Chen Ching-Yao, Huang C-W, Gadêlha Hermes, Miranda José A
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016306. doi: 10.1103/PhysRevE.78.016306. Epub 2008 Jul 17.
A modified version of the usual viscous fingering problem in a radial Hele-Shaw cell with immiscible fluids is studied by intensive numerical simulations. We consider the situation in which the fluids involved are miscible, so that the diffusing interface separating them can be driven unstable through the injection or suction of the inner fluid. The system is allowed to rotate in such a way that centrifugal and Coriolis forces come into play, imposing important changes on the morphology of the arising patterns. In order to bridge from miscible to immiscible pattern forming structures, we add the surface tensionlike effects due to Korteweg stresses. Our numerical experiments reveal a variety of interesting fingering behaviors, which depend on the interplay between injection (or suction), diffusive, rotational, and Korteweg stress effects. Whenever possible the features of the simulated miscible fronts are contrasted to existing experiments and other theoretical or numerical studies, usually resulting in close agreements. A number of additional complex morphologies, whose experimental realization is still not available, are predicted and discussed.
通过密集的数值模拟研究了径向Hele-Shaw单元中具有不混溶流体的常见粘性指进问题的一个修改版本。我们考虑所涉及的流体是可混溶的情况，这样分隔它们的扩散界面可以通过内部流体的注入或抽吸而变得不稳定。系统以这样一种方式旋转，使得离心力和科里奥利力起作用，对所产生图案的形态产生重要变化。为了从可混溶的图案形成结构过渡到不混溶的图案形成结构，我们添加了由于科特韦格应力引起的类似表面张力的效应。我们的数值实验揭示了各种有趣的指进行为，这些行为取决于注入（或抽吸）、扩散、旋转和科特韦格应力效应之间的相互作用。只要有可能，就将模拟的可混溶前沿的特征与现有的实验以及其他理论或数值研究进行对比，通常会得到密切的一致。预测并讨论了一些额外的复杂形态，其实验实现仍然不可用。
