Slow translation and rotation of a composite sphere within a nonconcentric spherical cavity normal to their common diameter

Abstract A semi-analytical study of coupled translation and rotation of a composite spherical particle (a hard sphere core coated with a permeable porous layer) in a viscous fluid inside an eccentric spherical cavity normal to their common diameter is presented in the quasi-steady limit of low Reynolds number. To solve the Stokes and Brinkman equations for the flow fields outside and inside the porous layer, respectively, a general solution is constructed from the fundamental solutions in the two spherical coordinate systems based on both the composite particle and the cavity. The boundary conditions at the cavity wall and inner and outer surfaces of the porous layer are satisfied by a collocation method. Numerical results for the force and torque exerted on the particle by the fluid are obtained with good convergence for various values of the relevant parameters in practical applications. For the translation and rotation of a composite sphere inside a concentric cavity, our force and torque results agree well with the available solutions in the literature. The force and torque on a translating and rotating particle increase monotonically with increases in the ratios of particle radius to porous layer permeation length, core-to-particle radii, and particle-to-cavity radii. In general, they also increase with an increase in the relative distance between the particle and cavity centers. The boundary effect of the cavity on the translation of the particle is much more pronounced than that on the rotation. The coupling effect in the simultaneous translation and rotation inside an eccentric spherical cavity is complicated and not a monotonic function of the particle-to-cavity radius ratio.