Interfacial instabilities in fluid films

具有自由表面覆盖在固体材料（衬底）上的薄流体薄膜在各种情况下经常出现。在工业环境中，它们用于涂覆和保护表面或促进质量和热量的传递。在生物体中，它们发挥着至关重要的作用，例如，覆盖眼睛的泪膜或肺部气道的液体衬里。在环境中也会遇到流体膜，例如地下水渗透到非饱和裂隙岩石中。另一个例子是熔岩流和冰川动力学，它们与长度尺度短得多的流体膜受相同的物理机制支配。流体膜受到界面不稳定性的影响，也就是说，在某些条件下，会产生流动，导致膜的厚度不均匀。随着时间的推移，界面不稳定会导致膜破裂，如果流动足够快，可以形成大振幅波并沿表面传播。界面不稳定性的出现往往对流体膜的预期功能产生不利影响。例如，在与制造工艺相关的涂层应用中，不均匀的薄膜流动可能导致涂层材料的不规则分布。同样，具有生物功能的流体薄膜如果变得太薄或出现孔洞，就会失效。然而，在某些工业部门，界面不稳定性可以优化过程。例如，在热交换器和质交换器中，界面波的形成改善了设备的运行，因为液气界面的表面积增加了，这有利于传输。数学流体流动模型可以用来预测不稳定发生的条件和预测其演变。我建议实施理论模型，研究影响流体膜稳定性的各种因素的综合效应，这些因素在现实世界中是相关的。值得注意的因素包括热效应、表面活性剂（影响表面张力的化学溶质）的存在、流体通过多孔基材的渗透，以及具有起伏或波纹的非平面表面的基材。

Thin fluid films with a free surface overlying a solid material (substrate) occur frequently in a variety of situations. In industrial settings they serve to coat and protect surfaces or facilitate the transfer of mass and heat. In living organisms they perform vital functions as does, for example, the tear film covering the eye or the fluid lining of airways in the lungs. Fluid films are also encountered in the environment, such as groundwater permeating unsaturated fractured rock. Other examples are lava flows and glacial dynamics which are governed by the same physical mechanisms as fluid films with much shorter length scales. Fluid films are subject to interfacial instability, in the sense that, under certain conditions, a flow will develop resulting in non-uniformity in the thickness of the film. In time, interfacial instability can lead to the rupture of the film, and if the flow is sufficiently fast, large amplitude waves can form and propagate along the surface. The appearance of interfacial instability often has an adverse effect on the intended function of the fluid film. In coating applications connected to manufacturing processes, for example, a nonuniform film flow can result in an irregular distribution of the coating material. Similarly, fluid films serving a biological function can be ineffective if they become too thin or develop holes. In certain industrial sectors, however, interfacial instability can optimize the process. For example, in heat and mass exchangers the formation of interfacial waves improves the operation of the device due to the fact that there is an increase in the surface area of the liquid-gas interface, which facilitates the transport. A mathematical fluid flow model can be used to anticipate the conditions for the onset of instability and predict its evolution. I propose to implement theoretical models that will investigate the combined effect of various factors affecting the stability of a fluid film that are relevant in real-world situations. Notable factors that will be considered include thermal effects, the presence of surfactants (chemical solutes affecting surface tension), the permeation of fluid through a porous substrate, as well as substrates with nonplanar surfaces exhibiting undulations or corrugations.