The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that Γi(nl)>3D/M provides a simple criterion for enhanced stability, where Γi(nl), D, and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

中文翻译：

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由于表面粘度，自由粘性膜的稳定性增强

在存在不溶性表面活性剂的情况下检查由两个自由表面包围的薄液膜的稳定性。这项研究的主要目的是了解随着表面活性剂表面浓度的增加，乳液的稳定性增强。表面活性剂不仅会导致表面张力梯度，而且还会使表面粘度变得很大，这可能会随表面浓度而变化。我们对表面粘度采用两种现象学模型，即线性粘度模型和非线性粘度模型。在后者中，表面粘度在临界浓度处发散，这被称为“堵塞”极限。我们表明，高表面粘度可以显着延迟破裂。对“干扰”限制的分析表明，Γi(nl)> 3D/M 为增强稳定性提供了一个简单的标准，其中 Γi(nl)、D 和 M 分别是归一化的初始表面活性剂浓度、分离压力数和 Marangoni 数。非线性模拟表明，高表面粘度使自由膜在干扰极限下非常稳定，并且它们的自由表面表现得像与实验观察一致的固定界面。此外，还表明可以通过调整初始表面活性剂浓度来任意增加破裂时间，从而为薄膜的稳定提供了流体动力学途径。并且它们的自由表面表现得像与实验观察一致的固定界面。此外，还表明可以通过调整初始表面活性剂浓度来任意增加破裂时间，从而为薄膜的稳定提供了流体动力学途径。并且它们的自由表面表现得像与实验观察一致的固定界面。此外，还表明可以通过调整初始表面活性剂浓度来任意增加破裂时间，从而为薄膜的稳定提供了流体动力学途径。