Conditions of compatibility for the solid-liquid interface Academic Article uri icon


  • The seminal theory of singular surfaces propounded by Hadamard and Thomas is examined within the context of the dynamics of a solid-liquid interface. It is shown that most of the hypotheses upon which Clapeyrons equation is based can be weakened and two generalized versions of it are derived: with and without curvature effects. The remaining part of the paper is mainly focused on the interface conditions for the classical Stefan problem. The counterpart of Clapeyrons equation for such a problem will give an explicit expression for the supercooling temperature without recourse to linearization procedures. Furthermore, a decay law for the latent heat of melting is given which shows, in an explicit way, its complex dependence upon the curvature and the normal speed of the interface. Finally, a transport equation for the interface temperature is derived and a qualitative solution of a simplified version of it is given for the particular case in which the jump in the Helmoltz free energies of the bulk phases is a conserved quantity throughout the field.

published proceedings

  • Quarterly of Applied Mathematics

author list (cited authors)

  • Baldoni, F., & Rajagopal, K. R.

citation count

  • 6

complete list of authors

  • Baldoni, F||Rajagopal, KR

publication date

  • January 1997