Thin film flows, whether driven by gravity, surface tension, or the relaxation of elastic boundaries, occur in many natural and industrial processes. Applications span problems of oil and gas transport in channels to hydraulic fracture, subsurface propagation of pollutants, storage of supercritical CO2 in porous formations, and flow in elastic Hele–Shaw configurations and their relatives. We review the influence of boundaries on the dynamics of thin film flows, with a focus on gravity currents, including the effects of drainage into the substrate, and the role of the boundaries to confine the flow, force its convergence to a focus, or deform, and thus feedback to alter the flow. In particular, we highlight reduced-order models. In many cases, self-similar solutions can be determined and describe the behaviors in canonical problems at different timescales and length scales, including self-similar solutions of both the first and second kind. Additionally, the time transitions between different solutions are summarized. Where possible, remarks about various applications are provided.

中文翻译：

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边界对重力流和薄膜的影响：排水、约束、收敛和变形效应


薄膜流动，无论是由重力、表面张力还是弹性边界松弛驱动，都会发生在许多自然和工业过程中。应用涵盖水力压裂通道中的石油和天然气输送、污染物的地下传播、多孔地层中超临界二氧化碳的储存以及弹性 Hele-Shaw 配置及其相关结构中的流动等问题。我们回顾了边界对薄膜流动动力学的影响，重点关注重力流，包括排水到基底的影响，以及边界限制流动、迫使其会聚到焦点或变形的作用，从而反馈以改变流量。我们特别强调降阶模型。在许多情况下，可以确定自相似解并描述典型问题在不同时间尺度和长度尺度上的行为，包括第一类和第二类自相似解。此外，还总结了不同解决方案之间的时间转换。在可能的情况下，提供了有关各种应用程序的注释。