Effective medium treatment of laminar flow in magnetic filtration

Abstract

A theory for laminar flow through randomly distributed magnetic spheres which uses an effective medium treatment (EMT) is presented. In the EMT, the system of fluid and spheres is replaced by a composite sphere—a representative sphere of radius a enclosed by a fluid shell of radius b—embedded in an effective medium of different viscosity. The velocity fields in the fluid shell and in the effective medium as a function of sphere volume packing fraction (γ3=a3/b3) or density of spheres in liquid are determined by using Green’s theorem and proper boundary conditions. The results are applied to study the capture of paramagnetic and diamagnetic particles by an assemblage of spheres. The capture radius as a function of γ and applied magnetic field (H0) is obtained and compared with results from previous study based on Happel’s theory. The dependence of capture radius on H0 is also given for various fixed values of γ. Finally, filter efficiency is predicted for varying γ and H0.