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arXiv 2108.01475physics.flu-dyn
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弯月面振荡过程中接触线不动的液膜动力学

Liquid film dynamics with immobile contact line during meniscus oscillation

Xiaolong Zhang, Vadim Nikolayev

摘要:

本文从理论上分析了圆柱形毛细管中液体和蒸汽之间弯月面振荡时的液膜动力学。通过使用泰勒气泡理论,在润滑近似下计算了沉积液膜的动态轮廓,该润滑近似考虑了膜长度的有限性,即考虑了接触线的存在。后者被假定为固定在表面缺陷上,因此是固定的;接触角允许变化。流体流动对弯月面中心部分曲率的影响被忽略。由于薄膜的变化,该曲率随时间变化,并作为解的一部分确定。膜动力学取决于初始接触角,其是在振荡期间获得的最大接触角。平均膜厚作为系统参数的函数进行了研究。数值结果与现有的实验数据和准稳态近似的结果进行了比较。最后,振荡弯月面的问题被认为是占相对于饱和温度,这导致蒸发的毛细管壁的过热。当过热超过一个相当低的阈值时,与钉扎接触线的振荡是不可能的,并且需要考虑由蒸发引起的接触线衰退。

英文摘要:

This paper presents a theoretical analysis of the liquid film dynamics during the oscillation of a meniscus between a liquid and its vapour in a cylindrical capillary. By using the theory of Taylor bubbles, the dynamic profile of the deposited liquid film is calculated within the lubrication approximation accounting for the finiteness of the film length, i.e. for the presence of the contact line. The latter is assumed to be pinned on a surface defect and thus immobile; the contact angle is allowed to vary. The fluid flow effect on the curvature in the central meniscus part is neglected. This curvature varies in time because of the film variation and is determined as a part of the solution. The film dynamics depends on the initial contact angle, which is the maximal contact angle attained during oscillation. The average film thickness is studied as a function of system parameters. The numerical results are compared to existing experimental data and to the results of the quasi-steady approximation. Finally, the problem of an oscillating meniscus is considered accounting for the superheating of the capillary wall with respect to the saturation temperature, which causes evaporation. When the superheating exceeds a quite low threshold, oscillations with a pinned contact line are impossible and the contact line recession caused by evaporation needs to be accounted for.

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