Free-convective dissolution of a solid spherical particle

The dissolution of a solid spherical particle is a canonical problem that finds many industrial applications, ranging from pharmaceutical and food products to chemicals, detergents, and paints. A particular situation of interest is when a solid particle dissolves in a quiescent solvent; in this case, perhaps contrary to expectation, dissolution need not necessarily be diffusion-dominated, since the dissolved material may affect the local density of the solvent, resulting in free convection. In this paper, we account for this problem theoretically by extending the framework established in the recent work for the case of forced-convective dissolution. Nondimensionalization of the appropriate time-dependent mass, momentum, and solute balance equations yields an axisymmetric moving-boundary problem, which can be formulated in terms of four dimensionless parameters. Asymptotic and numerical approaches to the problem are considered, with a key outcome being a numerical method, implemented in the finite-element software Comsol Multiphysics. A simpler approach involving a mass-balance argument and based on correlations for steady flow past a sphere is also considered; by and large, the two approaches give reasonable agreement for a wide range of the relevant dimensionless parameters. Finally, the application of the model to pharmaceutical dissolution experiments is discussed.