扩散界面模型输运问题精确解的张量导纳
Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces
摘要：
分析了相场模型中两相输运的一般问题：守恒量的通量由势的梯度驱动通过由两个不同相的区域组成的介质，所述两个不同相被扩散界面分开。结果表明，有限厚度的接口引起两个效果，是不存在的类似的尖锐的接口问题：一个表面过电流和潜在的接口跳跃。结果表明，这两种效果可以同时消除，只有当之间的比例系数的通量和电势梯度（流动性）被允许成为一个张量的接口。这为精确和有效地模拟有限界面厚度的输运问题提供了可能性。
英文摘要：
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by diffuse interfaces. It is shown that the finite thickness of the interfaces induces two effects that are not present in the analogous sharp-interface problem: a surface excess current and a potential jump at the interfaces. It is shown that both effects can be eliminated simultaneously only if the coefficient of proportionality between flux and potential gradient (mobility) is allowed to become a tensor in the interfaces. This opens the possibility for precise and efficient simulations of transport problems with finite interface thickness.
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