Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.