THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
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DOI：
10.1142/s0218202511500138
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发表时间：
2012-03-01
影响因子：
3.5
通讯作者：
Gruen, Guenther
中科院分区：
文献类型：
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作者：
Abels, Helmut;Garcke, Harald;Gruen, Guenther
利用合理连续介质力学的方法，建立了两种不同密度不可压缩流体两相流动的扩散界面模型。该模型满足局部和全局耗散不等式，并且是框架无关的。此外，它被推广到具有可溶物种的情况。利用匹配的渐近展开法，我们导出了当界面厚度趋于零时，极限情况下的各种尖锐界面模型。根据扩散方程中迁移率的大小，我们要么推导出经典的尖锐界面模型，要么推导出在极限条件下体扩散或表面扩散的模型。在后一种情况下，由表面扩散引起的新项出现在界面的动量平衡中。最后，我们证明了所有的尖锐界面模型都满足自然能量不等式。
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation, we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.