Mathematical modeling of drop solidification

Drop solidification is widespread as in environment, as in different technologies. The solidification of drop starts from the outer boundary and at the very initial time period enough thin solid layers is formed on the outer drop boundary. After that the solidification process progresses as an ordinary phase transition process, as a rule, with spherical symmetry. However most of phase transitions lead to sharp density change. As a rule, density of solid phase is more, than liquid one, but the created surface solid layer resists to any radial load and saves the shape of drop, thus a hole is formed in the center of the drop. Otherwise, for example, for water, ice density is less than water density and, as a result, sufficient residual stresses take place after drop solidification. Solution of correspondent problem for spherical drop is presented.