Fundamentals of Particle Fouling in Membrane Processes

  • Bhattacharjee Subir (Civil and Environmental Engineering Department, Korea University) ;
  • Hong Seungkwan (Department of Mechanical Engineering, University of Albertit Edmonton)
  • Published : 2005.12.01


The permeate flux decline due to membrane fouling can be addressed using a variety of theoretical stand-points. Judicious selection of an appropriate theory is a key toward successful prediction of the permeate flux. The essential criterion f3r such a decision appears to be a detailed characterization of the feed solution and membrane properties. Modem theories are capable of accurately predicting several properties of colloidal systems that are important in membrane separation processes from fundamental information pertaining to the particle size, charge, and solution ionic strength. Based on such information, it is relatively straight-forward to determine the properties of the concentrated colloidal dispersion in a polarized layer or the cake layer properties. Incorporation of such information in the framework of the standard theories of membrane filtration, namely, the convective diffusion equation coupled with an appropriate permeate transport model, can lead to reasonably accurate prediction of the permeate flux due to colloidal fouling. The schematic of the essential approach has been delineated in Figure 5. The modern approaches based on appropriate cell models appear to predict the permeate flux behavior in crossflow membrane filtration processes quite accurately without invoking novel theoretical descriptions of particle back transport mechanisms or depending on adjust-able parameters. Such agreements have been observed for a wide range of particle size ranging from small proteins like BSA (diameter ${\~}$6 nm) to latex suspensions (diameter ${\~}1\;{\mu}m$). There we, however, several areas that need further exploration. Some of these include: 1) A clear mechanistic description of the cake formation mechanisms that clearly identifies the disorder to order transition point in different colloidal systems. 2) Determining the structure of a cake layer based on the interparticle and hydrodynamic interactions instead of assuming a fixed geometrical structure on the basis of cell models. 3) Performing well controlled experiments where the cake deposition mechanism can be observed for small colloidal particles (< $1\;{\mu}m$). 4) A clear mechanistic description of the critical operating conditions (for instance, critical pressure) which can minimize the propensity of colloidal membrane fluting. 5) Developing theoretical approaches to account for polydisperse systems that can render the models capable of handing realistic feed solutions typically encountered in diverse applications of membrane filtration.



  1. G. Belfort, R. H. Davis, and A. L. Zydney, The Behavior of Suspensions and Macromolecular Solutions in Crossflow Microfiltration. J Membrane Sci., 96, 1-58 (1994)
  2. M. Cheryan, Ultrafiltration and microfiltration Handbook (1999)
  3. A. L. Zydney, Protein Separations Using Membrane Filtration - New Opportunities For Whey Fractionation. International Dairy Journal, 8, 243-250 (1998)
  4. A. D. Marshall, P. A. Munro, and G. Tragardh, The Effect of Protein Fouling in Microfiltration and Ultrafiltration On Permeate Flux, Protein Retention and Selectivity - a Literature-Review. Desalination, 91, 65-108 (1993)
  5. R. H. Davis, Modeling of Fouling of Cross-Flow Microfiltration Membranes. Separation and Purification Methods, 21, 75-126 (1992)
  6. A. G. Fane and C. J. D. Fell, A Review of Fouling and Fouling Control in Ultrafiltration. Desalination, 62, 117-136 (1987)
  7. G. Tragardh, Membrane Cleaning. Desalination, 71, 325-335 (1989)
  8. R. D. Cohen and R. F. Probstein, Colloidal Fouling of Reverse Osmosis Membranes. J. Colloid Interface Sci., 114, 194-207 (1986)
  9. E. Fountoukidis, Z. B. Maroulis, and D. Marinoskouris, Modeling of Calcium-Sulfate Fouling of Reverse-Osmosis Membranes. Desalination, 72, 293-318 (1989)
  10. P. Gagliardo, S. Adharn, R Trussell, and A. Olivieri, Water Repurification Via Reverse Osmosis. Desalination, 117, 73-78 (1998)
  11. M. Nystrom, L. Kaipia, and S. Luque, Fouling and Retention of Nanofiltration Membranes. J. Membrane Sci., 98, 249-262 (1995)
  12. R. J. Peterson, Review: Composite reverse osmosis and nanofiltration membranes. J. Membrane Sci., 83, 81-150 (1993)
  13. X. H. Zhu and M. Elimelech, Colloidal Fouling of Reverse Osmosis Membranes - Measurements and Fouling Mechanisms. Environ. Sci. Technol., 31, 3654-3662 (1997)
  14. A. Braghetta and F. A. DiGiano, Organic Solute Association with Nanofiltration Membrane Surface: Influence of pH and Ionic Strength on Membrane Permeability. in American Water Works Association Annual Conference. New York, NY. (1994)
  15. P. Bacchin, P. Aimar, and V. Sanchez, Model For Colloidal Fouling of Membranes. AIChE J., 41, 368-376 (1995)
  16. R W. Field, D. Wu, J. A. Howell, and B. B. Gupta, Critical Flux Concept For Microfiltration Fouling. J. Membrane Sci., 100, 259-272 (1995)
  17. A. S. Jonsson and B. Jonsson, Colloidal fouling during ultrafiltration. Sep. Sci. Technol., 31, 26112620 (1996)
  18. R. J. Wakeman and G. Akay, Flux Decay and Rejection During Micro-Filtration and Ultra-filtration of Hydrophobically-Modified Water-Soluble Polymers. J. Membrane Sci., 91, 145-152 (1994)
  19. E. S. Tarleton and R. J. Wakeman, Understanding Flux Decline in Cross-Flow Microfiltration. 3. Effects of Membrane Morphology. Chem. Eng. Res. Des., 72, 521-529 (1994)
  20. P. Blanpain and M. Lalande, Investigation of Fouling Mechanisms Governing Permeate Flux in the Crossflow Microfiltration of Beer. Filtration Sep., 34, 1065-1069 (1997)
  21. C. Legallais, E. Dore, L. Ploux, M. Fauchet, and M. Y. Jaffrin, A Scintigraphic Study of Ldl-Cholesterol Irreversible Trapping in a Plasma Fractionation Membrane. Chem. Eng. Sci., 53, 2623 ff. (1998)
  22. E. M. Tracey and R. H. Davis, Protein Fouling of Track-Etched Polycarbonate Microfiltration Membranes. J. Colloid Inuerface Sci., 167, 104-116 (1994)
  23. K. J. Kim, A. G. Fane, C. J. D. Fell, and D. C. Joy, Fouling Mechanisms of Membranes During Protein Ultrafiltration. J. Membrane Sci., 68, 79-91 (1992)
  24. W. S. Opong and A. L. Zydney, Diffusive and Convective Protein-Transport Through Asymmetric Membranes. AIChE J., 37, 1497-1510 (1991)
  25. W. M. Clark, A. Bansal, M. Sontakke, and Y. H. Ma, Protein Adsorption and Fouling in Ceramic Ultrafiltration Membranes. J. Membrane Sci., 55, 21-38 (1991)
  26. W. Zhang, B. G. Park, Y. K. Chang, H. N. Chang, X. J. Yu, and Q. Yuan, Factors Affecting Membrane Fouling in Filtration of Saccharomyces Cerevisiae in an Internal Ceramic Filter Bioreactor. Bioproc. Eng., 18, 317-322 (1998)
  27. F. Meyer, I. Gehmlich, R. Guthke, A. Gorak, and W. A. Knorre, Analysis and Simulation of Complex Interactions During Dynamic Microfiltration of Escherichia Coli Suspensions. Biotechnol. Bioeng., 59, 189-202 (1998)<189::AID-BIT7>3.0.CO;2-D
  28. M. R. Torres, A. J. Ramos, and E. Soriano, Ultrafiltration of Blood Proteins By Experimental Polyamide Membranes. Bioproc. Eng., 19, 213-215 (1998)
  29. P. Blanpain-Avet, N. Doubrovine, C. Lafforgue, and M. Lalande, The effect of oscillatory flow on crossflow micro filtration of beer in' a tubular mineral membrane system - Membrane fouling resistance decrease and energetic considerations. J. Membrane Sci., 152, 151-174 (1999)
  30. C. Jucker and M. M. Clark, Adsorption of Aquatic Humic Substances On Hydrophobic Ultrafiltration Membranes. J. Membrane Sci., 97, 37-52 (1994)
  31. G. Crozes, C. Anselme, and J. Mallevialle, Effect of Adsorption of Organic-Matter On Fouling of Ultrafiltration Membranes. J. Membrane Sci., 84, 61-77 (1993)
  32. F. A. DiGiano, A. Braghetta, and B. Utne, Nanofiltration Fouling by Natural Organic Matter and Role of Particles in Flux Enhancement. in American Water Works Association 1993. Membrane Technology Conference. Baltimore, MD. (1993)
  33. L. Giomo, L. Donato, S. Todisco, and E. Drioli, Study of Fouling Phenomena in Apple Juice Clarification By Enzyme Membrane Reactor. Sep. Sci. Technol., 33, 739-756 (1998)
  34. A. Maartens, P. Swart, and E. P. Jacobs, Humic Membrane Foulants in Natural Brown Water Characterization and Removal. Desalination, 115, 215-227 (1998)
  35. G. Belfort, Artificial Particulate Fouling of HyperFiltration Membranes. 4. Dynamic Protection From Fouling. Desalination, 34, 159-169 (1980)
  36. Y. Shimizu, K. Uryu, Y. Okuno, and A. Watanabe, Cross-flow microfiltration of activated sludge using submerged membrane with air bubbling. J. Ferment. Bioeng., 81, 55-60 (1996)
  37. S. Chellam and M. R. Wiesner, Particle-Transport in Clean Membrane Filters in Laminar-Flow. Environ. Sci. Technol., 26, 1611-1621 (1992)
  38. P. S. Cartwright, Industrial Waste-Water Treatment With Membranes - a United- States Perspective. Water Sci. Technol., 25, 373-390 (1992)
  39. O. Kutowy, W. L. Thayer, J. Tigner, S. Sourirajan, and G. K. Dhawan, Tubular Cellulose-Acetate Reverse-Osmosis Membranes For Treatment of Oily Wastewaters. Ind. Eng. Chem. Prod. Res. Dev., 20, 354-361 (1981)
  40. R. J. Lahiere and K. P. Goodboy, Ceramic Membrane Treatment of Petrochemical Waste-Water. Environ. Progr., 12, 86-96 (1993)
  41. R. V. Lopez, S. Elmaleh, and N. Ghaffor, CrossFlow Ultrafiltration of Hydrocarbon Emulsions. J. Membrane Sci., 102, 55-64 (1995)
  42. S. Elmaleh and W. Naceur, Transport of Water Through an Inorganic Composite Membrane. J. Membrane Sci., 66, 227-234 (1992)
  43. D. Clifford, S. Subramonian, and T. J. Sorg, WaterTreatment Processes. 3. Removing Dissolved Inorganic Contaminants From Water. Environ. Sci. Technol., 20, 1072-1080 (1986)
  44. E. H. Bouhabila, R. Benaim, and H. Buisson, Microfiltration of Activated Sludge Using Submerged Membrane With Air Bubbling (Application to Wastewater Treatment). Desalination, 118, 315-322 (1998)
  45. L. Defrance and M. Y. Jaffrin, Comparison between filtrations at fixed transmembrane pressure and fixed permeate flux: application to a membrane bioreactor used for wastewater treatment. J. Membrane Sci., 152, 203-210 (1999)
  46. K. H. Ahn, H. Y. Cha, I. T. Yeom, and K. G. Song, Application of Nanofiltration For Recycling of Paper Regeneration Wastewater and Characterization of Filtration Resistance. Desalination, 119, 169-176 (1998)
  47. S. Elmaleh and L. Abdelmoumni, Experimental test to evaluate performance of an anaerobic reactor provided with an external membrane unit. Water Sci. Technol., 38, 385-392 (1998)
  48. E. Tardieu, A. Grasmick, V. Geaugey, and J. Manem, Hydrodynamic Control of Bioparticle Deposition in a Mbr Applied to Wastewater Treatment. J. Membrane Sci., 147, 1-12 (1998)
  49. J. N. Wu, M. A. Eiteman, and S. E. Law, Eval- uation of Membrane Filtration and Ozonation Processes For Treatment of Reactive-Dye Wastewater. J. Environ. Eng.-ASCE, 124, 272-277 (1998)
  50. K. Welsch, R. M. McDonogh, A. G. Fane, and C. J. D. Fell, Calculation of Limiting Fluxes in the Ultrafiltration of Colloids and Fine Particulates. J. Membrane Sci., 99, 229-239 (1995)
  51. G. Belfort, Membrane Modules - Comparison of Different Configurations Using Fluid-Mechanics. J. Membrane Sci., 35, 245-270 (1988)
  52. W. Doyen, Latest Developments in Ultrafiltration For Large-Scale Drinking Water Applications. Desalination, 113, 165-177 (1997)
  53. M. R. Wiesner, M. M. Clark, and J. Mallevialle, Membrane Filtration of Coagulated Suspensions. J. Environ. Eng.-ASCE, 115, 20-40 (1989)
  54. F. Rouvet, K. Fiaty, P. Laurent, and J. K. Liou, Modelling and Simulation of Membrane Fouling in Batch Ultrafiltration On Pilot Plant. Comput. Chem. Eng., 22, S 901-S 904 (1998)
  55. S. Hong, R. S. Faibish, and M. Elimelech, Kinetics of Permeate Flux Decline in Crossflow Membrane Filtration of Colloidal Suspensions. J. Colloid Interface Sci., 196, 267-277 (1997)
  56. I. H. Huisman, D. Elzo, E. Middelink, and A. C. Tragardh, Properties of the cake layer formed during crossflow microfiltration. Colloids and Surfaces a-Physicochemical and Engineering Aspects, 138, 265-281 (1998)
  57. L. H. Huang and M. T. Morrissey, Fouling of Membranes During Microfiltration of Surimi Wash Water - Roles of Pore Blocking and Surface Cake Formation. J. Membrane Sci., 144, 113-123 (1998)
  58. H. Li, A. G. Fane, H. G. L. Coster, and S. Vigneswaran, Direct Observation of Particle Deposition On the Membrane Surface During Crossflow Microfiltration. J. Membrane Sci., 149, 83-97 (1998)
  59. A. B. Koltuniewicz and R. W. Field, Process factors during removal of oil-in-water emulsions with cross-flow microfiltration. Desalination, 105, 79-89 (1996)
  60. J. Hermia, Constant Pressure Blocking Filtration Laws-Application to Power-Law Non-Newtonian Fluids. Transactions of the Institution of Chemical Engineers, 60, 183-187 (1982)
  61. E. S. Tarleton and R. J. Wakeman, Understanding Flux Decline in Cross-Flow Microfiltration. 1. Effects of Particle and Pore-Size. Chem. Eng. Res. Des., 71, 399-410 (1993)
  62. S. S. Madaeni, Ultrafiltration of Very Dilute Colloidal Mixtures. Colloids Surf. A-Physicochem. Eng. Asp., 131, 109-118 (1998)
  63. J. M. K. Timmer, H. C. Vanderhorst, and J. P. Labbe, Cross-Flow Microfiltration of Beta-Lactoglobulin Solutions and the Influence of Silicates On the Flow Resistance. J. Membrane Sci., 136, 41-56 (1997)
  64. R. F. Boyd and A. L. Zydney, Analysis of Protein Fouling During Ultrafiltration Using a Two-Layer Membrane Model. Biotechnol. Bioeng., 59, 451-460 (1998)<451::AID-BIT8>3.0.CO;2-F
  65. D. J. Carlsson, M. M. Dalcin, P. Black, and C. N. Lick, A Surface Spectroscopic Study of Membranes Fouled By Pulp Mill Effluent. J. Membrane Sci., 142, 1-11 (1998)
  66. J. Lindau, A. S. Jonsson, and A. Bottino, Flux Reduction of Ultrafiltration Membranes With Different Cut-Off Due to Adsorption of a Low-MolecularWeight Hydrophobic Solute-Correlation Between Flux Decline and Pore Size. J. Membrane Sci., 149, 11-20 (1998)
  67. D. Belhocine, H. Grib, D. Abdessmed, Y. Comeau, and N. Mameri, Optimization of Plasma Proteins Concentration By Ultrafiltration. J. Membrane Sci., 142,159-171 (1998)
  68. L. Gourley, M. Britten, S. F. Gauthier, and Y. Pouliot, Characterization of Adsorptive Fouling On Ultrafiltration Membranes By Peptides Mixtures Using Contact-Angle Measurements. J. Membrane Sci., 97, 283-289 (1994)
  69. Z. Amjad, Applications of Antiscalants to Control Calcium-Sulfate Scaling in Reverse-Osmosis Systems. Desalination, 54, 263-276 (1985)
  70. J. M. Jackson and D. Landolt, About Mechanism of Formation of Iron Hydroxide Fouling Layers On Reverse-Osmosis Membranes. Desalination, 12, 361-378 (1973)
  71. M. Okazaki and S. Kimura, Scale Formation On Reverse-Osmosis Membranes. J. Chem. Eng. Jpn., 17, 145-151 (1984)
  72. L. F. Song, Flux Decline in Crossflow Microfiltration and Ultrafiltration - Mechanisms and Modeling of Membrane Fouling. J .Membrane Sci., 139, 183-200 (1998)
  73. H. Ohya, J. J. Kim, A. Chinen, M. Aihara, S. I. Semenova, Y. Negishi, O. Mori, and M. Yasuda, Effects of Pore Size On Separation Mechanisms of Microfiltration of Oily Water, Using Porous Glass Tubular Membrane. J. Membrane Sci., 145, 1-14 (1998)
  74. W. R Bowen, N. Hilal, R W. Lovitt, A. O. Sharif, and P. M. Williams, Atomic force microscope studies of membranes: Force measurement and imaging in electrolyte solutions. J. Membrane Sci., 126, 77-89 (1997)
  75. J. Lindau and A. S. Jonsson, Cleaning of Ultrafiltration Membranes After Treatment of Oily WasteWater. J. Membrane Sci., 87, 71-78 (1994)
  76. J. Lindau, A. S. Jonsson, and R Wimmerstedt, The Influence of a Low-Molecular Hydrophobic Solute' on the Flux of Polysulfone Ultrafiltration Membranes With Different Cutoff. J. Membrane Sci., 106, 9-16 (1995)
  77. A. Maartens, P. Swart, and E. P. Jacobs, Enzymatic Cleaning of Ultrafiltration Membranes Fouled in Wool-Scouring Effluent. Water SA, 24, 71-76 (1998)
  78. S. Chellam, C. A. Serra, and M. R. Wiesner, Estimating Costs For Integrated Membrane Systems. Journal American Water Works Association, 90, 96-104 (1998)
  79. S. Chellam, J. G. Jacangelo, and T. P. Bonacquisti, Modeling and Experimental Verification of Pilot- Scale Hollow Fiber, Direct Flow Microfiltration With Periodic Backwashing. Environ. Sci. Technol., 32, 75-81 (1998)
  80. R. S. Faibish, M. Elimelech, and Y. Cohen, Effect of Interparticle Electrostatic Double Layer Interactions On Permeate Flux Decline in Crossflow Membrane Filtration of Colloidal Suspensions - an Experimental Investigation. J. Colloid Interface Sci., 204, 77-86 (1998)
  81. M. Kennedy, S. M. Kim, I. Mutenyo, L. Broens, and J. Schippers, Intermittent Crossflushing of Hollow Fiber Ultrafiltration Systems. Desalination, 118, 175-187 (1998)
  82. M. W. Chudacek and A. G. Fane, The dynamics of polarization in unstirred and stirred ultrafiltration. J. Membrane Sci., 21, 145 (1984)
  83. R. H. Davis and S. A. Birdsell, Hydrodynamic Model and Experiments For Cross-Flow Microfiltration. Chem. Eng. Commun., 49, 217-234 (1987)
  84. M. H. Lojkine, R. W. Field, and J. A. Howell, Crossflow Microfiltration of Cell Suspensions: A Review of Models with Emphasis on Particle Size Effects. Transactions of the Institution of Chemical Engineers, 70 (1992)
  85. P. Schmitz, D. Houi, and B. Wandelt, Hydrodynamic Aspects of Cross-Flow Microfiltration Analysis of Particle Deposition At the MembraneSurface. J. Membrane Sci., 71, 29-40 (1992)
  86. F. W. Altena, G. Belfort, J. Otis, F. Fiessinger, J. M. Rovel, and J. Nicoletti, Particle Motion in a Laminar Slit Flow - a Fundamental Fouling Study. Desalination, 47, 221-232 (1983)
  87. F. W. Altena and G. Belfort, Lateral Migration of Spherical-Particles in Porous Flow Channels Application to Membrane Filtration. Chem. Eng. Sci., 39, 343-355 (1984)
  88. R. H. Davis and D. T. Leighton, Shear-Induced Transport of a Particle Layer Along a Porous Wall. Chem. Eng. Sci., 42, 275-281 (1987)
  89. C. A. Romero and R. H. Davis, Global-Model of Cross-Flow Microfiltration Based On Hydrodynamic Particle Diffusion. J. Membrane Sci., 39, 157-185 (1988)
  90. W. R. Bowen and F. Jenner, Theoretical descriptions of membrane filtration of colloids and fine particles: An assessment and review. Advances in Colloid and Interface Science, 56, 141-200 (1995)
  91. C. A. Romero and R. H. Davis, Transient Model of Cross-Flow Microfiltration. Chem. Eng. Sci., 45, 13-25 (1990)
  92. S. Sethi and M. R. Wiesner, Modeling of Transient Permeate Flux in Cross-Flow Membrane Filtration Incorporating Multiple Particle Transport Mechanisms. J. Membrane Sci., 136, 191-205 (1997)
  93. W. R. Bowen and F. Jenner, Dynamic Ultrafiltration Model For Charged Colloidal Dispersions - a Wigner-Seitz Cell Approach. Chem. Eng. Sci., 50, 1707-1736 (1995)
  94. W. J. C. Holt, S. L. Carnie, and D. Y. C. Chan, Colloidal interactions in low volume fraction pressurized ultrafiltration systems. J. Colloid Interface Sci., 173, 304-318 (1995)
  95. L. F. Fu and B. A. Dempsey, Modeling the Effect of Particle Size and Charge On the Structure of the Filter Cake in Ultrafiltration. J. Membrane Sci., 149, 221-240 (1998)
  96. R. M. McDonogh, H. Bauser, N. Stroh, and H. Chmiel, Concentration Polarization and Adsorption Effects in Cross-Flow Ultrafiltration of Proteins. Desalination, 79, 217-231 (1990)
  97. W. F. Blatt, A. Dravid, A. S. Michaels, and L. Nelson, Solute Polarization and Cake Formation in Membrane Ultrafiltration: Causes, Consequences, and Control Techniques. in Membrane Science and Technology: Industrial, Biological, and Waste Treatment Processes. Columbus, Ohio: Plenum Press (1970)
  98. V. L. Vilker, C. K. Colton, and K. A. Smith, Concentration polarization in protein ultrafiltration. AIChE J, 27, 632 (1981)
  99. D. R. Trettin and M. R. Doshi, eds. Pressure independent ultrafiltration: is it gel limited or os- motic pressure limited? Synthetic Membranes Vol II: Ultrafiltration and Hyperfiltration Uses, ed. A. F. Turbak. Vol. 154. ACS Symposium Series. 373. (1983)
  100. J. G. Wijmans, S. Nakao, and C. A. Smolders, Flux Limitation in Ultrafiltration - Osmotic-Pressure Model and Gel Layer Model. J. Membrane Sci., 20, 115-124 (1984)
  101. D. R. Trettin and M. R. Doshi, Limiting Flux in Ultrafiltration of Macromolecular Solutions. Chem. Eng. Commun., 4, 507-522 (1980)
  102. S. Bhattacharjee, A. Sharma, and P. K. Bhattacharyya, A unified model for flux prediction during batch cell ultrafiltration. J. Membrane Sci., 111, 243-258 (1996)
  103. M. Elimelech and S. Bhattacharjee, A Novel Approach For Modeling Concentration Polarization in Crossflow Membrane Filtration Based On the Equivalence of Osmotic Pressure Model and Filtration Theory. J. Membrane Sci., 145, 223-241 (1998)
  104. G. B. Van den Berg and C. A. Smolders, Flux decline in ultrafiltration processes. Desalination, 77, 101 (1990)
  105. J. G. Wijmans, S. Nakao, J. W. A. Vandenberg, F. R. Troelstra, and C. A. Smolders, Hydrodynamic Resistance of Concentration Polarization Boundary- Layers in Ultrafiltration. J. Membrane Sci., 22, 117-135 (1985)
  106. G. B. Vandenberg and C. A. Smolders, The Boundary-Layer Resistance Model For Unstirred Ultrafiltration - a New Approach. J. Membrane Sci., 40, 149-172 (1989)
  107. L. Song and M. Elime1ech, Theory of concentration polarization in crossflow filtration. Journal of Chemical Society Faraday Transactions, 91, 3389-3398 (1995)
  108. W. R. Bowen, A. Mongruel, and P. M. Williams, Prediction of the rate of cross-flow membrane ultrafiltration: A colloidal interaction approach. Chem. Eng. Sci., 51, 4321-4333 (1996)
  109. W. B. Russell, D. A Saville, and W. R Schowalter, Colloidal Dispersions. Cambridge (1989)
  110. S. Bhattacharjee, A. S. Kim, and M. Elimelech, Concentration polarization of interacting solute particles in cross-flow membrane filtration. J. Colloid Interface Sci., 212, 81-99 (1999)
  111. D. N. Petsev, V. M. Starov, and I. B. Ivanov, Concentrated Dispersions of Charged Colloidal Particles - Sedimentation, Ultrafiltration and Diffusion. Colloids and Surfaces a-Physicochemical and Engineering Aspects, 81, 65-81 (1993)
  112. W. R. Bowen and P. M. Williams, Dynamic ultrafiltration model for proteins: A colloidal interaction approach. Biotechnology and Bioengineering, 50, 125-135 (1996)<125::AID-BIT2>3.0.CO;2-O
  113. R. M. McDonogh, C. J. D. Fell, and A. G. Fane, Surface charge and permeability in the ultrafiltration of non-flocculating colloids. J. Membrane Sci., 21, 285-294 (1984)
  114. R. M. McDonogh, C. J. D. Fell, and A. G. Fane, Charge effects in the cross-flow filtration of colloids and particulates. J. Membrane Sci., 43, 69-85 (1989)
  115. R. M. McDonogh, K. Welsch, A. G. Fane, and C. J. D. Fell, Incorporation of the Cake Pressure Profiles in the Calculation of the Effect of Particle Charge On the Permeability of Filter Cakes Obtained in the Filtration of Colloids and Particulates. J. Membrane Sci., 72, 197-204 (1992)
  116. L. Song and M. Elimelech, Particle Deposition onto a Permeable Surface in Laminar Flow. J. Colloid Interface Sci., 173, 165-180 (1995)
  117. P. Bacchin, P. Aimar, and V. Sanchez, Influence of surface interaction on transfer during colloid ultrafiltration. J. Membrane Sci., 115, 49-63 (1996)
  118. P. Harmant and P. Aimar, Coagulation of Colloids in a Boundary Layer During Cross-Flow Filtration. Colloids Surf. A-Physicochem. Eng. Asp., 138, 217-230 (1998)
  119. V. Lahoussineturcaud, M. R. Wiesner, J. Y. Bottero, and J. Mallevialle, Coagulation Pretreatment For Ultrafiltration of a Surface-Water. Journal American Water Works Association, 82, 76-81 (1990)
  120. V. Lahoussineturcaud, M. R. Wiesner, and J. Y. Bottero, Fouling in Tangential-Flow Ultrafiltration -the Effect of Colloid Size and Coagulation Pretreatment. J. Membrane Sci., 52, 173-190 (1990)
  121. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics. Dordrect: Kluwer (1991)
  122. S. Bhattacharjee, A. Sharma, and P. K. Bhattacharya, Surface Interactions in Osmotic-Pressure Controlled Flux Decline During Ultrafiltration. Langmuir, 10, 4710-4720 (1994)
  123. R. M. McDonogh, A. G. Fane, and C. J. D. Fell, Influence of Polydispersity On the Hydraulic Behaviour of Colloidal Fouling Layers On Membranes - Perturbations On the Behaviour of the Ideal Colloidal Layer. Colloids Surf. A-Physicochem. Eng. Asp., 138, 231-244 (1998)
  124. A. S. Jonsson and B. Jonsson, Ultrafiltration of colloidal dispersions - A theoretical model of the concentration polarization phenomena. J. Colloid Interface Sci., 180, 504-518 (1996)
  125. J. Happel, AIChE J., 4, 197 (1958)
  126. G. K. Batchelor, Sedimentation in a dilute dispersion of spheres. Journal of Fluid Mechanics, 52, 245-268 (1972)
  127. G. K. Batchelor, Journal of Fluid Mechanics, 74, 1 (1976)
  128. N. D. Denkov and D. N. Petsev, Physica A, 183, 462 (1992)
  129. W. Xu, A. Nikolov, and D. T. Wasan, J. Colloid Interface Sci., 197, 160 (1998)
  130. N. Arora and R. H. Davis, Effects of axial pressure drop on the length-averaged permeate flux in crossflow microfiltration. Chem. Eng. Commun., 132, 51-67 (1995)
  131. J. Altmann and S. Ripperger, Particle deposition and layer formation at the crossflow microfiltration. J. Membrane Sci., 124, 119-128 (1997)
  132. S. Chellam and M. R. Wiesner, Particle back- transport and permeate flux behavior in crossflow membrane filters. Environ. Sci. Technol., 31, 819-824 (1997)
  133. H. S. Alkhatim, M. I. Alcaina, E. Soriano, M. I. Iborra, J. Lora, and J. Arnal, Treatment of Whey Effluents From Dairy Industries By Nanofiltration Membranes. Desalination, 119, 177-183 (1998)
  134. M. H. Almalack and G. K. Anderson, Use of Crossflow Microfiltration in Wastewater Treatment. Water Res., 31, 3064-3072 (1997)
  135. J. Cakl and P. Mikulasek, Flux and Fouling in the Cross-Flow Ceramic Membrane Microfiltration of Polymer Colloids. Sep. Sci. Technol., 30, 3663-3680 (1995)
  136. E. S. Tarleton and R J. Wakeman, Understanding Flux Decline in Cross-Flow Microfiltration. 2. Effects of Process Parameters. Chem. Eng. Res. Des., 72, 431-440 (1994)
  137. D. X. Wu, J. A. Howell, and R W. Field, Critical flux measurement for model colloids. J. Membrane Sci., 152, 89-98 (1999)
  138. R. W. Field and P. Aimar, Ideal Limiting Fluxes in Ultrafiltration - Comparison of Various Theoretical Relationships. J. Membrane Sci., 80, 107-115 (1993)
  139. C. Hosten, Cake Filtration-Rate Equations - a Review of Classical and Modem Approaches. Minerals Engineering, 6, 775-783 (1993)
  140. Y. Z. Xujiang, J. Dodds, and D. Leclerc, Cake Characteristics in Cross-Flow and Dead-End Microfiltration. Filtration Sep., 32, 795-798 (1995)
  141. F. M. Tiller, J. R. Crump, and F. Ville, A Revised Approach to the Theory of Cake Filtration. in International Symposium on Fine Particles Processing. Las Vegas, Nevada: American Institute of Mining (1980)
  142. A. B. Koltuniewicz, R W. Field, and T. C. Arnot, Cross-Flow and Dead-End Microfiltration of OilyWater Emulsion. 1. Experimental-Study and Analysis of Flux Decline. J.. Membrane Sci., 102, 193207 (1995)
  143. J. A. Howell, D. Wu, and R. W. Field, Transmission of bovine albumin under controlled flux ultrafiltration. J. Membrane Sci., 152, 117-127 (1999)
  144. V. Chen, Performance of Partially Permeable Microfiltration Membranes Under Low Fouling Conditions. J. Membrane Sci., 147,265-278 (1998)
  145. D. Y. Kwon, S. Vigneswaran, H. H. Ngo, and H. S. Shin, An Enhancement of Critical Flux in Crossflow Microfiltration With a Pretreatment of Floating Medium Flocculator/Prefilter, Water Sci. Technol., 36, 267-274 (1997)
  146. S. S. Madaeni, The Effect of Operating Conditions On Critical Flux in Membrane Filtration of Latexes. Proc. Safety Environ. Prot., 75, 266-269 (1997)
  147. M. Manttari, J. Nuortilajokinen, and M. Nystrom, Influence of Filtration Conditions On the Performance of Nf Membranes in the Filtration of Paper Mill Total Effluent. J. Membrane Sci., 137, 187-199 (1997)
  148. W. R. Bowen and A. O. Sharif, Hydrodynamic and Colloidal Interactions Effects On the Rejection of a Particle Larger Than a Pore in Microfiltration and Ultrafiltration Membranes. Chem. Eng. Sci., 53, 879-890 (1998)
  149. D. Y. Kwon and S. Vigneswaran, Influence of particle size and surface charge on critical flux of crossflow microfiltration. Water Sci. Technol., 38, 481-488 (1998)
  150. X. Zhu and M. Elimelech, Fouling of Reverse Osmosis Membranes by Aluminium Oxide Colloids. Journal of Environmental Engineering, 121, 884-892 (1995)
  151. L. Vera, R. Villarroellopez, S. Delgado, and S. Elmaleh, Cross-Flow Microfiltration of Biologically Treated Wastewater. Desalination, 114, 65-75 (1997)
  152. L. Vera, R. Villarroel, S. Delgado, and S. Elmaleh, Can microfiltration of treated wastewater produce suitable water for irrigation? Water Sci. Technol., 38, 395-403 (1998)