On the mesoscopic description of locally nonequilibrium solidification of pure substances

A phase field model of locally nonequilibrium solidification of a supercooled melt of a pure substance has been proposed. To derive thermodynamically consistent equations of the model, the method of extended irreversible thermodynamics has been used. It has been assumed that Gibbs potentials describing thermodynamically equilibrium states in terms of experimental data are known. The limit of a sharp interface of the model has been considered and an analytical dependence of the velocity of a flat solidification front on the temperature has been obtained.