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首页> 外文期刊>Journal of Fluid Mechanics >The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate
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The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate

机译：载有表面活性剂的液滴在倾斜的预湿基材上的铺展和稳定性

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摘要

We consider a viscous drop, loaded with an insoluble surfactant, spreading over an inclined plane that is covered initially with a thin surfactant-free liquid film. Lubrication theory is employed to model the flow using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the late-time multi-region asymptotic structure of the spatially one-dimensional spreading flow. A simplified differential-algebraic equation model is derived for key variables characterising the spreading process, using which the late-time spreading and thinning rates are determined. Focusing on the neighbourhood of the drop's leading-edge effective contact line, we then examine the stability of this region to small-amplitude disturbances with transverse variation. A dispersion relationship is described using long-wavelength asymptotics and numerical simulations, which reveals physical mechanisms and new scaling properties of the instability.
机译：我们考虑了一种粘性液滴，该液滴中装有不溶性表面活性剂，并散布在一个倾斜的平面上，该平面最初被无表面活性剂的薄膜覆盖。润滑理论用于对膜厚和表面活性剂浓度使用耦合的非线性演化方程对流动进行建模。利用高分辨率数值模拟，我们描述了空间一维扩展流的后期多区域渐近结构。推导了简化的微分-代数方程模型，以描述表征扩展过程的关键变量，从而确定了后期的扩展和稀疏率。然后，着眼于液滴前沿有效接触线的附近，我们研究了该区域对横向变化的小振幅干扰的稳定性。使用长波长渐近线和数值模拟描述了色散关系，揭示了不稳定性的物理机制和新的缩放性质。

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