Latva-Kokko M, Rothman Daniel H
Department of Earth Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):056702. doi: 10.1103/PhysRevE.71.056702. Epub 2005 May 12.
We study the diffusion and phase separation properties of a gradient-based lattice Boltzmann model of immiscible fluids. We quantify problems of lattice pinning associated with the model, and suggest a scheme that removes these artifacts. The interface width is controlled by a single parameter that acts as an inverse diffusion length. We derive an analytic expression of a fully developed interfacial curve and show that interfaces evolve towards this stable distribution if no fluid is trapped. Fluid can become trapped inside a competing phase if no connecting path to the bulk phase exists. Such trapped bubbles also evolve towards the fully developed interfacial curve but constraints on mass conservation limit this development. We also show how small numerical errors lead to spontaneous phase separation for all values of the diffusion length.
我们研究了基于梯度的互不相溶流体晶格玻尔兹曼模型的扩散和相分离特性。我们量化了与该模型相关的晶格钉扎问题，并提出了一种消除这些伪影的方案。界面宽度由一个充当逆扩散长度的单一参数控制。我们推导了充分发展的界面曲线的解析表达式，并表明如果没有流体被困住，界面会朝着这种稳定分布演化。如果不存在通向主体相的连接路径，流体可能会被困在竞争相中。这种被困气泡也会朝着充分发展的界面曲线演化，但质量守恒的限制会限制这种发展。我们还展示了对于所有扩散长度值，小的数值误差如何导致自发相分离。
