Hydrophobic effects on a solid sphere translating in a Brinkman couple stress fluid covered by a concentric spherical cavity

Abstract

In this study, a fluid flow with an incompressible axisymmetric steady couple stress translated through a porous media is analyzed between a hollow sphere and a concentric rigid sphere. In the permeable region, the flow field is regulated by Brinkman's equation. The slip and spin slip conditions are applied on both the rigid sphere and spherical cavity surfaces. Modified Bessel functions provide a systematic approach to the problem by utilizing the principle of a stream function. On the inner sphere, the wall correction factor that an incompressible couple stress fluid encounters is calculated. The effects of the slip, spin slip, coupling stress parameter, separation distance, and permeability parameter on the field functions and the normalized drag force are also graphically shown. The corresponding results are contrasted with the outcomes reported for particular cases of couple stress fluid and viscous fluid flow in two permeability-free concentric circles. Furthermore, graphs of the streamlines for various values of the relevant parameters have been included.