In this paper we analyse the effect of mass diffusion in a Stefan-like problem, referring to the interaction between ice shelves and seawater in Antarctica. This interaction is particularly important, being responsible for the vast majority of ice loss from Antarctica. We conclude that, in our specific case, the results obtained with the model which takes into account mass diffusion are almost indistinguishable from those obtained from the mass diffusion free model, and that therefore possible inversion layers are to be attributed to effects other than mass transfer of salt.