Interaction between a non-concentric rigid sphere immersed in a micropolar fluid and a spherical envelope with slip regime

Abstract

A semi-analytical investigation of a quiescent micropolar fluid between a rigid sphere and a non-concentric spherical envelope with a slip regime is obtained. Two different cases have been considered one is the hydrodynamic drag strength and the translational wall correction factor (TWCF) exerted by the fluid on the inner sphere are proportional to the translational velocities and the second is the hydrodynamic torque and the rotational wall correction factor (RWCF) are applied to the inner sphere which is proportional to the angular velocities. The numerical solution is composed of the superposition of the fundamental solutions in the two spherical coordinate systems setups on the poles of the rigid sphere and the spherical envelope by using a collocation scheme. The boundary conditions, slip, and spin-slip are presented on the sphere’s surfaces. The results were achieved numerically with excellent convergence for the parameters, size ratio, separation distance, micropolarity parameter, slip, slip-spin parameters. Limiting cases are agreeable with the obtainable results in the literature.