A time-dependent process of directional crystallization with a two-phase (mushy) region with allowance for vigorous convection in the liquid phase is analytically described. An exact solution of non-linear mushy layer equations is found in a parametric form. The temperature and solute concentration distributions, as well as the solid phase fraction profile, are determined in the two-phase and liquid regions. The moving boundary of phase transition, which is placed between the two-phase zone and liquid is defined as a function of time. The present analytical solutions are in good agreement with laboratory experiments on ice grown from aqueous solutions of isopropanol.

中文翻译：

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关于强对流两相区定向结晶的理论

分析性地描述了随时间变化的定向结晶过程，该过程具有两相（糊状）区域，允许在液相中剧烈对流。以参数形式找到了非线性糊状层方程的精确解。在两相和液相区域中确定温度和溶质浓度分布以及固相分数分布。置于两相区和液体之间的相变运动边界被定义为时间的函数。本分析溶液与从异丙醇水溶液中生长的冰上的实验室实验非常吻合。