Slow motion of a slip spherical particle parallel to one or two plane walls

A combined analytical-numerical study for the creeping flow caused by a rigid spherical particle translating and rotating in a viscous fluid parallel to two flat plates at an arbitrary position between them is presented. The fluid, which may be a slightly rarefied gas, is allowed to slip at the surface of the particle. To solve the Stokes equations for the fluid velocity field, a general solution is constructed from fundamental solutions in both rectangular and spherical coordinate systems. Boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the hydrodynamic drag force and torque acting on the particle are obtained with good convergence for various values of the slip coefficient of the particle and of the separation distances between the particle and the walls. For the motion of a no-slip sphere and a perfectly-lip sphere parallel to a single plane wall or to two walls, our drag and torque results are in good agreement with the available solutions in the literature for all particle-to-wall spacings. The boundary-corrected drag force and torque exerted on the particle in general decrease with an increase in the slip coefficient for any given geometry.