Diffusion and Viscosity in a Spherical Cavity

Publisher Website
Google Scholar
Abstract
A system consisting of two, in principle concentric, spherical surfaces separated by a fluid, is considered. The torque and force required to rotate and translate the inner sphere is calculated, as well as the work necessary to maintain fluid flow around it, the flow pattern at the outer sphere being specified. Using this, general expressions for the diffusion constants for rotation and translation for the inner sphere and for the effective viscosity of the bulk liquid are obtained. The inner sphere (a) can be viscous, its surface may slip or adsorb fluid. The effect of a perturbation in the flow pattern at the outer surface (R) is examined. For a small value of a/R, the expressions become those given by Stokes and Einstein for dilute solutions. For the ratio a/R≈1, the expressions apply to liquids flowing through membranes or porous media. Rotational diffusion of paramagnetic hydrates in diamagnetic environment, translational diffusion of ions through membranes, the viscosity of concentrated suspensions and fluid flow through porous media are discussed.

This publication has 13 references indexed in Scilit: