An Impact of the Particle Size Distribution on CP Degree at the Mechanism of Shear-Induced Diffusion in Cross-Flow Microfiltration

Sergey P. Agashichev

doi:10.6000/1929-6037.2015.04.04.2

Authors

Sergey P. Agashichev NEWRC (ADWEA), PO Box 54111, Abu Dhabi, UAE

DOI:

https://doi.org/10.6000/1929-6037.2015.04.04.2

Keywords:

Shear-induced diffusion, concentration polarization, cross-flow microfiltration, modeling

Abstract

Model for concentration profile at the mechanism of shear- induced back migration has been proposed. The model is based on the following assumptions: (1) Flow is assumed to be isothermal, incompressible, fully developed and steady– state. The model implies the position dependence of transverse velocity and shear rate; (2) Dispersed phase consists of rigid bodies characterized by identity variables and particle- size distribution; (3) Back migration being non- diffusive in nature is characterized by certain kinetic behavior. The migration of particle is determined by shear- induced force (moving force) and drag forces (resistance force); (4) The migration of particles was assumed to occur within the zone referred to as shear-diffusion migration zone. Migration zone ranges from membrane to its threshold value at the upper boundary where the state of pseudo-equilibrium takes place; Vector sum of the forces acting the particle (shear and drag forces) ranges from its maximum value at the surface of membrane to zero at the upper boundary of migration zone where the state of pseudo-equilibrium takes place; (5) The driving force being degree of deviation from the state of equilibrium was expressed as the difference between local shear rate and its threshold value at the upper boundary of migration zone; Transport mechanisms such as Brownian diffusion, inertial lift, interaction based on Van der Waals or electrostatic forces, combined effects of particle-particle and particle–membrane interactions are outside the scope of the model. The proposed model has the following possible implications: (A) It can be used for quantitative estimation of the probability of fouling caused by different fractions at existing hydrodynamic conditions; (B) The model allows analyzing the impact of hydrodynamic conditions (such as shear stress and transverse velocity) on the probability of fouling caused by certain dispersed fraction; (C) It allows estimation of the threshold value of the shear rate specific for the certain fraction that should be exceed in order to prevent accumulation of this fraction; (D) Proposed model permits analyzing the influence of shear rate at the surface of membrane on the transverse concentration distribution; (E) The model can be used for quantitative analysis of CP distribution of individual fraction while considering poly-disperse systems as soon as any fraction is characterized by its individual migrating behavior.

References

Zydney AL, Colton CK. Concentration polarization model for filtrate flux in cross flow microfiltration of particulate suspensions. Chem. Eng. Comm. 1986; 47: 1-21. http://dx.doi.org/10.1080/00986448608911751 DOI: https://doi.org/10.1080/00986448608911751

Zydney AL, Colton CK. Fundamental studies and design analysis for cross flow membrane plasmapheresis. In: J. D. Andrade et al., editors. Proceedings of International Symposium on Artificial Organs, Biomedical Engineering and Transplantation, New York, VCH Publishers, 1987: p. 343-358.

Davis RH, Leighton DH. Shear-induced transport of a particles layer along a porous wall. Chem Eng Sci 1987; 42: 275-281. http://dx.doi.org/10.1016/0009-2509(87)85057-1 DOI: https://doi.org/10.1016/0009-2509(87)85057-1

Romero CA, Davis RH. Global model of cross-flow microfiltration based on hydrodynamic particle diffusion. Journal of Membrane Science. 1988; 39: 157-185. http://dx.doi.org/10.1016/S0376-7388(00)80987-4 DOI: https://doi.org/10.1016/S0376-7388(00)80987-4

Romero CA, and RH Davis. Transient model of cross-flow microfiltration Chemical Engineering Science 1990; 45: 13-25. http://dx.doi.org/10.1016/0009-2509(90)87076-5 DOI: https://doi.org/10.1016/0009-2509(90)87076-5

Romero CA, Davis RH. Experimental verification of the shear-induced hydrodynamic diffusion model of cross-flow microfiltration. Journal of Membrane Science 1991; 62: 249-273. http://dx.doi.org/10.1016/0376-7388(91)80042-5 DOI: https://doi.org/10.1016/0376-7388(91)80042-5

Davis RH, Sherwood JD. A similarity solution for steady-state cross-flow microfiltration. Chemical Engineering Science 1990; 45: 3203-3209. http://dx.doi.org/10.1016/0009-2509(90)80212-W DOI: https://doi.org/10.1016/0009-2509(90)80212-W

Hoek Eric MV, Kim AS, Elimelech M. Influence of cross-flow membrane filter geometry and shear rate on colloidal fouling in reverse osmosis and nano-filtration separation. Environmental Engineering Science 2002; 19: 357-372. http://dx.doi.org/10.1089/109287502320963364 DOI: https://doi.org/10.1089/109287502320963364

Mondor M, Moresoli C. Shear-induced hydrodynamic diffusion model for cross-flow microfiltration: role of the particle volume fraction. Desalination 2002; 145: 123-128. http://dx.doi.org/10.1016/S0011-9164(02)00396-X DOI: https://doi.org/10.1016/S0011-9164(02)00396-X

Kromkamp J, et al. Shear-induced diffusion model for microfiltration of poly-disperse suspensions, Desalination 2002; 146: 63-68. http://dx.doi.org/10.1016/S0011-9164(02)00489-7 DOI: https://doi.org/10.1016/S0011-9164(02)00489-7

Breedveld van den Ende VD, Bosscher M, Jongchaap RJJ, Mellema J. Measurement of the full shear-induced self-diffusion tensor of non-colloidal suspensions, Journal of Chemical Physics 2002; 116: 10529-10535. http://dx.doi.org/10.1063/1.1478770 DOI: https://doi.org/10.1063/1.1478770

Bian R, Yamamoto K, Watanabe Y. The effect of shear rate on controlling the concentration polarization and membrane fouling. Desalination 2000; 131: 225-236. http://dx.doi.org/10.1016/S0011-9164(00)90021-3 DOI: https://doi.org/10.1016/S0011-9164(00)90021-3

Kromkamp J, Bastiaanse A, Swarts J, Brans G, R. van Sman GM, Boom RМ. A suspension flow model for hydrodynamics and concentration polarization in cross flow micro filtration. Journal Membrane Science 2005; 253: 67-79. http://dx.doi.org/10.1016/j.memsci.2004.12.028 DOI: https://doi.org/10.1016/j.memsci.2004.12.028

Belfort G, Davis RH, Zydney AL. The behavior of suspensions and macromolecular solutions in cross-flow microfiltration Journal of Membrane Science 1994, 96: 1-58. http://dx.doi.org/10.1016/0376-7388(94)00119-7 DOI: https://doi.org/10.1016/0376-7388(94)00119-7

Green G, Belfort G. Fouling of ultrafiltration membranes: Lateral migration and the particle trajectory model. Desalination. 1980; 35: 129-147. http://dx.doi.org/10.1016/S0011-9164(00)88607-5 DOI: https://doi.org/10.1016/S0011-9164(00)88607-5

van Reis R, Zydney A. Bioprocess membrane technology. Journal of Membrane Science 2007; 297: 16-50. http://dx.doi.org/10.1016/j.memsci.2007.02.045 DOI: https://doi.org/10.1016/j.memsci.2007.02.045

Jiang T, Kennedy MD, Chang Kyoo Yoo, Nopens I, van der Meer W, Futselaar H, Schippers JC, Vanrolleghem PA. Controlling submicron particle deposition in a side-stream membrane bioreactor: A theoretical hydrodynamic modeling approach incorporating energy consumption. Journal of Membrane Science 2007; 297: 141-151. http://dx.doi.org/10.1016/j.memsci.2007.03.033 DOI: https://doi.org/10.1016/j.memsci.2007.03.033

Ould-Dris A, Jaffrin MY, Si-Hassen D, Neggaz Y. Effect of cake thickness and particle poly-dispersity on prediction of permeate flux in microfiltration of particulate suspensions by a hydrodynamic diffusion model. Journal of Membrane Science 2000; 164: 211-227. http://dx.doi.org/10.1016/S0376-7388(99)00194-5 DOI: https://doi.org/10.1016/S0376-7388(99)00194-5

Li H, Fane AG, Coster HG, Vigneswaran S. Direct observation of particle deposition on the membrane during cross flow micro filtration. Journal of Membrane Science 1998; 149: 83-97. http://dx.doi.org/10.1016/S0376-7388(98)00181-1 DOI: https://doi.org/10.1016/S0376-7388(98)00181-1

Mung-man Kim, Zydney A. Theoretical analysis of particle trajectories and sieving in two-dimensional cross-flow filtration system. Journal of Membrane Science 2006; 281: 666-675. http://dx.doi.org/10.1016/j.memsci.2006.04.037 DOI: https://doi.org/10.1016/j.memsci.2006.04.037

Bachini P, Aimar P, Feld RW. Critical and sustainable fluxes: Theory, experiments and applications. Journal of Membrane Science 2006; 281: 42-69. http://dx.doi.org/10.1016/j.memsci.2006.04.014 DOI: https://doi.org/10.1016/j.memsci.2006.04.014

Lifia MY, Le-Cheh P, Stuetz RM, Vicki Chen. Characterisation of membrane fouling deposition and removal by direct observation technique. Journal of Membrane Science 2009; 341: 163-171. http://dx.doi.org/10.1016/j.memsci.2009.06.001 DOI: https://doi.org/10.1016/j.memsci.2009.06.001

Thorsen T. Concentration polarization by natural organic matter (NOM) in NF and UF. Journal of Membrane Science 2004, 233: 79-91. http://dx.doi.org/10.1016/j.memsci.2004.01.003 DOI: https://doi.org/10.1016/j.memsci.2004.01.003

Zhang YP, Fane AG, Law AWK. Critical flux and particle deposition of bidisperse suspensions during cross-flow microfiltration. Journal of Membrane Science 2006; 282: 189-197. http://dx.doi.org/10.1016/j.memsci.2006.05.022 DOI: https://doi.org/10.1016/j.memsci.2006.05.022

Ghidossi R, Veyret D, Moulin P. Computational fluid dynamics applied to membranes: State of the art and opportunities. Chemical Engineering and Processing 2006; 45: 437-454. http://dx.doi.org/10.1016/j.cep.2005.11.002 DOI: https://doi.org/10.1016/j.cep.2005.11.002

Agashichev SP. Pressure Driven Membrane Processes (Modeling and Analysis). New York: Nova Science Publishers 2012. ISBN: 978-1-61942-411-1.

Berman AS. Laminar flow in channels with porous walls, Journal of Applied Physics 1953; 24: 1232-1235. http://dx.doi.org/10.1063/1.1721476 DOI: https://doi.org/10.1063/1.1721476