Exact solution of the problem of dissolved gas segregation by the plane crystallization front

Analytical solution of the segregation problem was found for the arbitrary crystal growth law using the quasi-steady-state approximation. The segregation is caused by the displacement of dissolved gas by moving plane crystallization front. The effect of solidification shrinkage on the crystallization process was taken into account. It is shown that in the case of "equilibrium crystallization" (when the growth rate is in inverse ratio to time) the solution of the problem becomes self-similar. In this case gas concentration at the crystallization front stays the same during the whole process while the diffusion layer thickness increases with time.