Analytical solutions of the segregation problem

New analytical solutions of the segregation problem were found. The segregation is caused by the dissolved gas displacement by a moving crystallization front. The displacement is caused by the low solubility of the volatiles in solid, so the dissolved gas is withdrawn from the crystallizing melt towards the surrounding melt. Two different modes of crystallization were considered. The first one is the case of constant crystal growth rate which takes place in the case of intensive heat removal or when only initial stage of crystallization process is considered. The second mode is the “normal growth law” which is a self-similar solution of the crystal growth problem. In this case the crystal growth rate is inversely proportional to a square root of time. In contrast to the already existing solutions here the solidification shrinkage is taken into account