(372i) Motion of a Spherical Particle Near a Porous Boundary

The flow of suspensions near porous boundaries occurs in a variety of industrial processes, such as shear-enhanced filtration, and in living systems, such as blood flowing through capillaries. Some of the important questions that arise are how the permeability of the porous walls and the concomitant velocity slip affect the dynamics of individual particles, and the effective rheology of the suspension. In this study, we consider the motion of a single rigid sphere near a plane permeable wall; the Stokes equations are solved by obtaining the velocity and pressure fields as eigenfunction expansions in the bispherical co-ordinate system. The boundary conditions at the porous wall are Darcyâ??s flux condition normal to the surface and Saffmanâ??s slip condition in the tangential direction. In addition, we impose the condition of zero net flux across the porous wall, and obtain the non-zero pressure on the other side of the porous wall. The drag and torque on the particle moving near a porous wall are computed and compared with those obtained for an impermeable wall. The effect of various parameters such as distance of the particle from the wall, permeability, slip coefficient and wall thickness are studied. Finally, we comment on the implications of our results on recent measurements of the suspension stress near porous boundaries.