通过应用匹配渐近展开法和多变量展开法研究了各向异性界面动力学与各向异性表面张力的相互作用对定向凝固过程中深胞晶生长的影响.结果表明:当各向异性界面动力学与各向异性表面张力的偏好方向之间相差角度为θo时,θ0会对深胞晶生长形态产生影响;当0≤θo≤π/4时,随着θo的增大,深胞晶的指状界面全长减小,深胞晶根部的深度减小,根部附近界面的曲率减小,而曲率半径增大;当π/4≤θo≤π/2时,随着θ0的增大,深胞晶的指状界面全长增大,深胞晶根部的深度增大,根部附近界面的曲率增大,而曲率半径减小.%In this paper,we study the effects of anisotropic interface kinetics and surface tension on deep cellular crystal growth in directional solidification.The following assumptions are made:the process of solidification is viewed as a twodimensional problem;the minor species in this binary mixture system is considered as an impurity;the solute diffusion in the solid phase is negligible;the thermodynamic properties other than the diffusivities are the same for both solid and liquid phases;there is no convection in the system;the anisotropic interface kinetics and the anisotropic surface tension are a four-fold symmetry function each;neither the preferred directions of the anisotropic interface kinetics nor the anisotropic surface tensions are necessarily the same as their counterparts for the solid and liquid phases respectively;the angle between the preferred directions of the two anisotropies is θ0.By using the matched asymptotic expansion method and the multiple variable expansion method,we obtain the diagram of interface morphology for a deep cellular crystal in directional solidification.The results show that there exists a discrete set of the steady-state solutions subject to the quantization condition (35).The quantization condition yields the eigenvalue ξ* as a function of parameter ε and other parameters of the system,which determines the interface morphology of the cell.The results also show the variation of the minimum eigenvalue ξ*(0) with parameter ε.It is seen that when the preferred directions of the two anisotropies are the same,i.e.,θ0 =0,the minimum eigenvalue ξ*(0) reduces with the increase of anisotropic surface-tension coefficient α4,increases with the augment of parameter ε,and is unrelated to anisotropic interface kinetic coefficientβ4 in the low order;when the angle 0 ≤ θ0 ≤ π/4,as the θ0 increases,the minimum eigenvalue ξ*(0) increases;when the angle π/4 ≤ θ0 ≤ π/2,as the θo increases,the minimum eigenvalue ξ*(0) decreases.In addition,the results show the composite solution for the interface shape function ηB described on (X,Y) plane.It is seen that both of the anisotropy and the angle θ0 have a significant effect on the total length and the root of deep cellular crystal,however,have little influence on the other solid-liquid interface,such as the top of deep cellular crystal.When the angle θo is 0,as anisotropic coefficient increases,the total length of the finger increases,the curvature of the interface near the root increases or the curvature radius decreases.It is found that the influence of the anisotropic surface-tension coefficient on interface morphology is more remarkable than that of the anisotropic interface kinetics coefficient.when the angle 0 ≤ θ0 ≤ π/4,as the θ0 increases,the total length of the finger decreases,the curvature of the interface near the root decreases or the curvature radius increases;when the angle π/4 ≤ θ0 ≤ π/2,as θ0 increases,the total length of the finger increases,the curvature of the interface near the root increases or the curvature radius decreases.
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