Diffusion-controlled dissolution of a binary solid into a ternary liquid with partially molten zone formation

We build a theoretical model of equilibrium dissolution of a homogeneous, solid mixture of two salts A and B, KCl and NaCl being used as the type example, into an aqueous solution of the two salts, with diffusive transport. We find that there are two sharp dissolution fronts, separating fluid, a partially-molten zone containing a single solid, and mixed solid. The phase change happens almost entirely at the two sharp fronts. In equilibrium, the leading front exhibits a small amount of precipitation of NaCl, simultaneous with complete dissolution of KCl. There is a unique surface in the space of far-field fluid KCl concentration, far-field fluid NaCl concentration, and solid composition, dividing conditions where NaCl is the solid in the partially-molten zone, from conditions where KCl is the solid in the partially-molten zone. The movement rates of the dissolution fronts decrease as the concentration of either salt in the far-field fluid is increased. The movement rates of the dissolution fronts increase as either far-field temperature is increased, but this effect is smaller than that of concentration. In most circumstances, the dissolution front for a given salt moves more slowly, the more of that salt is present in the original solid, although the mass dissolution rate is not greatly affected by the solid composition.