流体驱动的弹性弯月面指进不稳定性
Fluid driven fingering instability of a confined elastic meniscus
摘要：
当流体在临界压力下被泵入受限弹性层中的空腔时，流体的不稳定指状物沿着其弯月面侵入弹性固体（Saintyves，Dauchot和Bouchaud，2013）。这些指状物在没有断裂或失去粘附的情况下发生，并且是可逆的，当压力降低时消失。我们开发了一个渐近理论的加压高弹性层之间的刚体被困解释这些意见，与预测的临界流体压力指，和手指波长。我们还表明，该理论联系起来，而不是由横向拉伸的弹性层的流体驱动的指进与类似的过渡驱动。我们进一步验证这些预测，通过使用有限元模拟的两个系统，这表明，在这两种情况下，指状过渡是一阶（突然），因此有一个区域的双稳性。我们的预测是在很好的协议与最近观察到的经典Saffman-Taylor界面不稳定性的弹性模拟流体力学。
英文摘要：
When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves, Dauchot, and Bouchaud, 2013). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies to explain these observations, with predictions for the critical fluid pressure for fingering, and the finger wavelength. We also show that the theory links this fluid-driven fingering with a similar transition driven instead by transverse stretching of the elastic layer. We further verify these predictions by using finite-element simulations on the two systems which show that, in both cases, the fingering transition is first-order (sudden) and hence has a region of bistability. Our predictions are in good agreement with recent observations of this elastic analog of the classical Saffman-Taylor interfacial instability in hydrodynamics.
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