Axisymmetric creeping motion caused by a spherical particle in a micropolar fluid within a nonconcentric spherical cavity

摘要

The problems of the quasisteady translation and steady rotation of a solid spherical particle located at a non-concentric position of a spherical cavity filled with an incompressible micropolar fluid are investigated semi-analytically in the limit of low Reynolds numbers. General solutions are constructed from the superposition of the basic solutions in the two spherical coordinate systems based at the centers of the particle and cavity. The boundary conditions on the particle surface and cavity wall are satisfied by a collocation numerical method. The hydrodynamic drag force and torque exerted by the fluid on the particle which are proportional to the translational and angular velocities respectively are obtained numerically with good convergence for a range of values of the ratio of particle-to-cavity radii, the relative distance between the centers of the particle and cavity and micropolarity parameter. In the limit of the motion of a spherical particle in a concentric position in the cavity and in the lubrication limit, the hydrodynamic drag force and torque are in good agreement with the available results in the literature. As expected, the boundary-corrected drag force and torque exerted on the particle is a monotonic increasing function of the micropolarity parameter. (C) 2019 Elsevier Masson SAS. All rights reserved.