Low-Reynolds-number rotation of a soft particle inside an eccentric cavity

Abstract

The steady low-Reynolds-number rotation of a spherical soft particle (a hard core coated with a permeable porous layer) in a viscous fluid within a nonconcentric spherical cavity about their common diameter is semi-analytically studied. To solve the Stokes and Brinkman equations for the fluid velocity, a solution is constituted by the general solutions in two spherical coordinate systems originated from the particle and cavity centers and the boundary conditions are satisfied by a collocation technique. Numerical results of the hydrodynamic torque on the soft sphere are obtained as a function of the core-to-particle radius ratio, particle-to-cavity radius ratio, relative center-to-center distance of the particle and cavity, and ratio of the particle radius to the permeation length in the porous layer over the entire ranges. The effect of the cavity on the torque of a rotating soft particle is weaker than that of a corresponding hard particle (or soft one with lower permeability or thinner thickness of its porous layer). While the normalized torque of a soft sphere in general is an increasing function of the particle-to-cavity radius ratio, a weak minimum of it (surprisingly, less than the value of an unconfined particle) may occur for a particle with a small to mediate core-to-particle radius ratio and a high permeability inside a nonconcentric cavity at a moderate value of the particle-to-cavity radius ratio. Also, this torque in general is an increasing function of the eccentricity of the particle location, but it may decrease slightly with an increase in the eccentricity for a particle with a small to mediate core-to-particle radius ratio and a high permeability.