Thin films can become unstable when attractive van der Waals forces overcome the stabilizing effects of surface tension and viscous forces. In many applications, the effect of the surrounding bulk fluid cannot be neglected when considering a thin film subject to perturbations. In this work, we examine the two limits of potential flow and Stokes flow in the surrounding bulks to derive dispersion relations in each limit. We show that the effect of the surrounding bulks cannot be ignored for many film–bulk fluid pairings and film thicknesses and present conditions for the validity of each regime. In particular, the potential-flow regime exists when van der Waals forces are sufficiently strong, while the Stokes-flow regime exists when the bulk dynamic viscosity is sufficiently large. Due to the nature of the dispersion relation in the Stokes-flow limit, several distinct scenarios are identified in the corresponding stability diagram, each involving the interplay of different forces. For example, a novel instability regime involving capillary–viscous interactions is identified for large film thicknesses. Finally, by enlisting multiple realistic fluid pairings and film thicknesses wherein such instabilities can occur, we demonstrate the practical relevance of our theoretical findings. This work enables the extension of thin film stability theory to the analysis of antibubbles, splashing molten metals and ionic liquids, Mesler entrainment of microbubbles in breaking waves, and emulsion stability.

中文翻译：

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薄流体膜与其周围大量流体相互作用的线性稳定性

当范德华力克服表面张力和粘性力的稳定作用时，薄膜会变得不稳定。在许多应用中，当考虑受扰动的薄膜时，不能忽略周围大量流体的影响。在这项工作中，我们检查了周围体积中势流和斯托克斯流的两个极限，以推导出每个极限中的色散关系。我们表明，对于许多膜 - 体流体配对和膜厚度以及每个制度有效性的当前条件，周围体的影响不能被忽略。特别是，当范德华力足够强时，势流状态存在，而当体积动态粘度足够大时，斯托克斯流状态存在。由于斯托克斯流极限中离散关系的性质，在相应的稳定性图中确定了几个不同的场景，每个场景都涉及不同力的相互作用。例如，对于大膜厚，确定了一种涉及毛细管-粘性相互作用的新型不稳定状态。最后，通过在可能发生这种不稳定性的情况下获得多个现实的流体配对和薄膜厚度，我们证明了我们的理论发现的实际相关性。这项工作使薄膜稳定性理论能够扩展到反气泡、熔融金属和离子液体飞溅、碎波中微气泡的梅斯勒夹带以及乳液稳定性的分析。例如，对于大膜厚，确定了一种涉及毛细管-粘性相互作用的新型不稳定状态。最后，通过在可能发生这种不稳定性的情况下获得多个现实的流体配对和薄膜厚度，我们证明了我们的理论发现的实际相关性。这项工作使薄膜稳定性理论能够扩展到反气泡、熔融金属和离子液体飞溅、碎波中微气泡的梅斯勒夹带以及乳液稳定性的分析。例如，对于大膜厚，确定了一种涉及毛细管-粘性相互作用的新型不稳定状态。最后，通过在可能发生这种不稳定性的情况下获得多个现实的流体配对和薄膜厚度，我们证明了我们的理论发现的实际相关性。这项工作使薄膜稳定性理论能够扩展到反气泡、熔融金属和离子液体飞溅、碎波中微气泡的梅斯勒夹带以及乳液稳定性的分析。