| Abstract: |
| The dissolution of a solid spherical particle in a surrounding quiescent solvent is a canonical problem that is found in many industrial and consumer applications, ranging from pharmaceutical and food products, to chemicals, detergents, and paints. Mathematically, this constitutes a moving-boundary problem, akin to a classical Stefan problem. However, analysis of a time-dependent, spherically symmetric diffusion-dominated problem indicates a variety of possible pitfalls with the modelling of this problem, even when adopting the seemingly uncontroversial common assumption that the dissolution (reaction) kinetics at the interface are fast compared to mass transfer from the interface, i.e. the limit of infinite Damkohler number. Much of the discussion centres on the appropriate boundary condition that should be used at the dissolution surface in the situation when the density of the solvent is different to that of the particle, as is almost always the case in practice. In particular, we find that the radial solvent flow which dissolution sets into motion results in velocity and pressure singularities when dissolution begins, although the first of these is removed if the Damkohler number is finite. |
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