One-dimensional motion of an emulsion with solidification

A mathematical model is proposed for the process of solidification of an emulsion with a small disperse-phase concentration moving under the action of thermocapillary forces and microgravity. The first-approximation problem that arises when solutions are represented as asymptotic series in a small parameter is examined. Conditions for the partial and complete displacement of the impurity from the solidified part and conditions for the accumulation of the impurity in the solidified mixture are obtained. The problem of producing a composite with a specified disperse-phase distribution is considered. Exact solutions that adequately reflect various features of the qualitative behavior of the general solution under different input data are obtained and examined.