrode distance for electrophoresis cell (cm)m mass of particle (g)Pe = ReSc, Peclet number for experimental channel (dimensionless)Q flow rate (cm3/sec)R electrical resistance (ohm)R universal gas constantRe VmcIIV, Reynolds number for experimental channel (dimensionless)S sticking probabilitySc = vIDB, Schmidt number for particlest time (sec)T absolute temperature (K)v fluid velocity (rn/see)v = v(f72)”2,friction velocity (cm/see)yE true electrophoretic velocity at stationary levels (cm/see)Vm average suspension flow velocity in experimental channel (cm/see)Vd dimensionless particle deposition velocityW width of test section (cm)x longitudinal distance (cm)y distance normal to median plane of experimental channel (cm)a. Stokes’ law correction factor (dimensionless)= (1/Pe)(8x/3b), dimensionless longitudinal distanceNomenclature 77thickness of wall regione eddy difihisivity (cm2/sec)C zeta potential (mV)conductivity (mholcm)0 = C/C0, dimensionless suspension concentrationK inverse double layer thickness (cm’)fluid viscosity (g/cm-sec)v = t/p, fluid kinematic viscosity (cm2/sec)p fluid density (g/cm3)fluid shear stress at surface (Pa)• particle deposition flux (particles/cm2-se rglcm2-sec)= bfDC0,dimensionless particle deposition fluxw (h), potential distribution of the double layer (mV)Subscriptsexpt experimentally measured valuedummy index 1,2,3,...particlesurfacetheoiy theoretically predicted valuechannel wallinitial valuebulk property-too_+ dime.onIess valueNomenclatun 78References 79REFERENCES1. Bowen, B.D., (1978), Fine Particles Deposition in Smooth Channels, Ph.D.Thesis, University of British Columbia.2. Epstein, N., (1988), Particulate Fouling of Heat Transfer Surfaces:Mechanisms and Models, in Fouling Science and Technology, Melo, L.F.,Bott, T.R., and Bemardo, C.A., eds., 143-194, Kluwer Academic Publishers,the Netherlands.3. Papavergos, P.G., and Hedley, A.B., (1984), Particle Deposition Behaviorfrom Turbulent Flows, Chem. Eng. Res. Des., 62, 275-295.4. van de Ven, T.G.M., (1989), Colloidal Hydrodynamics, Academic Press,London.5. Friedlander, S. K. and Johnstone, H. F., (1957), Deposition of SuspendedParticles from Turbulent Gas Streams, mci Eng. Chem., 49, 1151-1156.6. Lin, C. S., Moulton, R. W. and Putman, G. L.,(1952), Mass Transfer betweenSolid Wall and Fluid Streams, md. Eng. Chem., 45, 636-640.7. Davies, C. N., (1966), Aerosol Science, p. 393, Academic Press, New York.8. Beal, S. K., (1970), Deposition of Particles in Turbulent Flow on Channel orPipe Walls, Nuci. Sci. Eng., 40, 1-11.9. Hutchinson, P. C., Hewitt, G. F., and Dukler, A. E., (1971), Deposition ofLiquid or Solid Dispersions from Turbulent Gas Streams: a Stochastic Model,Chem. Eng. Sd., 26, 419-439.10. Epstein, N., (1993), The Velocity Effect on Initial Fouling Rates, IsraelChemical Engineering: I ofIsrael Institute of Chemical Engineers, April, 32-37.11. Bowen, B.D., Levine, S., and Epstein, N., (1976), Fine Particle Deposition inLaminar Flow Through Parallel-Plate and Cylindrical Channels, I Colloid andInterface Sd., 54, 375-390.12 Ruckenstein, E., and Prieve, D.C., (1973), Rate of Deposition of BrownianParticles under the Action of London and Double-layer Forces, I Chem. Soc.Faraday, II 69, 1522-1536.References 8013. Spielman, L.A., and Friedlander, SE., (1974), Role of the Electrical DoubleLayer in Particle Deposition by Convective Difihision, I Coioid Interface Sci.,46, 22-3 1.14. Dahneke, B., (1974), Difilisional Deposition of Particles, .1 Colloid InterfaceSd., 48, 520-522.15. Adamczyk, Z., and van de Ven, T.G.M., (1981), Deposition of Particles underExternal Forces in Laminar Flow through Parallel-Plate and CylindricalChannels, I Colloid Interface Sd., 80, 340-356.16. Bowen, B.D., and Epstein, N., (1979), Fine Particle Deposition in SmoothParallel-Plate Channels, I Colloid andInterface Sd., 72, 8 1-97.17. Berger, F.P. and Hau, K.F., (1977), Mass Transfer in Turbulent Pipe FlowMeasured by Electrochemical Method, mt. I Heat Mass Transf, 20, 1185-1194.18. Forney, L.J., and Spielman, L.A., (1974), Deposition of Coarse Aerosol fromTurbulent Flow, I Aerosol Sd., 5, 257-271.19. Wells, A.C. and Chamberlain, A.C., (1969), Deposition of Dust fromTurbulent Gas Stream, Atm Environment. 3, 494.20. Liu, B.Y.H. and Agarwal, J.K., (1974), Experimental Observation of AerosolDeposition in Turbulent Flow, I Aerosol Sd., 5, 145-155.21. Govan, A.H., Hewitt, G.F., and Ngan, C.F., (1989), Particle Motion in aTurbulent Pipe Flow, mt. I Multiphase Flow, 15, 471-481.22. Newson, I.H., Miller, G.A., Haynes, J.W., Bott, T.R., and Williamson, R.D.,(1989), Particulate Fouling: Studies of Deposition, Removal and StickingMechanisms in Hematite/Water System, 2nd UK National Heat TransferConference.23. Matsumoto, S., Harakawa, H., Suzuki, M., and Ohtani, S., (1986), SolidParticle Velocity in Vertical Gaseous Suspension Flows, mt. I MultiphaseFlow, 12, 445-458.24. Alexander, L.G. and Coldren, C.L., (1951), Droplet Transfer from SuspendingAir to Duct Wall, md. Eng. Chem., 43, 1325-1331.References 8125. Montgomery, T.L. and Corn, M., (1970), Aerosol Deposition in a Pipe withTurbulent Airflow, J Aerosol SeE., 1, 185-213.26. Hahn, L.A., Stukel, J.J., Leong, K.H., and Hopke, P.K., (1985), TurbulentDeposition of Submicron Particles on Rough Walls, .1 Aerosol Sd., 16, 81-86.27. Vasak, F., Bowen, B.D. and Epstein, N., (1991), Measurement of Fine ParticleDeposition from Flowing Suspensions by Image Analysis, Technology Today,1,31-35.28. Rashidi, M., Hetsroni, G. and Banerjee, S., (1990), Particle-TurbulenceInteraction in a Boundary Layer, mt. J Multiphase Flow, 16, 93 5-949.29. Shimada, M., Okuyama, K. and Asai, M., (1993), Deposition of SubmicronAerosol Particles in Turbulent and Transitional Flow, AIChE Journal, 39,17-26.30. Marshall, R.A. and Kitchener, J.A. (1966), The Deposition of ColloidalParticles on Smooth Solids, J Colloid Interface SeE., 22, 342-35 1.31. Dabros, T. and van de Ven, T.G.M., (1987), Deposition of Latex Particles onGlass Surfaces in an Impinging Jet, PCH PhysicoChemical Hydrodynamics, 8,161-172.32. Hull, M. and Kitchener, J.A., (1969), Interaction of Spherical ColloidalParticles with Planar Surfaces, Trans. Faraday Soc., 65, 3093-3104.33. Fan, B., McFarland, R.A. and Anand, N.K., (1992), Characterization of theAerosol Particle Lift Force, .1 Aerosol SeE., 23, 379-388.34 Abuzeid, S., Busnaina, A.A. and Ahmadi, 0., (1991), Wall Deposition ofAerosol Particles in a Turbulent Channel Flow, J Aerosol SeE., 22, 43-62.35. Jurcik, B. and Wang, H.C., (1991), The Modeling of Particle Resuspension inTurbulent Flow, J Aerosol SeE., 22, Suppl. 1, S149-S152.36. Berlemont, A., Desjonqueres, P. and Gouesbet, G., (1990), ParticleLagrangian Simulation in Turbulent Flows, mt. Multzphase Flow, 16, 19-34.37. Jansen, J.P. and Laheij, G.M.H., (1990), On the Transport of Particles throughTurbulent Boundary Layers, .J Aerosol Sd., 21, Suppl. 1, S97-S100.References 8238. Ounis, H., Ahmadi, G. and McLaughlin, J.B., (1991), Dispersion andDeposition of Brownian Particles from Point Sources in a Simulated TurbulentChannel Flow, J Colloid and Interface Sd., 147, 233-250.39. Johansen, S. T., (1991), The Deposition of Particles on Vertical Walls, mt ..JMuitiphase Flow, 17, 3 55-376.40. Kallio, G. A., and Reeks, M. W., (1989), A Numerical Simulation of ParticleDeposition in Turbulent Boundary Layers, mt J Multiphase Flow, 15, 433-446.41. Vatistas, N., (1989), The Effect of Adhesion Time on Particle Deposition,Chem. Eng. SeE., 44, 1603-1608.42. Yung, B.P.K., Merry, H. and Bott, T.R., (1989), Effects of Particle-SurfaceInteractions on Deposition and Re-entrainment of a Particulate FoulingSystem, Geothermics, 18, 327-335.43. Im, K.H. and Ahluwalia, R.K., (1989), Turbulent Eddy Deposition of Particleson Smooth and Rough Surfaces, JAerosoi Sd., 20, 431-436.44 Fichman, M., Gutfinger, C. and Pnueli, D., (1988), A Model for TurbulentDeposition of Aerosols, J Aerosol Sd., 19,123-136.45. Fissan, H. and Turner, J.R., (1987), Particle Deposition from Turbulently-Mixed Gases, J Aerosol Sd., 18, 623-626.46. Lee, S.L. and Wiesler, M.A., (1987), Theory on Transverse Migration ofParticles in a Turbulent Two-Phase Suspension Flow Due to TurbulentDifThsion, mt. Multiphase Flow, 13, 99-111.47. Lee, S.L. and Borner, T. (1987), Fluid Flow Structure in a Dilute TurbulentTwo-Phase Suspension Flow in a Vertical Pipe, mt. Multzphase Flow, 13, 233-246.48. Wood, N.B. (1981), A Simple Method for the Calculation of TurbulentDeposition to Smooth and Rough Surfaces, I Aerosol Sd., 12, 275-290.49. El-Shobokshy, M.S. and Ismail, l.A., (1980), Deposition of Aerosol ParticlesFrom Turbulent Flow onto Rough Pipe Wall, Atmospheric Environmeni, 14,297-304.References 8350. Cleaver, J. W., and Yates, B., (1975), A Sub-Layer Model for the Depositionof Particles from a Turbulent Flow, Chem. Eng. Sci., 30, 983-992.51. Sebmel, G.A., (1971), Complexities of Particle Deposition and Re-entrainmentin Turbulent Pipe Flow, .1 Aerosol Sd., 2, 63-72.52. Rouhiainen, P.O., and Stachiewicz, J. W., (1970), On the Deposition of SmallParticles from Turbulent Streams, I Heat Transfer, 92,169-177.53. Davies, J.T., (1983), A New Theory of the Deposition of Colloidal Particlesfrom Turbulent Fluids, Annals New YorkAcademy ofSd., Vol. 404, 313-326.54. Davies, J.T., (1983), A New Theory of the Deposition of Colloidal Particlesfrom Turbulent Fluids, Chem. Eng. Sd., 38, 135-139.55. Adamczyk, Z. and van de Ven, T.G.M., (1982), Particle Transfer to a Plate inUniform Flow, Chem. Eng. Sci., 37, 869-880.56. Reeks, M.W., (1983), The Transport of Discrete Particles in InhomogeneousTurbulence, I Aerosol Sci., 14, 729-73 9.57. Alince, B. and van de Ven, T.G.M., (1993), Kinetics of Colloidal ParticleDeposition on Pulp Fibers, Colloids and Surfaces A: Physicochemical andEngineering Aspects, 71, 105-114.58. Shimada, M., Okuyama, K., Kousaka, Y. and Seinfeld, J.H., (1988), A ModelCalculation of Particle Deposition onto a Rough Wall by Brownian andTurbulent Diffusion, I Colloid and Interface Sci., 125, 198-211.59. Lee, S.L., (1984), Recent Development of Particle Deposition in a TurbulentSuspension Flow, Proceeding Energy Sources Tech. Conference, NewOrleans, Louisiana, 3-7.60. Oron, A. and Gutfinger, C.,(1986), On Turbulent Deposition of Particles toRough Surfaces, .1 Aerosol Sci., 17, 903-920.61. Ounis, H., Ahmadi, G. and McLaughlin, J.B., (1992), Brownian ParticleDeposition in a Directly Simulated Turbulent Channel Flow, Report, ClarksonUniversity, Potsdam, N.Y.62. Epstein, N., (1993), A Model of the Chemical Reaction Fouling Rate for Flowwithin a Heated Tube and Its Verification, submitted for publication.References 8463. Watkinson, A.P. and Epstein, N., (1970), Particulate Fouling of Sensible HeatExchangers, Proc. 4th Intern. Heat Transfer Conf Vol. 1, paper HE 1.6, 1-12,Elsevier.64. Goldenberg, M. and Gallily, I., (1990), Deposition of Nonspherical Particles inTurbulent Air Flows, J Aerosol Sd., 21, Suppi. 1, S105-S 108.65. Turner, C.W. and Lister, D.H., (1991), A Study of the Deposition of Silt ontothe Surface of Type 304 Stainless Steel, Canadian I Chem. Eng., 69, 203-205.66. Mollinger, A.M., Nieuwstadt, F.T.M., Marijnissen, J.C.M. and Scarlett, B.,(1992), Entrainment of Particles in a Turbulent Boundary Layer, I AerosolSci., 23, Suppl. 1, S47-S50.67. Han, J.C., Gilcksman, L.R. and Rohsenow, W.M., (1978), An Investigation ofHeat Transfer and Friction fro Rib-Roughened Surfaces, mt. J Heat MassTransfer, 21, 1143-1156.68. Fromentin, A., (1989), Time Dependent Particle Resuspension from a Multi-Layer Deposit by Turbulent Flow, .1 Aerosol Sci., 20, 911-914.69. Hubbe, M.A., (1985), Detachment of Colloidal Hydrous Oxide Spheres fromFlat Solids Exposed to Flow, Colloids and Surfaces, 16, 227-248.70. Turner, J.R. and Fissan, H.J. (1989), Convective Diffi.ision of Particles inExternal Force Fields, Chem. Eng. Sci., 44, 1255-1261.71. Yung, B.P.K., Merry, H. and Bott, T.R., (1989), The Role of Turbulent Burstsin Particle Re-entrainment in Aqueous System, Chem. Eng. Sci., 44, 873-8 82.72. Cleaver, J.W. and Yates, B., (1976), The Effect of Re-entrainment on ParticleDeposition, Chem. Eng. Sd., 31, 147-151.73. Cleaver, J.W. and Yates, B., (1973), Mechanism of Detachment of ColloidalParticles from a Flat Substrate in Turbulent Flow, I Colloid and InterfaceSd., 44, 464-474.74. Hall, D., (1989), The Time Dependence of Particle Resuspension, I AerosolSd., 20, 907-910.75. Hall, D. and Reed, J., (1989), The Time Dependence of the Resuspension ofParticles, I Aerosol Sci., 20, 839-842.References 8576. Vatistas, N. T., (1992), Effect of Adhesion Time on Particle Deposition:Reentrainment and Rolling, mci Eng. Chem. Res., 31, 1549-1554.77. Hubbe, M.A., (1985), Detachment of Colloidal Hydrous Oxide Spheres fromFlat Solids Exposed to Flow, Colloids and Surfaces, 16, 249-270.78. Tan, C., Bowen, B.D. and Epstein, N., (1987), Production of MonodisperseColloidal Silica Spheres: Effect of Temperature, .1 Colloid and Interface SeE.,118, 290-293.79. van Blaaderen, A. and Vrij, A., (1993), Synthesis and Characterization ofMonodisperse Colloidal Organo-silica Spheres, I Coioid and Interface Sd.,156, 1-18.80. Fitch, R.M. (ed.), (1971), Polymer Colloids, Plenum Press, New York.81. Watillon, A. and Dauchot, J., (1968), Optical Properties of Selenium Sols, IColloid Interface SeE., 27, 507-5 15.82. Demchak, R. and Matijevic, E.J., (1969), Preparation and Particle SizeAnalysis of Chrominum Hydroxide Hydrosols of Narrow Size Distribution, IColloid Interface SeE., 31, 257-262.83. Brace, R. and Matijevic, E., (1973), Aluminum Hydrous Oxide Sols, I Inorg.Nuci. Chem., 35, 3691-3705.84. Stober, W., Fink, A. and Bohn, E., (1968), Controlled Growth ofMonodisperse Silica Spheres in the Micron Size Range, I Coioid InterfaceSd., 26, 62-69.85. Matijevic, E., Budnik, M. and Meites, L., (1977), Preparation and Mechanismof Formation of Titanium Dioxide Hydrosols of Narrow Size Distribution, IColloid Interface SeE., 61, 302-311.86. Pearson, E.S. and Hartley, H.O, (1966), Biometrika Tables for Statisticians,Vol. 1, 3nd Ed., Cambridge University Press, Cambridge.87. Flachsbart, H. and StOber, W., (1969), Preparation of Radioactively LabelledMonodisperse Silica Spheres of Colloidal Size, I Colloid Interface SeE., 30,568-373.References 8688. Riley, D.J. and Carbonell, R.G., (1993), Mechanisms of Particle Depositionfrom Ultrapure Chemicals onto Semiconductor Wafers: Deposition from BulkLiquid during Wafer Submersion, J Colloid Interface Sd., 158, 259-273.89. Moore, W.J., (1962), Physical Chemistry, 3rd Ed., Prentice Hall, EnglewoodCliffs, N.J.90. Vasak, F., Bowen, B.D. and Hou, L., (1990), Program for AutomaticProcessing of Sessile Drop Profiles for Contact Angle and Interfacial TensionEvaluation, Technology Today, 3, 170.91. Mickley, H.S., Sherwood, T.K. and Reed, C.E., (1957), Applied Mathematicsin Chemical Engineering, 2nd Ed., McGraw-Hill, New York.92. Guttman, I. and Willis, S.S., (1965), Introductory Engineering Statistics, JohnWiley and Sons, New York.93. Visser, J., (1988), Adhesion and Removal of Particle I, in Fouling Science andTechnology, L.F. Melo et al. (eds.), 87-104, Kluwer Academic Publishers, theNetherlands.94. Visser, J., (1988), Adhesion and Removal of Particle I, in Fouling Science andTechnology, L.F. Melo et al. (eds.), 105-123, Kluwer Academic Publishers, theNetherlands.95. Turner, C.W., (1993), Rates of Particle Deposition From AqueousSuspensions in Turbulent Flow: A Comparison of Theory with Experiment,Chem. Eng. Sci., 48, 2189-2195.96. Parkins, W.E., (1961), Surface Film Formation in Reactor Systems, inProceedings of the Tripartite Conference on Transport of Material inPressurized-water Nuclear Systems., Chalk River, Canada, Report AECL1265, Paper 9, Atomic Energy of Canada Ltd.97. Kern, D.Q. and Seaton, R.E., (1959), A Theoretical Analysis of ThermalSurface Fouling, Brit. Chem. Eng., 4, 25 8-262.98. Epstein, N., (1981), Fouling in Heat Exchangers and Fouling: TechnicalAspects, in Fouling of Heat Transfer Equipment, Somerscales, E.F.C. andKnudsen, J.G., eds., 701-734 and 31-53, Hemisphere, Washington.References 8799. Visser, J., (1970), Measurement of the Forces of Adhesion BetweenSubmicron Carbon-Black Particles and A Cellulose Film in Aqueous Solution,J Colloid Interface Sd., 34, 26-3 1.100. Crittenden, B.D., (1988), Chemical Reaction Fouling of Heat Exchangers, inFouling Science and Technology, Melo, L.F., Bott, T.R. and Bernardo, C.A.,eds., 315-332, Kluwer Academic Publishers, the Netherlands.101. Brenner, H., (1961), The Slow Motion of A Sphere Through a Viscous FluidTowards a Plane Surface, Chem. Eng. Sci., 16, 242.102. Hodgeman, C.D. (ed.) (1962), Handbook of Chemistry and Physics, 44th Ed.,p.2691, Chemical Rubber Publishing Co., Cleveland, Ohio.103. Melo, L.F. and Pinheiro, J.D., (1988), Particle Transport in Fouling Caused byKaolin-Water Suspensions on Copper Tubes, Canadian .J Chem. Eng., 66, 36-41.104. Wiersema, P.H., Loeb, A.L. and Overbeek, J.Th.G., J., (1966), Calculation ofthe Electrophoretic Mobility of a Spherical Colloid Particle, .1 ColloidInterface Sci., 22, 78-87.105. Shah, R.K. and London, A.L., (1978), Laminar Flow Forced Convection InDucts, Academic Press, Inc., New York.Appendix A 88Appendix ATHEORETICAL CONSIDERATIONS ON PARTICLE DEPOSITIONA.1 LAMINAR FLOWSBowen (1) developed a theory of particle deposition for fuliy developed laminarflow through parallel-plate channels. In the present study, fine particle deposition ontoa rectangular channel was investigated. In this section, Bowen’s theory for parallel-plate channels is modified to apply to the case of a rectangular channel. Thismodification was carried out originally by Vasak (personal communication).__________I 2aFigure Al. A rectangular ductThe fully developed velocity profile for rectangular ducts is given by Shah andLondon (105) asl6a2 2fRe 1 ziF cosh(nity/2a)1 (nitz’u =— u _(_l)211_ icosl—i [A.!]X 3 2 m 3 iit de n=1,3,... n [ cosh(nitb/2a)j . 2a JAppendix A 89where a and b represent the half-width and half-thickness of the rectangular channel,respectively, de the hydraulic diameter of the actual duct, u, the average fluid flowvelocity, andf Re 24[1— 1.3553(b / a)+ 1.9467(b / a)2 + 1.7012(b / a)3+ O9564(b la)4 — O.2537(b / a)5]According to Bowen (1), the particle balance over a differential volume of thecore region is given byu —=D — [A.2]Xwhere C the suspension concentration.Assuming that the concentration boundary layer does not grow significantlyfrom the wall then, near the wall, the fine particle velocity in the x direction, u,, isapproximatelyu=c’y [A.3]where the constant c’ is given by[A.4]dy ybOIn dimensionless terms, the convection-diffusion equation [A.2] can be writtenAppendix A 90[A.5]3 Urn 6Y ã2where 0 = 0(’y, ) = C/C0, = y/b, and y = (D/4umb)(8xI3b).By comparing Equation [A.5J with Equation [12], the constant 2 in the parallelplate development should be replaced by (2b/3)(c’/um) for flow in a rectangular duct.The dimensionless mass transfer controlled particle deposition rate developed byBowen (1) for a parallel-plate channel (Equation [16]) is thus modified for arectangular duct as((2bI3)(C’/Um)/9Y) [A.6]T(4 / 3)where16a 2fRe-(—1)tanh(nitb/2a)Urn 7t de n=1,3,.. n 2aThe deposition rate is= [.!L_J.O.6163.__J(P)C0 [A.7]3Um wx bwhere Q is the suspension flow rate, w the width of the experimental channel, x thelongitudinal distance, Drn the bulk particle diffusion coefficient, b the half-thickness ofthe experimental channel, and C0 the homogeneous suspension concentration at thechannel inlet.Appendix A 91A.2 SUMMARY OF MAJOR THEORIES ON TURBULENT PARTICLETRANSPORTType of Range oftheoretical model application Additional featuresInvestigator Remarks and conclusionsFriediander and Particle diffusion- Where particle inertia U,,, = 0.9u = u. Theory makes questionableJohnstone7 projection to the wall, is the main deposition c,,, = e. assumptions, which tend to limit itsadopting the concept mechanism Multilayered wall concept application in cases other thanof stopping distance those were particle inertia is thedominant mechanismOwen12 Particle diffusion- Where gravity effects c5,, oc e,. Lengthy expressions for the particleprojection to the wall, influence particle Multilayered wall concept deposition rate on the floor, roofincorporating the deposition and side walls are derived, withouteffect of gravity the support of reliable experimentalevidenceDavies” Inertial and diffusive Intended to cover=r,,. Theory underpredicts deposition(eddy and molecular) all cases, ie Multilayered wall concept. rates and is complex to use inmechanisms considered, 0.001 d,, 100 pm Empirical aquaxion for routine design, but provides morewhile retaining the in the absence of r. to apply across the physical insight into the occurringôoncept of stopping extraneous forces entire boundary layer phenomena than the previous theoriesdistanceDeal’5 Similar to Davies’, Cases involving Free flight velocity is In spite of the unrealistic freewith the addition of a particles ranging from taken to be one half of flight velocities assumed, thesteady state particle molecular size to the axial fluid velocity predictions tend to fit theaccumulation near the 100 pm in experimental data morewall satisfactorily than the previoustheoriesSehmel2 Similar to Davies’, Empirical relationships The empirical The theory was tested over a narrowadopting empirical limit application of relationships adopted are range of experimental conditions,expressions for c,,,, theory to within the physically incorrect and therefore lacks generality. Theto fit experimental specified range empirical relationships undermineresults the theoryLiu and hon37 Similar to Davies’. Intended for a wide s = D5 + s. + e’. Despite the questionable assumptionsNew relationship for range of conditions, e’ = (u)2r of the theory, better fit with thea,,, introduced but reliable only available experimental data waswithin 2 < <20 obtained than the previous theoriesof Friedlander and Johnstone, andDaviesWasan Similar to Beal’s. Cases involving e. = a,,,; two layered Ihe expressions ot particleet al9 a. expressed as a particles of wall region: deposition rates are based on masscontinuous function 4<< 100pm 0 y ÷ 19.75 and momentum analogies, andy * 19.75 a... = a,,,. Later work revealedthat these analogies are not validHutchinson Probabilistic theory- Intended to cover all e, 0 a.. Simple The theory is more realistic thanet a12° random walk concept cases, with no definition of the all the previous theories and‘ extraneous forces relevant turbulence satisfactorily predicts depositionpresent parameters rates of particles of d 10 pmCleaver and Probabilistic theory, All cases not involving Quasi-steady two- Provides physical insight into theYates43 including the extraneous forces dimensional flow picture mechanics of deposition, withoutoccurrence of ‘bursts’ near the boundary wall taking into account particlenear the boundary wall behaviour in the turbulent core.Sasisfactory agreement betweenpredictions and availableexperimental dataReeks and Similar to Hutchinson All cases involving Diffusion appears to stop The theory is very difficult toSkyrme” Ct al’s in principle particles outside the at an arbitrary ‘diffusion verify experimentally and thereforemolecular range edge’ near the wall its validity remains uncertainPapavergos and Combined Hutchinson Cases involving all Two stages for particle Theory examines- particle behaviourHedley47 et al’s with Cleaver particle sizes, and deposition: from the turbulent core to the walland Yates’ theories free from (a) macro-mechanism until its final deposition.extraneous effects (b) micro-mechanism satisfactory agreement withexperimental dataFirst published by The Institution of Chemical Engineers in Chemical Engineering Research & Design, pp. 275-295, Sept. 1984Appendix B 92Appendix BEXPERIMENTAL RESULTSB.1 CALIBRATIONSB.1.1 Conductivity of NaC1 SolutionsAt high electrolyte concentrations, the electrolyte conductivity was assumed tobe mainly due to the presence of NaC1. A calibration curve relating the concentrationofNaCl in solution to the measured conductivity was obtained in the following manner.Various NaCl solutions of known concentrations were prepared and their temperature-corrected conductivities were measured with the Siebold Conductivity meter. Thecalibration results are illustrated in Figure B. 1.B.1.2 Flow RateThe rotameter used in the experiment was calibrated by timing and weighing theamount of water collected at a known temperature. These calibration results arepresented in Figure B.2.B.1.3 Electrophoresis ApparatusB. 1.3. Jlnterelectrode DistanceThe inter-electrode distance in the micro-electrophoretic cell was required toevaluate the potential gradient applied for mobility measurements. If R and A. are theelectrical resistance and conductivity, respectively, of a solution placed in the cell, thenthe effective inter-electrode distance is given by = RXA, where A is the cross-sectional area of the viewing region.Appendix B 93i03-0-E1O21=0Dz00I ai1IJ— , • I ii.,.— . I I I 11111 I I I 11111io io io4 io2NaCI CONCENTRA11ON (moles/L)Figure B. 1 NaC1 concentration versus measured conductivityAppendix B 94200 -__150-C)ci)0)100-0-IIi-50-0 1 2 3ROTAMETER READING (U.S. gal/mm)Figure B.2 Rotameter reading versus flow rateAppendix B 95Two flat cells were calibrated, one as a spare. The width of the rectangularsection of the cell was measured by means of a traveling microscope. The cell wasplaced in an upright position on a horizontal level and was then filled with a coloredpotassium permanganate (KMnO4)solution. Several measurements were taken for anaverage value.The thickness of the cell was measured using the micrometer focusingadjustment of the electrophoresis microscope. The cell and the cell bath were filledwith distilled water and the microscope was focused at both the far and near innersurfaces that determine the thickness. All measurements were made at the center of thecell in the viewing plane and several measurements were also taken in this case andaveraged.The product R in the expression for the interelectrode distance was determinedby measuring the resistance across a solution of known conductivity placed in the cellwith the electrodes in position. A solution of known conductivity was prepared bycarefhlly dissolving 7.4555 g of KC1 in 1 liter of distilled and deionised water. Aquantity of this 0.0 iN solution was placed in the cell to fill it. The electrodes were putinto position and the cell clamped in the electrophoresis water bath. The water bath andits contents were allowed to stand for 12 hours to ensure thermal equilibrium.The interelectrode resistance for each cell was determined as follows. Thetemperature of the bath (and its contents) was measured, and the resistance across thecell was obtained by means of a Beckman Model 16B2 A.C. conductivity bridgeoperating at 1000 Hz. to avoid polarization. The conductivity of the solution at theAppendix B 96equilibrated temperature (25 °C) was then obtained from standard sources (102). Theresults from these measurements is given in Table B. 1.Table B.1Interelectrode DistancesCell # 1 Cell #2Cell width, cm 0.98 10 ± 0.0012 1.0084 ± 0.0019Cell thickness, cm 0.1071 ±0.0025 0.1041 ±0.0036A,cm2 0.1051 0.1050R,ohms 51000 516002, ohmcm 1.409x103 1.409x103t, cm 7.545 7.634B. 1.3.2Eyepiece GraticuleThe graticule spacing in the eyepiece of the electrophoresis microscope overwhich the particles were timed during mobility measurements required calibration. Thiswas done by observing a “stage micrometer”, a glass slide which is engraved with 1 mmdivided into 100 equal parts. The stage micrometer was held in a vertical position inthe water bath filled with distilled water. Several measurements were taken andaveraged, from which one graticule spacing was found to be 60.67 ± 0.05 rim.Appendix B 97B. 2 Sample CalculationsB.2.1 DoubJe Layer Thickness, 1/icThe reciprocal double layer thickness is given byI 22”I 8itne0z [B.1]ekT )where n is the counterion concentration (number of ions/cm3), z is the valence of theion, e0 is the electronic charge, E is the dielectric constant of the medium, k is theBoltzmann constant, and T is the absolute temperature. At 25 °C and for univalentcounter-ions, Equation [B. 1] reduces to (102)ic = 0.3286 x 108 x C [B.2]where C is the counter-ion concentration in molesfL. A knowledge of C is thus vital tothe calculation of ic. The nature of the ionic content of the initial suspensions was verycomplex and its estimation was based on the measured conductivity and certainassumptions. In the case of freshly prepared suspension it was assumed (102) that thecontributions of the individual species to the overall conductivity through theirmobilities were additive, in which case (102)[B.3]1000where is the conductivity of the solution, N0 is Avogacko’s number, C, theconcentration of ionic species, Z the valence of the ion, e0 the charge of an electron,and U, the mobility of the ion.At higher solution conductivities, such as in the series III runs where theelectrolyte concentration was adjusted by adding NaC1, the concentrations of ionicAppendix B 98species were readily determined by measuring the conductivity of the suspension andusing the concentration-conductivity calibration curve given in Figure B. 1.In the series II runs, for instance, the suspension was freshly prepared and thelikely ionic species present were H and OW from the complete dissociation of water,as well as NH, HSiO3 and HC03, from the incomplete desorption of NH3,dissolution of silica and absorption of C02, respectively.Consider for example run 11-3. At the start of this run,A 1.38 x lO6mho/cmp11=5.6[H] = 1056 = 2.5 12 x 106 molesfLTherefore,[OW] = 10’/[H] = 0.004 x 10 molesfLThe mobility of HSiO3 could not be found in the literature and thus it wasassumed to have a value similar to that of HC03. Therefore, HC03 and HSiO3 werelumped together as the single species HC03 in the calculations.If[NH]=y x 106 molesfLthen, to maintain electroneutrality,[HC03]=(y + 2.5 12 - 0.004) x 106= (y + 2.508) x 106 molesfLThe relevant ionic mobilities at 25 °C are (89)Appendix B 99UH+ =36.30X10 cm2/volt -secUOH_ =20.50X10 cm2/volt -secU± = 7.60 X10 cm2/volt -secUHC0_= 4.60 X10 cm2 I volt -secSubstituting these values into equation [B.3], one obtains6 023 1023 1 0623 10_19•* [2.512x36.30+0.004x21.50+7.6y1 o+4.6(y +2.508)]x io x 10_6= 1.38 x 10_6 =and solving for y yields[NH] = 3.294 x 106 moles/LTherefore[HC03]= (3.294 + 2.508) x 1o5.806 x 10 molesfLThe total counterion concentration C is obtained asC = [H] + [NH]= (2.5 12 + 3.294) x 106= 5.806 x 106 molesfLand from Equation [B•2],K0.3286X 108x(5.806x 106)U2= 7.918 x i04 cmAppendix B 100B.2.2 Particle C-potentialWiersema et al.’s (104) tabulated numerical results were employed in convertingthe particle electrophoretic mobility measurements to a-potentials. Dimensionlessvariables were used in their results, thus the dimensionless electrophoretic mobility,E=61reoUeKT=0.7503 x 104U [B.4]the dimensionless double layer thickness,q0=ica [B.5Jthe dimensionless c-potential,—Yo-:= at 25 °C [B.6J25.69and the dimensionless mobilities of the positive and negative ions in suspension,NeKTZm= —± 6r X°1.1286at 25 °C for univalent cations and anions [B.7Jwheree0 = the unit of electrostatic charge, (statcoulombs)= viscosity of the solution, (glcm-sec)6 = the dielectric constant of solutionK = the Boltzmann constant, (ergs/K)T = the absolute temperature, (K)Appendix B 101U = the measured electrophoretic mobility, (cm2/volt-sec)= the particle -potentia1, (mV)K = the inverse double layer thickness, (cm’)a = the particle radius, (cm)N Avogadro’s constantZ± = the valences of the cations and anions, respectively, in solution= the limiting ionic conductances of the ions in solution, (cm2/oh -equiv.)The dimensionless variables have been tabulated in the form ofE=E(y0,qm+) [B.8JThus for a known value of q0, E and Yo can be obtained from interpolation of thetabulated results in Table I of Wiersema Ct al. (104). Also, since this table shows onlythe results obtained for m = 0.184, the interpolated values of E must be corrected tocorrespond to the actual m÷ and m. Each corrected value E’ is given byE’= E+(m —0.184)---+(m — 0.184).— [B.9]where the value is interpolated form Table III of reference (104). The value of Yocorresponding to the experimental value of E’, Eexpt, is then extracted from a final plotof E’ versus y0.Run 11-3 is used as a sample for calculation, whereU = 2.44 x iOcm2/volt-secand the double layer thickness has been evaluated in Section B.2. 1. From Equation[B.4],Appendix B 102Eexp = 0.7503 X i04 x 2.44 x i0= 1.8307Alsoq0 = ica = 7.918 x i04 x 0.4405 x= 3.488The dimensionless mobilities m are then obtained from the numerical averages ofFor various ions known to be present in the solution, the individual limitingionic mobilities (104), +°, as well as their corresponding values of m+ calculated fromEquation [B.7] are listed below:ion[H] 349.82 0.0368[NH] 73.40 0.1750[OW] 198.00 0.0649[HC03] 44.43 0.2890Subsequently, from the concentrations of the various species in the solution obtained inSection B.2. 1, the number average values of m are2.512x10 3.294x106m = xO.0368+ xO.175+ 5.806x10 5.806x10= 0.1150.004 x 106 5.802 x 10_6m = xO.0649+ xO.289-5.806x106 5.806x106= 0.289Appendix B 103Values for E are obtained by interpolation of Wiersema et al. ‘s Table I (104) atq0= 3.488 for various y0. Also, values for 0E/ôm÷ and ôEI8m are obtained for the samevalues of y0 by graphical extrapolation. E is then corrected to E’ through equation[B.9] as listed in Table B.2.Table B.2E versus Yo (Run 11-3)y0 E ÔE/8m+ 8E/ãm E’1 1.10 -0.0894 -0.1674 1.0942 2.00 -0.1883 -0.3979 2.2043 2.65 -0.2728 -0.7464 2.6924 3.05 -0.3634 -1.2537 3.0405 3.20 -0.4398 -1.8345 3.1826 3.20 -0.5403 -2.5834 3.160The E versus Yo curve is then plotted. The corresponding Yo value for Ee,t (1.8307) is then read off from this plot as 1.8655. The zeta potential of the particles inthis run is thus obtained from Equation [B.6] as=25.69x 1.8655=47.95mVAs indicated by the direction of the particles in relation to the applied voltage duringthe mobility measurements, the particle c-potential is in fact negative.Appendix B 104B.2.3 Wall C-potentialThe wall C-potential was determined by a combined electrophoresis-electroosmosis experiment as described in Section 3.5. For a rectangular cell, Bowen (1)derived the expression for calculating the wall a-potential as[B.10]where t. is the wall potential (V), ji the solution viscosity (glcm-sec), a and b the half-width and half-thickness of the rectangular cell, respectively, the permittivity(coulombs/volt-cm), USL and U1 the electrophoretic mobility measured at thestationary level and at the mid-plane (cm2/volt-sec), respectively.For cell #1 and at 25 °C,= 2.092 x x (USL - U112) mV [B. 11]while USL and U112 are calculated from[B.12]Etwhere n the number of grid spaces over which the particles were timed (n=2 in all themeasurements), the length of each grid space (cm), the interelectrode distance (cm),E the applied potential difference (volts), and I the average electrophoretic timemeasured at the stationary level and mid-plane (corresponding to USL and U112,respectively).Consider Run 11-3 as an example, wheren=26Appendix B 105tSL 7.61 sect112 5.l0secE =50V= 6.6067 x iO-3 cmte = 7.545 cmFrom Equation [B. 12],u — 2x 6.067 x i03 x 7.545SL 50x7.612.41 x 10 cm2 / volt - Secand—2x6.067x103x7.545i/2 50x5.10= 3.60 x 10 cm2 I volt - secUsing Equation [B. 11], the wall c-potential is thus calculated as= 2.092 x iO x (2.41 - 3.60) x 10= -24.89 mVFrom the direction of the particle motion relative to the direction of the appliedpotential gradient, it is known that the wall -potentiaI is in fact positive.B.2.4 Initial Deposition RatesB. 2.4.1 Laminar Flow CaseConsider for example Run 11-3.a = 0.5cmb = 0.6cmde = 1.09 cmAppendix B 106Re = 1636Q = 16.09 cm3/secw = 1cmx 0.5cmk = 1.38 x 1016 erg/KT =298K8.90 x io glcm•secv = 8.94 x 1 cr3 cm2/secC0 = 1.64 x 1 o particles/cm3d = 8.81 x cmThe particle Brownian diffusivityDkT— 6iqi(d/2)— 1.38x106x298— 6xitx8.90x103x(8. 1x15/ )= 5.57 x 10 cm2 / seeandfRe = 24[1— 1.3553(0.6/0.5)+ 1.9467(0.6/ 0.5)2 + 1.7012(0.6/ 0.5)+ 0.9564(0.6/ 0.5) — 0.2537(0.6/ 0.5)]= 155.25ThusAppendix B 107c’ 16a2 2fRe-(—1)tanh(n3tb/2a)Urn It d n=1,3,... n 2a= 16x(0.5)22x155.25 tanh(nitx0.6/2x0.5)it3 (l.09) n3 2 x 0.5=8.412 mTherefore, the particle initial deposition rate is16.09 (5.57x101644107i.. 3 ) ‘1.0x0.5} 0.6 )= 170.01 particles/cm2.secB.2.4.2 Turbulent Flow CaseEpstein model Consider for example Series III. Use 4max = 284.96 as referencecondition,v = 0.166 rn/secRe = 2021C0 = 1.644 x i07 particles/cm3m = 7.805 x 1013 g/particleD = 5.57 x 1 o cm2/secv = 8.94 x 1 o cm2/sec= C0xm= 1.644 x iO x 7.805 x 1O g/cm3Sc = vfD,= 8.94 x 10/5.57 x= 1.61 x 106From Equation [71Appendix B 108=(cb—cSv’24v CjThusC. = Cb/3= 1.283 x 10/3= 4.280 x 10.6 g/cm3, at the critical conditionand= 280.66 x 7.805 x iO2.2 x 10b0 g/cm2-secThereforekm = - C,)= 2.2 x 10bO/(1.28 x i05- 4.28 x 106)= 2.60 x 1 o- cmlsec, at the critical conditionBut1_____—k1ScXAdopting the classical Blasius equation for smooth pipe flow, the friction factor isf = 0.0791/Re25thenAppendix B 109v* =10.0791=v IV 2Re°5=0.166 I 0.07912(202l)°= 1.283 x 10_2Thusk=kmSC1.283 x 10_22.60 x i0 x (1.61 x 1O6)= 3.582x 10_2Thereforek— 3.582x 102ScFrom Equations [4] and [7], one obtainsk1 = 3.582 x 102 x (1.61 x 106)2/3=4.907x 102and— 4.907 xio2k22(1.276 X102)=1.181 X108 sec3/mFrom Equation [6], the particle initial deposition rate isAppendix B 110C,— k1v + k2vCb4.907 x 102v+1.181x 108 x vConsider for example run 111-7 wherev = 0.3 84 rn/secRe = 4683ThenI 0. 0792v=0.384 i 2(4683)025= 0. 0266Therefore, the particle initial deposition rate isCb‘‘—1 2k1v + k2v1.283 x4.907 x 102 x (0.027)’ + 1.181 x 108 x (0.027)2=1.26x10’° g/cm2.sec— 1.26x1(T’° g/cm2.sec— 7.805 x io’ g/ particles= 161.65 particles / cm2•secAppendix B 11]Berger andHauc model Consider for example run 111-4, Re = 2021. FromEquation [2], one obtains4) == DCb.00165Re086ScXde5.57x109x1.64xl700165(2 2)O8161106= 113.11 particles/cm2 secB.3 ERRORSB.3.1 Errors in measurementThe accuracy with which the experimental results were obtained depended onseveral factors. Experimental errors can be attributed to such factors as variations inparticle size, incompletely dispersed suspensions, deposition in the entrance section,roughness of the experimental channel surface, fluctuations in suspension flow rate, anduncertainties in the various measurements. Another source was associated with thetreatment of the data, such as the graphic method used to determine the initialdeposition rate.B.3.2 Errors in Electrophoresis MeasurementsThere are wide ranges of electrophoretic times measured (see Section [B .4]) forparticles in one set of measurements. This is due to a number of inherent problemsassociated with such measurements (1). Errors due to Brownian motion and depth-offield are difficult to eliminate and therefore constitute the primary source of error.Appendix B 112To determine the error limits, it will be assumed that the measuredelectrophoretic times are approximately normally distributed and the 95% confidencelimits based on the student t-distribution will be adopted to predict the closeness of thesample mean to the population mean. Therefore, if the measured electrophoreticmobility is U, the 95% confidence interval for U is (92)2!L.kN—1,O.O25T 3/where tNI,o025 is the t-distribution with N-i degrees of freedom at the 95% level ofprobability, N is the sample size and a the sample standard deviation. Theelectrophoretic mobility is a function of the measured electrophoretic time; theelectrophoretic mobility variance is thus also a function of the variance of theelectrophoretic times. Mickley et al. (91) have determined the standard deviation for y= f(x1, x2, ..., x) as[B.14]By substituting Equation [B. 121 into Equation [B. 14], one obtainsnetuE?t [B.15]where the standard deviation of t is given by (92)N(t, _)2i=1 [B.16]N-iA table of the t-distribution is given by Pearson and Hartley (86). Therefore,from Equations [B. 131 and [B. 15], together with the t-distribution from reference (86),Appendix B 113the range of mobilities are estimated and consequently the errors in the particle -potential are calculated.Considering Run 11-3, whereN 111 =7.61= 0.7633n =2E =50Vtg = 6.6067 x iO cm7.545 cmand using Equation [B. 15],2 x 6.6067 x iO x 7.545 x 0.7633= 50x(7.61)2=0.263x10 cm/volt-secWhen N = 11, t 0.025 = 2.201 (86), Thus from Equation [B.13], the 95%confidence interval on USL, L\USL, is±2.201x0.263x1011)= ±0.175x 10and using Equation [B.4], the confidence limits on E areAE=±0.7503 x x 0.175 1O=±0.131Appendix B 114From Section B.2.2, E was found to be 1.83 1, the range of E then becomes E = 1.700andE= 1.962The corresponding Yo values obtained from a plot of E versus y are 1.61 and1.95, respectively. It follows from Equation [B.6] that the confidence limits on theparticle a-potential are -41 mV and -50 mV, respectively. Because the E’ versus Yocurves are not linear, the confidence limits are thus not symmetrically positioned aboutthe mean value.B.3.3. Errors in Electro-osmosis MeasurementIn Section B.2.3, the wall c-potential is given as= 2.092 x 10 x ((-JSL - U112)where USL and U112 are given by Equation [B. 121 corresponding with SL and 1/2’respectively, c and are determined by Equation [B. 15] corresponding to cand 112’ respectively.Assuming that the USL and U112 are approximately normally distributed, then the95% confIdence limits on z4, can be calculated from the equation given below(92)= ± 2.092 x x(t0025).[+ 2][B. 17]SL 1/2whereP2_____[B.18]M NSL —1 N1,2—1andAppendix B 115a2/N2SL [B.19]a a—- + —uNSL N112Consider Run 11-3 as an example, wheren 2NSL= 11tSL = 7.61a- = 0.7633tsLN112= 10t112 = 5.10a- = 0.2325LI’2E =50Veg = 6.6067 x i0 cmte = 7.545 cmFrom calculations in Section B.2.3, USL and U1,2 were 2.41 x iO and 3.60 x iOcm2/volt-sec, respectively, a was 0.263 x 1 Ocm2/volt-sec, and— 2x6.6067x103x7.545x0.2325aU,—50x(5.10)2= 0.178x 10 cm2 /volt-secTherefore, from Equations [B. 18] and [B. 19],Appendix B 116(0.263x10)/1— (O.263x10) (0.178x104211 10=0.665and1 (0.665)2 (1_0665)2M 11—1 10—1orM= 17.6From Table 12 of reference (86), t005 = 2.106 corresponding to M = 17.6.Therefore, by Equation [B. 17], the 95% confidence limits on AC, arezC=±4.28 mVAppendix B 117B. 4 EXPERIMENTAL DATAThe symbols used in the tables are defined below.CONDI initial conductivity of suspension (p.mho/cm)CONDF final conductivity of suspension (jmho/cm)CSI initial concentration of suspended particles (particles/cm3)CSF final concentration of suspended particles (particles/cm3)CW concentration of deposited particles (particles/cm2)DCW 95% confidence limits on CWKA ratio of particle radius to double layer thickness, i.e. icaPHI initial pH of suspensionPHF final pH of suspensionQAVG average flow rate of suspension (cm3/sec)QI initial flow rate of suspension (cm3/sec)REAVG average Reynolds numbers of flowing suspensionREI initial Reynolds number of flowing suspensionTEMPAVG average suspension temperature (°C)TEMPI initial suspension temperature (°C)UPI initial electrophoretic mobility of particles (cm2/volt-sec)ZPI initial zeta potential of particles (my)ZWI initial zeta potential of wall (my)Appendix B 118RUN I and VIRUN I-i 1-2 1-3 1-4 VT-iQI 38.5 39.5 130.5 132 35QAVO 37.5 38.5 131.4 131.5 34.8RET 3929 4031 13318 13471 3572REAVG 3827 3929 13410 13420 3551TI 23.5 24.0 24.2 24.0 23.8TAVG 23.5 24.0 25.4 25.0 24.0CONDI 1.24 1.43 1.32 1.48 21.0CONDF 1.36 1.43 1.74 2.40 22.0PHI 5.8 5.6 5.7 5.7 9.5PHF 5.8 5.7 5.7 5.7 9.5CSI(x107) 1.117 1.117 1.761 1.761 1.644CSF(x107) 1.105 1.112 1.721 1.701 -KA 3.12 3.51 3.49 3.11 15.56UPI 3.42 2.89 4.18 4.63 3.56ZPI -71.26 -73.83 -70.36 -78.25 -45.61ZWI 32.14 30.93 30.31 26.44 -0.94CW - - - 1.188 x 106DCW - - 1.02 x i05Appendix B 119RUN111218923.624. 1 2 3 4 5 6 7 8 9 10 11QI 6.50 10.10 16.14 19.45 19.90 34.66 38.50 99.00 120.22 133.45 158.80QAVG 6.62 10.09 16.09 19.56 19.87 34.69 38.86 98.41 119.86 132.47 157.711I 663 1031 1647 1985 2031 3537 3929 10104 12270 13615 16207REAVG 674 1026 1636 1989 2021 3529 3925 10008TI 24.5 25.0 24.2 25.0 23.8 24.5 25.5 25.0TAVG 24.5 25.0 24.2 25.0 23.8 24.5 25.5 25.5CONDI 3.57 1.38 1.28 1.42 1.90 1.42 1.38 1.66CONDF 2.78 1.69 1.94 1.42 1.95 1.48 1.55 1.54PHI 5.6 5.7 5.7 5.5 5.7 5.6 5.7 5.7PHF 5.6 5.7 5.6 5.6 5.7 5.6 5.7 5.7CSI(x107) 1.644 1.644 1.644 1.644 1.644 1.644 1.644 1.644CSF(x107) 1.642 - - 1.640 - - - 1.604 - - -KA 3.49 3.49 3.49 3.59 3.48 3.11 3.49 3.73 3.49 4.65 3.56UPI 3.56 3.32 2.59 2.85 2.90 3.07 4.18 3.08 2.58 3.00 4.18ZPI -70.36 -71.26 -72.33 -72.83 -71.88 -67.41 -71.26 -81.13 -71.26 -89.84 -81.25ZWI 28.99 30.03 24.89 30.03 22.48 25.55 37.61 26.36 23.58 24.93 23.54CW(x106) - - - - 1.48 2.96 - - - 5.06 0.00DCW(x105) - - - - 2.83 2.70 - - - 1.89 0.001347224. B 120RUN ifiRUN 1 2 3 4 5 6 7 8 9 10 11QI 9.50 12.00 16.20 21.00 25.00 32.00 46.20 54.50 70.00 84.50 90.00QAVG 9.46 11.99 15.77 19.87 24.60 31.54 46.05 54.25 69.08 84.53 91.47RE 970 1225 1653 2143 2551 3266 4715 5562 7144 8624 9185REAVG 962 1219 1604 2021 2502 3208 4683 5517 7025 8579 9302TI 24.5 25.0 24.2 25.0 23.8 24.5 25.5 25.0 23.6 24.0 25.0TAVG 24.5 25.0 24.2 25.0 23.8 24.5 25.5 25.5 24.0 24.6 26.2CONDI 68.0 67.0 68.0 71.0 70.0 73.0 70.0 69.0 71.0 73.0 72.0CONDF 72.8 71.0 68.0 71.0 70.0 73.0 71.0 70.0 71.0 73.0 72.0PHI 5.7 5.7 5.7 5.6 5.7 5.6 5.7 5.7 5.7 5.6 5.6PHF 6.0 5.7 5.7 5.7 5.7 5.6 5.7 5.7 5.6 5.6 5.7CSI(x107) 1.644 1.644 1.644 1.644 1.644 1.644 1.644 1.644 1.644 1.644 1.644CSF (x107) 1.642 - - - - - - 1.644 - - -KA 34.56 35.75 35.01 35.75 35.46 36.19 35.75 35.46 35.75 36.19 35.75UPI 3.56 3.32 2.59 2.85 3.07 4.18 3.08 2.58 3.00 4.18 3.08ZPI -50.61 -47.27 -36.74 -40.59 -43.93 -62.68 -44.44 -37.25 -42.39 -62.68 -41.66ZWI 2.41 18.36 10.86 23.01 24.89 6.79 9.98 9.49 8.12 6.79 22.36CW(x10) 4.46 3.79 - - - 2.78 - 9.99 - - -DCW(x105) 1.37 4.65 - - - 1.02 - 0.71 - - -Appendix B 12]1 .2 -FE 0.8- IC)U)C.)I10CU 0.6-b f>< 0.4-(I10.2.200. I • I • I • I • I • I •0 20 40 60 80 100 120 140TIME (mm)Figure B.3 Deposition curve. Run 11-3cx106(particles/cm2)000o0)III 100•-a10!-t CDLr’.00ICD— —o000600000!!0Im00000,B0__0080091_01•000 -‘I0Appendix B 1230.6 -o.—-0.5-____0.4- —C.)C.) —0.3- oCDo 02->< 0 — c 0(_) — 00 001- 00I • I I • I •0 10 20 30 40 50TIME (mm)Figure B.5 deposition curve. Run 11-5Appendix B 1242.0E0Cl)U)C.)Cu81.0CD0x0.50.01.50TIME (mm)Figure B.6 Deposition curve. Run 11-7Appendix B 1250.14 -ID0.12 -— 00.10-EC)0.08-c 0.06-0x0.04-__0.02 -0.00— I • I • I •0 10 20 30 40TIME (mm)Figure B.7 deposition curve. Run 11-8Appendix B 1260.20 -0.15 -o —c%1EC)C’)_______0 CG)C)___E 0.10- COmf0 0Cx(1 0.05-0 0000.00- I I I •0 20 40 60 80 100TIME (mm)Figure B.9 Deposition curve. Run 11-9Appendix B 127—0.04 -CNEC)0.03-, 0.02-D0.01 -0.00-. I • I • I • I •0 20 40 60 80 100 120TIME (mm)Figure B.9 Deposition curve. Run 11-10Appendix B 1280.6 -00000c..jC.,0C cio— 04-C.)CU —CI -oCx —0.2-__0CooCO0C0.0_D• I I •0 10 20 30 40TIME (mm)Figure B. 10 Deposition curve. Run 111-3Appendix B 1290.5 -o0o00 0 004— 00 O0C...! 000E —Co C0 0U) 0.3- 00Cu .0cço 0.2ocfx0.100000.0- I • I • I •0 10 20 30 40TIME (mm)Figure B. 11 Deposition curve. Run 111-4Appendix B 1300.4 -00.3 -C(NE0Coa)___—o 0E 0.2•Cu 0ID 00CoCC) 0.1• 0 C 00—C00 0 0 00.0- I I • I •0 5 10 15 20 25TIME (mm)Figure B. 12 Deposition curve. Run 111-5Appendix B 1310.35 -Co0.30-oOOO 000ci 0.25- 0EC..)0.20-cq 0.150x 00.10-0.05 -00.00—• I • I • I • I • I0 5 10 15 20 25 30TIME (mm)Figure B. 13 Deposition curve. Run 111-8Appendix B 1326-5-E0Cl) 4-ciC)Cu% 3- aDcc0xc! 2-1cxo0—,. • I • I • I • I •0 20 40 60 80 100 120TIME (mm)Figure B.14 Deposition curve. Run 111-10


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