Elastic fingering in rotating Hele-Shaw flows.
Elastic fingering in rotating Hele-Shaw flows.
复制标题
DOI：
10.1103/physreve.89.053019
复制
发表时间：
2014-05
期刊：
影响因子：
--
通讯作者：
G. Carvalho;H. Gadêlha;J. Miranda
中科院分区：
文献类型：
--
作者：
G. Carvalho;H. Gadêlha;J. Miranda
当两种不同密度的不相容流体在旋转的Hele-Shaw槽中流动时，产生了离心力驱动的粘性指进问题。在这种传统的环境中，毛细管力和离心力之间的相互作用使流体-流体界面不稳定，导致形成动态竞争并达到不同长度的指状结构。在这种情况下，众所周知，手指竞争对流体之间的粘度对比的变化非常敏感。我们研究了这类旋转流问题的一种变体，其中流体发生反应并在其分离边界处产生凝胶状相。该界面假定为弹性的，呈现出依赖于曲率的弯曲刚度。用微扰弱非线性方法研究了界面的弹性性质如何影响手指比赛项目。我们的结果揭示了一种非常不同的动态情景，在这种情景中，手指长度的变异性不受粘度对比的调节，而是由两个控制量决定：特征半径和刚性分数参数。通过适当地调整这些量，即使粘度对比度保持不变，也可以描述手指竞争行为的整个范围。
The centrifugally driven viscous fingering problem arises when two immiscible fluids of different densities flow in a rotating Hele-Shaw cell. In this conventional setting an interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable, leading to the formation of fingered structures that compete dynamically and reach different lengths. In this context, it is known that finger competition is very sensitive to changes in the viscosity contrast between the fluids. We study a variant of such a rotating flow problem where the fluids react and produce a gellike phase at their separating boundary. This interface is assumed to be elastic, presenting a curvature-dependent bending rigidity. A perturbative weakly nonlinear approach is used to investigate how the elastic nature of the interface affects finger competition events. Our results unveil a very different dynamic scenario, in which finger length variability is not regulated by the viscosity contrast, but rather determined by two controlling quantities: a characteristic radius and a rigidity fraction parameter. By properly tuning these quantities one can describe a whole range of finger competition behaviors even if the viscosity contrast is kept unchanged.