Marangoni flow is the motion induced by a surface tension gradient along a fluid–fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.

中文翻译：

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Marangoni 驱动的薄膜在排水的预湿薄膜上爬升

Marangoni 流动是由沿流体-流体界面的表面张力梯度引起的运动。在这项研究中，我们报告了当表面活性剂浴接触垂直基板上预先润湿的去离子水膜时产生的 Marangoni 流。预湿膜的厚度分布由重力排水设定，因此随排水时间而变化。由于表面活性剂的作用，浴中的表面张力较低，因此由于表面张力的差异，液膜沿垂直基板向上爬升。执行粒子跟踪测速以测量薄膜中的动力学，其中当排水薄膜遇到攀爬薄膜的前部时，平均流体速度反转方向。然后研究表面活性剂浓度和预湿膜厚度对膜爬升的影响。高速干涉测量用于测量爬膜的前部位置和膜厚剖面。因此，较高的表面活性剂浓度会产生更快、更厚的攀爬膜。此外，对于高浓度的表面活性剂，Marangoni 驱动占主导地位，增加薄膜厚度会增加爬坡前沿的上升速度，因为粘性阻力不太重要。相比之下，对于低表面活性剂浓度，Marangoni 驱动平衡重力排水，增加薄膜厚度会降低爬升前沿的上升速度，同时增强重力排水。我们通过使用比较 Marangoni 应力和重力排水量的无量纲参数来合理化这些观察结果。建立模型来分析攀登前沿，无论是在马兰戈尼驾驶主导的地区还是在马兰戈尼平衡的排水区。我们的工作突出了重力排水对 Marangoni 流的影响，通过设置预湿薄膜的厚度和阻止薄膜爬升。