On the dissolution of a solid spherical particle

Abstract

The dissolution of a solid spherical particle is a canonical problem that finds many areas of application. In this work, we provide a generalized theory that takes into account the role of forced convection in the solvent (or, alternatively, the relative motion of the particle in the solvent), showing that the problem can be formulated in terms of four dimensionless parameters. Focusing on the case when one of these (the Reynolds number) is small, we consider asymptotic and numerical approaches to the problem, with a key outcome being a numerical method, implemented in the finite-element software Comsol Multiphysics, that is able to solve the resulting axisymmetric moving-boundary problem, even when over 90% of the particle has dissolved and its shape is far from spherical. We also demonstrate how this approach relates to and supersedes earlier efforts, providing a quantitative assessment of the often unquestioningly used Ranz–Marshall correlation for mass transfer from a sphere. In particular, we find that this correlation may overpredict the dissolution time by a factor of four, whereas a correlation by Clift et al. that is cited and used less often performs considerably better, even in the highly convection-dominated regime for which it was not originally intended.