The diffusion-controlled dissolution of spheres

Abstract

The partial differential equations which describe the diffusion controlled behaviour of an isolated sphere growing or dissolving in conditions of spherical symmetry are presented. These have been solved numerically by methods already shown, by comparison with analytical solutions for growth from zero size, to give accurate results for growing spheres. Computed radius-time relations, time to dissolve completely and concentration profiles are illustrated and discussed. The influences of radial motion of the boundary and convection in the liquid are considered and shown to be important even for very high solubility. The only simple approximation of any useful range of validity is the quasi-steady state model which is valid only for very low solubilities. The flat slab model which might be expected to apply for high solubilities is useful only for the early stages of dissolution because of the change in size of the sphere.