粘性薄膜上弹性流体动力学和随机水准的渐近状态
Asymptotic regimes in elastohydrodynamic and stochastic leveling on a viscous film
摘要：
在粘性流体中，弹性薄板在固体基底附近变形是与生物学、物理学和工程学中的各种动力学过程相关的情况。在这里，我们研究的松弛动力学的弹性板休息的薄粘性薄膜，支持由固体基板。通过结合尺度分析，数值模拟和实验，我们确定渐近制度的弹流调平的表面扰动的形式的凸块，当流动是由弹性弯曲的板或热波动。在这两种情况下，当凸块高度比预润湿粘性膜的厚度大得多或小得多时，识别出两种不同的状态。我们的分析揭示了一个明显的交叉之间的相似性指数的比值的扰动高度的膜的高度。
英文摘要：
An elastic sheet that deforms near a solid substrate in a viscous fluid is a situation relevant to various dynamical processes in biology, geophysics and engineering. Here, we study the relaxation dynamics of an elastic plate resting on a thin viscous film that is supported by a solid substrate. By combining scaling analysis, numerical simulations and experiments, we identify asymptotic regimes for the elastohydrodynamic leveling of a surface perturbation of the form of a bump, when the flow is driven by either the elastic bending of the plate or thermal fluctuations. In both cases, two distinct regimes are identified when the bump height is either much larger or much smaller than the thickness of the pre-wetted viscous film. Our analysis reveals a distinct crossover between the similarity exponents with the ratio of the perturbation height to the film height.
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