Motion through spherical droplet with non-homogenous porous layer in spherical container

Abstract

The problem of the creeping flow through a spherical droplet with a non-homogenous porous layer in a spherical container has been studied analytically. Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is calculated. Emphasis is placed on the spatially varying permeability of a porous medium, which is not covered in all the previous works related to spherical containers. The variation of hydrodynamic permeability and the wall effect with respect to various flow parameters are presented and discussed graphically. The streamlines are presented to discuss the kinematics of the flow. Some previous results for hydrodynamic permeability and drag forces have been verified as special limiting cases.