CONDITIONS OF COMPATIBILITY FOR THE SOLID-LIQUID INTERFACE

The seminal theory of singular surfaces propounded by Hadamard and Tho mas is examined within the context of the dynamics of a solid-liquid i nterface. It is shown that most of the hypotheses upon which Clapeyron 's equation is based can be weakened and two generalized versions of i t are derived: with and without curvature effects. The remaining part of the paper is mainly focused on the interface conditions for the cla ssical Stefan problem. The counterpart of Clapeyron's equation for suc h a problem will give an explicit expression for the supercooling temp erature without recourse to linearization procedures. Furthermore, a d ecay law for the latent heat of melting is given which shows, in an ex plicit way, its complex dependence upon the curvature and the normal s peed of the interface. Finally, a transport equation for the interface temperature is derived and a qualitative solution of a simplified ver sion of it is given for the particular case in which the jump in the H elmoltz free energies of the bulk phases is a conserved quantity throu ghout the field.