Dynamics of solidification in binary melts during rapid cooling I. The basic equations

In this paper we deal with the analysis of the general complex model which describes the solidification of the binary melt. Within the framework of this model we consider the mass and energy transport in the system and the kinetics of the phase transformation. The paper is divided into two parts. In the first part the set of equations is derived, which describe the evolution of the system within the framework of the theory of stochastic processes. The emphasis is laid on the rapid changes of temperature in the system. In the second part the analysis of the mentioned set of equations is presented. It results in the delimitation of the conditions under which the adiabatic approximation and the kinetic phase diagrams at the phase interface can be applied.