A corrected cake resistance expression by considering the deposition property of different feed suspensions/solutions

References

• Liang, H. W.; Wang, L.; Chen, P. Y.; Lin, H. T.; Chen, L. F.; He, D.; Yu, S. H. Carbonaceous Nanofiber Membranes for Selective Filtration and Separation of Nanoparticles. Adv. Mater. 2010, 22, 4691–4695. DOI: 10.1002/adma.201001863.
   PubMed Web of Science ®Google Scholar
• Mittal, N.; Peng, B.; Kelloway, A.; Siepmann, J. I.; Daoutidis, P.; Tsapatsis, M. A Mathematical Model for Zeolite Membrane Module Performance and Its Use for Techno-economic Evaluation of Improved Energy Efficiency Hybrid Membrane- Distillation Processes for Butane Isomer Separations. J. Membr. Sci. 2016, 520, 434–449. DOI: 10.1016/j.memsci.2016.06.041.
   Web of Science ®Google Scholar
• Luis, P.; Garea, A.; Irabien, A. Environmental and Economic Evaluation of SO2, Recovery in a Ceramic Hollow Fibre Membrane Contactor, Chem. Eng. Process. 2012, 52, 151–154. DOI: 10.1016/j.cep.2011.10.006.
   Web of Science ®Google Scholar
• Drews, A.; Arellano-Garcia, H.; Schöneberger, J.; Schaller, J.; Wozny, G.; Kraume, M. Model-based Recognition of Fouling Mechanisms in Membrane Bioreactors. Desalination. 2009, 236, 224–233. DOI: 10.1016/j.desal.2007.10.071.
   Web of Science ®Google Scholar
• Kim, M.; Sankararao, B.; Lee, S.; Yoo, C. K. Prediction and Identification of Membrane Fouling Mechanism in a Membrane Bioreactor Using a Combined Mechanistic Model. Ind. Eng. Chem. Res. 2013, 52, 17198–17205.
   Web of Science ®Google Scholar
• Boyle-Gotla, A.; Jensen, P. D.; Yap, S. D.; Pidou, M.; Wang, Y.; Batstone, D. J. Dynamic Multidimensional Modelling of Submerged Membrane Bioreactor Fouling. J. Membr. Sci. 2014, 467, 153–161. DOI: 10.1016/j.memsci.2014.05.028.
   Web of Science ®Google Scholar
• Ruth, B. F. Studies in Filtration III. Derivation of General Filtration Equations. Ind. Eng. Chem. 1935, 27(6), 708–723.  DOI: 10.1021/ie50306a024.
   Google Scholar
• Shin, J. H.; Kim, K. H.; Kim, J. H.; Lee, S. H. Development of a Numerical Model for Cake Layer Formation on a Membrane. Desalination. 2013, 309, 213–221. DOI: 10.1016/j.desal.2012.10.018.
   Web of Science ®Google Scholar
• Bai, R.; Leow, H. F. Microfiltration of Activated Sludge Wastewater—The Effect of System Operation Parameters. Sep. Purif. Technol. 2002, 29, 189–198. DOI: 10.1016/S1383-5866(02)00075-8.
   Web of Science ®Google Scholar
• Xiao, K.; Shen, Y.; Huang, X. An Analytical Model for Membrane Fouling Evolution Associated with Gel Layer Growth during Constant Pressure Stirred Dead-end Filtration. J. Membr. Sci. 2013, 427, 139–149. DOI: 10.1016/j.memsci.2012.09.049.
   Web of Science ®Google Scholar
• Robles, A.; Ruano, M. V.; Ribes, J.; Seco, A.; Ferrer, J. A Filtration Model Applied to Submerged Anaerobic MBRs (Sanmbrs). J. Membr. Sci. 2013, 444, 139–147. DOI: 10.1016/j.memsci.2013.05.021.
   Web of Science ®Google Scholar
• Xi, X. J.; Cui, Y. J.; Wang, Z.; Qian, J. H.; Wang, J.; Yang, L. Y.; Zhao, S. S. Study of Dead-end Microfiltration Features in Sequencing Batch Reactor (SBR) by Optimized Neural Networks. Desalination. 2011, 272, 27–35. DOI: 10.1016/j.desal.2010.12.049.
   Web of Science ®Google Scholar
• Xi, X. J.; Wang, Z.; Zhang, J.; Zhou, Y. N.; Chen, N.; Shi, L. Y.; Dong, W. Y.; Cheng, L. N.; Yang, W. T. Prediction of Impacts of Fabrication Conditions on the Filtration Performance of Homemade VC-co-VAc-OH Microfiltration Membrane by Support Vector Machine (SVM). Desalin. Water. Treat. 2013, 51, 3970–3978. DOI: 10.1080/19443994.2013.797066.
   Web of Science ®Google Scholar
• Chandler, M.; Zydney, A. High Throughput Screening for Membrane Process Development. J. Membr. Sci. 2004, 237, 181–188. DOI: 10.1016/j.memsci.2004.03.011.
   Web of Science ®Google Scholar
• Ni, L. A.; Yu, A. B.; Lu, G. Q.; Howes, T. Simulation of the Cake Formation and Growth in Cake Filtration. Miner. Eng. 2006, 19, 1084–1097. DOI: 10.1016/j.mineng.2006.03.012.
   Web of Science ®Google Scholar
• Paipuri, M.; Kim, S. H.; Hassan, O.; Hilal, N.; Morgan, K. Numerical Modelling of Concentration Polarisation and Cake Formation in Membrane Filtration Processes. Desalination. 2015, 365, 151–159. DOI: 10.1016/j.desal.2015.02.022.
   Web of Science ®Google Scholar
• Zhu, Z.; Wang, Z.; Wang, H.; Kong, Y.; Gao, K.; Li, Y. Cake Properties as a Function of Time and Location in Microfiltration of Activated Sludge Suspension from Membrane Bioreactors (Mbrs). Chem. Eng. J. 2016, 302, 97–110. DOI: 10.1016/j.cej.2016.05.031.
   Web of Science ®Google Scholar
• Chellam, S.; Xu, W. Blocking Laws Analysis of Dead-end Constant Flux Microfiltration of Compressible Cakes. J. Colloid Interface Sci. 2006, 301, 248. DOI: 10.1016/j.jcis.2006.04.064.
   PubMed Web of Science ®Google Scholar
• Trzaskus, K.; Elshof, M.; Kemperman, A.; Nijmeijer, K. Understanding the Role of Nanoparticle Size and Polydispersity in Fouling Development during Dead-end Microfiltration. J. Membr. Sci. 2016, 516, 152–161. DOI: 10.1016/j.memsci.2016.05.043.
   Web of Science ®Google Scholar
• Wang, Z.; Chu, J. S.; Zhang, X. M. Study of a Cake Model during Stirred Dead-end Microfiltration. Desalination. 2007, 217, 127–138. DOI: 10.1016/j.desal.2007.02.010.
   Web of Science ®Google Scholar
• Stickland, A. D.;. A Compressional Rheology Model of Fluctuating Feed Concentration during Filtration of Compressible Suspensions. Chem. Eng. Sci. 2012, 75, 209–219. DOI: 10.1016/j.ces.2012.03.023.
   Web of Science ®Google Scholar
• Tian, J. Y.; Ernst, M.; Cui, F.; Jekel, M. Effect of Different Cations on UF Membrane Fouling by NOM Fractions. Chem. Eng. J. 2013, 223, 547–555. DOI: 10.1016/j.cej.2013.03.043.
   Web of Science ®Google Scholar
• Huang, C.; Lin, J. L.; Lee, W. S.; Pan, J. R.; Zhao, B. Effect of Coagulation Mechanism on Membrane Permeability in Coagulation-assisted Microfiltration for Spent Filter Backwash Water Recycling. Colloids Surf. 2011, 378, 72–78. DOI: 10.1016/j.colsurfa.2011.01.054.
   Google Scholar
• Liu, H. B.; Yang, C. Z.; Pu, W. H.; Zhang, J. D. Formation Mechanism and Structure of Dynamic Membrane in the Dynamic Membrane Bioreactor. Chem. Eng. J. 2009, 148, 290–295. DOI: 10.1016/j.cej.2008.08.043.
   Web of Science ®Google Scholar
• Yingpei, L.; Mohammad, A. W. Effect of Solution Chemistry on Flux Decline during High Concentration Protein Ultrafiltration through a Hydrophilic Membrane. Chem. Eng. J. 2010, 159, 91–97. DOI: 10.1016/j.cej.2010.02.044.
   Web of Science ®Google Scholar
• Iritani, E.; Katagiri, N. Developments of Blocking Filtration Model in Membrane Filtration, Kona. Powder. Part. J. 2016, 33, 179–202.
   Google Scholar
• Ognier, S.; Wisniewski, C.; Grasmick, A. Influence of Macromolecule Adsorption during Filtration of a Membrane Bioreactor Mixed Liquor Suspension. J. Membr. Sci. 2002, 209, 27–37. DOI: 10.1016/S0376-7388(02)00123-0.
   Web of Science ®Google Scholar
• Miranda, J. M.; Campos, J. B. L. M. An Improved Numerical Scheme to Study Mass Transfer over a Separation Membrane. J. Membr. Sci. 2001, 188, 49–59. DOI: 10.1016/S0376-7388(01)00360-X.
   Web of Science ®Google Scholar
• Sablani, S. S.; Goosen, M.; Al-Belushi, R.; Wilf, M. Concentration Polarization in Ultrafiltration and Reverse Osmosis: A Critical Review. Desalination. 2001, 141, 269–289. DOI: 10.1016/S0011-9164(01)85005-0.
   Web of Science ®Google Scholar
• Villamil, J. A.; Monsalvo, V. M.; Lopez, J.; Mohedano, A. F.; Rodriguez, J. J. Fouling Control in Membrane Bioreactors with Sewage-sludge Based Adsorbents. Water Res. 2016, 105, 65. DOI: 10.1016/j.watres.2016.08.059.
   PubMed Web of Science ®Google Scholar
• Li, X. Y.; Wang, X. M. Modelling of Membrane Fouling in a Submerged Membrane Bioreactor. J. Membr. Sci. 2006, 278, 151–161. DOI: 10.1016/j.memsci.2005.10.051.
   Web of Science ®Google Scholar
• Fane, A. G.;. Ultrafiltration of Suspensions. J. Membr. Sci. 1984, 20, 249–259. DOI: 10.1016/S0376-7388(00)82002-5.
   Web of Science ®Google Scholar
• Kim, J.; Digiano, F. A. Fouling Models for Low-pressure Membrane Systems. Sep. Purif. Technol. 2009, 68, 293–304. DOI: 10.1016/j.seppur.2009.05.018.
   Web of Science ®Google Scholar
• Bourcier, D.; Féraud, J. P.; Colson, D.; Mandrick, K.; Ode, D.; Brackx, E.; Puel, F. Influence of Particle Size and Shape Properties on Cake Resistance and Compressibility during Pressure Filtration. Chem. Eng. Sci. 2016, 144, 176–187. DOI: 10.1016/j.ces.2016.01.023.
   Web of Science ®Google Scholar
• Chinese SEPA. Water and Wastewater Monitoring Methods, 3rd ed.; Beijing, China: Chinese Environmental Science Publishing House, 1997.
   Google Scholar
• Svetlanas, P.; Miodragn, T.; Mirjanas, D. Kinetic Models for Alkali and Detergent Cleaning of Ceramic Tubular Membrane Fouled with Whey Proteins. J. Food. Eng. 2009, 94, 307–315. DOI: 10.1016/j.jfoodeng.2009.03.022.
   Web of Science ®Google Scholar
• Foley, G.; MacLoughlin, P. F.; Malone, D. M. Preferential Deposition of Smaller Cells during Cross-flow Microfiltration of a Yeast Suspension. Biotechnol. Tech. 1992, 6, 115–120. DOI: 10.1007/BF02438815.
   Google Scholar
• Hwang, K. J.; Sz, P. Y. Membrane Fouling Mechanism and Concentration Effect in Cross-flow Microfiltration of BSA/dextran Mixtures. Chem. Eng. J. 2011, 66, 669–677. DOI: 10.1016/j.cej.2010.11.044.
   Web of Science ®Google Scholar
• Cornehl, B.; Overbeck, A.; Schwab, A.; Büser, J. P.; Kwade, A.; Nirschl, H. Breakage of Lysozyme Crystals Due to Compressive Stresses during Cake Filtration. Chem. Eng. Sci. 2014, 111, 324–334. DOI: 10.1016/j.ces.2014.02.016.
   Web of Science ®Google Scholar