Description of the phase division movement appears to be a common problem, which arises during research of structure formation in liquid consolidation. The model of "sharp interface" between phases, meaning the zero thickness of the border of phase division, is widely used for that. Parameter of order φ - phase field is being inserted for description of switch to the model of "sharp interface", which in a continuous way describes the border of solid and liquid phases. Such an extreme switch allows to compare parameters, used in the model of phase field, and real, experimentally measured parameters of researched physical system. It is a necessary methodological step for correct comprehension of the used model and theoretical approximations. At the same time the procedure of extreme switch is not trivial, since in basic asymptotic limit, where thickness of division surface δ → 0, but remaining parameters stay fast, model of phase field does not add up to the problem with a hard edge like Stephen problem. Assuming different conditions for remaining parameters of the model (surface tension, mobility of the phase field), generally speaking, different extreme problems with hard edge can be received.

The goal of this work is research of the asymptotic limit of "sharp interface" for the model of high speed phase field in a locally non-equilibrium binary system and receiving thermodynamic conditions, defining the border of two phase division.

The received equations set is an equivalent system of hyperbolical ratio on hard edge and in the volume of phases at locally non-equilibrium transfer of atoms. However, in addition to equations of transfer in volume of phases and mass balance on the phase border, system includes also thermodynamic conditions on density of free energy. In the local equilibrium limit, that is at instantaneous relaxation of diffuse stream τ_D→0, system switches to system analyzed by Kessler earlier.