(659e) Effect of Convective Hindrance On Microfiltration of Rod Shaped Particles

Microfiltraction and ultrafiltraction membranes are used in water and wastewater treatment facilities to produce biologically stable water. Efforts to develop theoretical models to quantify the reflection coefficient including hindrance and configurational effects on the particle transport date back several decades. These models have primarily focused on rejection of spherical particles [1]. However, numerous pathogenic microorganisms including bacteria and viruses are rod-shaped and it is not clear whether existing theories applicable for spheres can be directly applied to predict their transport and removal in membrane systems. The principal objective of our present study is to develop models describing transport of rod shaped particles across porous membrane.

 We have previously reported experimental results for the rejection of several non-spherical bacteria and viruses from microfiltration membranes [2]. Results were compared to a theoretical model for capsule shaped particles that only considers configurational effects.

 We have begun an effort to develop a more comprehensive model of particle transport that includes both (i) the steric constraints on the position and orientation of the particles and (ii) the convective hindrance (lag coefficient) experienced by rod shaped particles within cylindrical pores. As a first approximation, we have incorporated predictions for the lag coefficient for spherical particles into our previous model that includes steric restrictions for rod shaped particles. Predictions are made using different equivalent size parameters to describe the hydrodynamic resistance of the rod: the diameter of a sphere with equivalent volume, the rod length, and the rod diameter. Numerical results show that incorporating the lag coefficient for rejection coefficient predictions has a greater effect for particles with small aspect ratio (i.e, close to spherical shape).

 We have also begun to perform CFD calculations to predict the lag coefficient for capsule shaped particles within a narrow channel with a rectangular cross-section. The objective here is to simulate fluid-particle interactions to evaluate the translation motion of the particle in a confined channel by calculating the hydrodynamic forces on the particle boundary[3]. The ratio of the translation velocity of the particle to the maximum fluid velocity yields the lag coefficient. The arbitary Lagrangian – Eulerian (ALE) algorithm is employed to simulate the system [3]. Results from both modeling approaches will be presented and discussed. The ALE method is verified with several previously reported standard benchmark problems.

 [1] Dechadilok, P. and Deen, W.M., “Hindrance Factors for Diffusion and Convection in Pores,” Industrial and Engineering Chemistry Research, 45, 6953-6959 (2006).

 [2] Baltus, R.E., Xu, W., Badireddy, A.R. and Chellam, S. “Analysis of Configurational Effects on Hindered Convection of Non-spherical Bacteria and Viruses across Microfiltration Membranes,” Industrial and Engineering Chemistry Research, 48, 2404-2413 (2009).

 [3] S.M Davidson, K.V Sharp, “Boundary effect on the electrophoretic motion of cylindrical particles: concentrically and eccentrically positioned particles in a capillary” Journal of Colloid and Interface Science, 303, 288-297 ( 2006)