Axisymmetric motion of a solid particle embedded in a Brinkman micropolar fluid in the presence of a plane wall

Abstract

The axisymmetric motion of a solid spherical particle embedded in a hydrogel medium in the presence of a planar wall surface is investigated semi-analytically. The hydrogel medium is modeled as a porous medium saturated with a microstructure fluid of micropolar type. The no-slip velocity and no-slip spin boundary conditions are considered at both the particle surface and the plane wall surface. The sixth-order differential equation describing the stream function of the micropolar fluid flow through the voids of the porous medium is constructed under the assumption of low Reynolds numbers. The general solution of the equation satisfied by the stream function in the porous region is obtained from the superposition of basic solutions in both cylindrical and spherical coordinates. To satisfy first the boundary condition at the planar surface, we apply the Fourier–Bessel transforms and then at the surface of the particle by a boundary collocation technique. The collocation scheme for the normalized drag force acting on the particle is calculated with good convergence for various values of the relevant parameter. Our results are in good agreement with the available data in the literature. The findings of the present investigation demonstrate that the presence of the planar surface, micropolarity, and permeability parameters has significant effects on the drag force. This study is motivated by its potential application on micro- and ultra-filtration.