AI 中文总结
研究含可溶性表面活性剂薄膜在光滑斜坡流动时的扩展与破裂动力学，用润滑近似法推导方程，考虑吸附动力学速率的快速和慢速情况，分析外部剪切力等因素对薄膜厚度及破裂的影响，揭示相关作用机制及滑移参数的双重效应。
AI 中文摘要
本文探讨了在外部剪切作用下，光滑倾斜薄膜流动中表面活性剂局部分布的扩展和破裂情况。表面活性剂可吸附在自由表面或溶解在主体中，其浓度由主体及界面的对流和扩散方程控制，吸附 - 解吸速率由吸附动力学速率调节。考虑范德华力用于破裂动力学，采用润滑近似方法推导薄膜厚度和界面表面活性剂浓度的演化方程。研究了吸附动力学速率的两种不同情况：扩展现象中的快速和慢速。对于快速吸附动力学，还考虑了表面活性剂分布的两种情况；对于慢速吸附动力学，吸附 - 解吸速率慢，瞬态期导致界面处的马兰戈尼梯度降低，使薄膜厚度分布呈现脉冲型特征。外部剪切力和底部光滑表面对薄膜厚度有不同影响，范德华力是破裂机制的主要因素，线性稳定性分析表明外部剪切力使流动失稳，滑移参数基于邦德数、毛细管数和哈梅克常数显示出双重效应。
英文摘要
The spreading and rupture of local distribution of surfactant on a slippery inclined thin film flow in the presence of external shear is explored in this article. The surfactant can be adsorbed at the free surface or can be dissolved in the bulk. The surfactant concentrations are governed by advection and diffusion equations for bulk as well as the interface. Moreover, the adsorption-desorption rates of the bulk and interface surfactants are regulated by sorption kinetics rates. The van der Waals forces are considered for rupture dynamics. The lubrication approximation method is used to derive the evolution equations of film thickness and interface surfactant concentration. Two different scenarios are considered for sorption kinetics rates: (i) rapid and (ii) slow in the case of the spreading phenomenon. Then, two cases are considered related to the distribution of the surfactant in case of rapid sorption kinetics. The slippery bottom helps more fluid to flow and the capillary ridge to gain height for rapid sorption kinetics, and the external shear force amplifies the thinning of the film. However, in the case of slow sorption kinetics, the adsorption-desorption takes place at a slow rate, and the transient period results in a reduced Marangoni gradient at the interface. This leads to a pulse-type character in the film thickness profile. The external shear force reduces the pulse height, whereas a slippery surface at the bottom increases the pulse height. On the other hand, van der Waals forces are considered to be the major factor behind the rupture mechanism. The linear stability analysis depicts that external shear force destabilizes the flow, but the slip parameter displays a dual effect based on the Bond number, capillary number, and Hamaker constant.
Comments28 pages, 71 figures, comments are welcome
