Melting and dissolving of a vertical solid surface with laminar compositional convection

We consider laminar compositional convection of buoyant melt released by ablation of a vertical solid surface into a two-component fluid. Asymptotic solutions are used to describe separate cases: the ablation rate is either controlled by thermal transport, corresponding to melting, or by solutal transport, corresponding to dissolution. Melting is faster and generates a stronger flow than dissolving. We determine the temperature and solute concentration conditions leading to either melting or dissolving and find that these conditions do not vary with the strength of the buoyancy that drives convective flow.