We present new analytic results relating to the nonstationary Stefan-type problems for the unidirectional solidification of binary solutions or melts with a mushy layer. Our detailed analysis of the field data is based on the classical model of a mushy layer, which is modified in order to obtain explicit solutions (solid phase thickness and growth rate, temperature distributions, conductive and latent heat fluxes are determined). Predictions for the growth rate and temperature profiles of the mixed-phase and solid regions agree well with existing observations on young sea ice dynamics. (c) 2007 Elsevier Ltd. All rights reserved.