The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial effects
The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial 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：
O. Jensen
中科院分区：
文献类型：
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作者：
O. Jensen
一个局部的，不溶性的，表面活性剂单分子层，在表面张力梯度的作用下，在一个薄的液体膜的蔓延，在其前沿的可积应力奇异性，使传统的薄膜近似局部不均匀。在这里，高雷诺数渐近被用来探索的准稳态二维发展流附近的单层尖端，假设重力保持自由表面几乎平坦，弱的“污染物”表面活性剂正则化的奇异性和单层传播足够快的惯性效应是重要的，在一个区域，这是很长的相比，膜的深度，但这是短的相比，单层的长度。它示出了如何向下位移的无粘性核心流的次表面粘性边界层产生一个不均匀的压力分布，当单层蔓延足够快的横流压力梯度是显着的，在其尖端，创建一个短的自由表面驼峰是薄膜版本的雷诺脊。随着单分子层速度的减慢和污染物浓度的增加，脊和其他奇异流动结构变得平滑。润滑理论提供了一个统一的精确近似的条件下，这类表面扩散流的建立。
A localized, insoluble, surfactant monolayer, spreading under the action of surface-tension gradients over a thin liquid film, has at its leading edge an integrable stress singularity which renders conventional thin-film approximations locally non-uniform. Here high-Reynolds-number asymptotics are used to explore the quasi-steady two-dimensional developing flow near the monolayer tip, assuming that gravity keeps the free surface almost flat, that weak ‘contaminant’ surfactant regularizes the singularity and that the monolayer spreads fast enough for inertial effects to be important in a region which is long compared to the film depth but which is short compared to the length of the monolayer. It is shown how downward displacement of the inviscid core flow by the subsurface viscous boundary layer yields a non-uniform pressure distribution which, when the monolayer is spreading fast enough for cross-stream pressure gradients to be significant at its tip, creates a short free-surface hump which is the thin-film version of a Reynolds ridge. The ridge and other singular flow structures are smoothed as the monolayer slows and levels of contaminant are increased. The conditions under which lubrication theory provides a uniformly accurate approximation for this class of surfactant-spreading flows are established.