Analytical solution of the problem of dissolved gas segregation in melt by the plain crystallization front

Analytical solution of the segregation problem is found for the arbitrary crystal growth law using the quasi-steady-state approximation. The segregation in this case 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. The comparison made between obtained solution and existing exact solutions shows good agreement. It is shown that in the case of “equilibrium crystallization” (when the growth rate is inversely proportional to time) the solution of the problem becomes self-similar. In this case gas concentration at the crystallization front instantly increases to a certain value and than stays the same during the whole process. At the same time the diffusion layer thickness increases proportionally to time. The conditions for the inevitability of gaseous release leading to the formation of pores in solidified material is formulated for the general case.