Viscous fingering on soft substrates

这里提出的研究是由最近对软基材上的粘性指指不稳定性的惊人观察所激发的。如果粘性流体在刚性板之间的狭窄间隙中被粘性较低的流体取代，则容易产生这种不稳定性，并且通常会在两种流体之间的界面上产生复杂的高度分支的手指图案。粘性指法一直是长期的研究兴趣，因为它作为一个原型的前端传播模式形成现象，如细菌菌落的生长和火焰的传播锋。我们发现这种不稳定性可以通过用软基板代替底边界板来控制。首先，我们观察到不稳定性可以延迟，因此界面在注入速率下保持轴对称，而相应刚性系统中的模式已经表现出非线性增长。这与其他系统类似，其中流体流动与柔性边界相互作用，例如与薄弹性膜相互作用，尽管软基板的变形与那些不同。其次，软基板的厚度和刚度可以调整，以改变手指的结构，一旦圆形界面对非轴对称扰动变得不稳定，手指就会发育。由此产生的模式范围从在刚性系统中观察到的高度分支的手指到在两个以相同速度共旋转的圆柱体之间的半月板上发育的粗短的手指。因此，不稳定性受到软基材变形的强烈影响，而软基材又会响应两相流而变形，并且可能具有粘弹性。我们建议采用实验、理论和计算相结合的方法来充分表征导致这些新现象的复杂流固相互作用。

The research proposed here is motivated by recent striking observations of the viscous fingering instability on soft substrates. This instability readily develops if a viscous fluid is displaced by a less viscous fluid in a narrow gap between rigid plates, and typically results in complex highly branched patterns of fingers on the interface between the two fluids. Viscous fingering has been of long-standing research interest because it serves as an archetype for front-propagating pattern-forming phenomena, as diverse as the growth of bacterial colonies and the propagation of flame fronts. We find that this instability can be manipulated by replacing the bottom bounding plate with a soft substrate. Firstly, we observe that the instability can be delayed, so that the interface remains axisymmetric for injection rates at which the pattern in the corresponding rigid system already exhibits nonlinear growth. This is similar to other systems in which the fluid flow interacts with a compliant boundary, for example, with thin elastic membranes, although soft substrates deform differently compared to those. Secondly, the thickness and the stiffness of the soft substrate can be tuned to change the structure of the fingers that do develop once the circular interface becomes unstable to non-axisymmetric perturbations. The resulting patterns range from the highly branched fingering observed in rigid systems to the stubby fingers that develop on the meniscus between two cylinders co-rotating with the same speed. Thus, the instability is strongly influenced by the deformation of the soft substrate, which in turn deforms in response to the two-phase flow, and is likely to have viscoelastic properties. We propose to employ a combination of experimental, theoretical and computational approaches to fully-characterise the complex fluid-structure interactions that lead to these novel phenomena.