The stress singularity in surfactant-driven thin-film flows. Part 1. Viscous effects
The stress singularity in surfactant-driven thin-film flows. Part 1. Viscous effects
复制标题
表面活性剂驱动的薄膜流中的应力奇点。
DOI：
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发表时间：
1998
影响因子：
3.7
通讯作者：
D. Halpern
中科院分区：
文献类型：
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作者：
O. Jensen;D. Halpern
局部的，不溶性的表面活性剂单分子层的前缘，在薄的，粘性的，流体层的自由表面上的表面张力梯度的作用下前进，局部表现得像一个刚性板。由于润滑理论未能捕捉到单层尖端的可积应力奇异性，因此高估了单层长度，我们研究了尖端附近的准定常二维Stokes流，假设表面张力或重力使自由表面局部保持在。Wiener-Hopf和匹配的特征函数方法被用来计算的“粘滑”流时，奇异性存在的边界元方法被用来探索弱的“污染物”表面活性剂或表面扩散的非线性正则化效果。在重力强烈抑制膜变形的极限中，扩散单层驱动大部分单层下方的不稳定回流（由非线性扩散方程支配），以及尖端前方流体中的一系列弱涡流。随着污染物或表面扩散强度的增加，它们在短的长度尺度上平滑尖端奇异性，消除局部应力最大值并最终破坏旋涡。该理论很容易推广到薄膜在长尺度上自由变形的情况。传统的薄膜近似的局限性进行了讨论。
The leading edge of a localized, insoluble surfactant monolayer, advancing under the action of surface-tension gradients over the free surface of a thin, viscous, fluid layer, behaves locally like a rigid plate. Since lubrication theory fails to capture the integrable stress singularity at the monolayer tip, so overestimating the monolayer length, we investigate the quasi-steady two-dimensional Stokes flow near the tip, assuming that surface tension or gravity keeps the free surface locally at. Wiener–Hopf and matched-eigenfunction methods are used to compute the ‘stick-slip’ flow when the singularity is present; a boundary-element method is used to explore the nonlinear regularizing effects of weak ‘contaminant’ surfactant or surface diffusion. In the limit in which gravity strongly suppresses film deformations, a spreading monolayer drives an unsteady return flow (governed by a nonlinear diffusion equation) beneath most of the monolayer, and a series of weak vortices in the fluid ahead of the tip. As contaminant or surface diffusion increase in strength, they smooth the tip singularity over short lengthscales, eliminate the local stress maximum and ultimately destroy the vortices. The theory is readily extended to cases in which the film deforms freely over long lengthscales. Limitations of conventional thin-film approximations are discussed.