Carvalho Gabriel D, Miranda José A, Gadêlha Hermes
Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):053006. doi: 10.1103/PhysRevE.88.053006. Epub 2013 Nov 11.
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity.
我们研究了Hele-Shaw盒中经典粘性指进不稳定性的一个变体，其中分隔流体的界面是弹性的，并呈现出与曲率相关的弯曲刚度。通过采用二阶模式耦合方法，我们研究了界面的弹性性质如何影响新兴界面图案的形态。这是通过将注意力集中在一种传统上稳定的情况来实现的，即所涉及的流体具有相同的粘度。在此框架下，我们表明，纳入非线性效应在引发相当大的界面不稳定性以及确定图案形成结构的最终形状方面起着至关重要的作用。特别地，我们发现，通过调整刚度分数参数，可以调节窄指或宽指的出现。我们的弱非线性研究结果强化了所谓曲率弱化效应的重要性，该效应有利于在较低刚度区域形成指状结构。
