中文摘要：

利用匹配渐近展开法和多变量展开法求出定向凝固深胞晶生长的浓度场和界面形态的全局渐近解，研究各向异性表面张力对定向凝固深胞晶生长的影响．结果表明，各向异性表面张力对定向凝固过程深胞晶生长有显著的影响．随着各向异性表面张力增大，胞晶前端部分浓度减小而胞晶界面收缩；胞晶根部的浓度增大而界面曲率增大或根部的曲率半径减小，各向异性表面张力使得深胞晶界面振幅增加．本文结果能够计算定向凝固过程中深胞晶生长的浓度、界面形态．

英文摘要：

An asymptotic solution of the concentration and interface morphology for a deep cellular crystal in directional solidification is obtained by using the matched asymptotic expansion method and multiple variable expansion method, and the effect of anisotropic surface tension on deep cellular crystal growth is studied. Results show that the anisotropic surface tension has a significant effect on the concentration and interface shape of deep cellular crystal growth in directional solidification. As the anisotropic surface tension parameter increases, the concentration near the front part of deep cellular crystal decays and the interface shrinks; when as the concentration near the root increases and the curvature of the interface near the root increases or the curvature radius decreases; and the amplitude of the deep cellular crystal increases. The concentration and interface shape of the deep cellular crystal in directional solidification can be calculated with the results obtained in this paper.