A fully coupled mixed finite element method for surfactants spreading on thin liquid films
A fully coupled mixed finite element method for surfactants spreading on thin liquid films
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表面活性剂在液膜上铺展的全耦合混合有限元方法
DOI：
10.1016/j.cma.2018.10.045
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发表时间：
2019
影响因子：
7.2
通讯作者：
J. Dolbow
中科院分区：
文献类型：
--
作者：
Yingjie Liu;Christian Peco;J. Dolbow
提出了一种表面活性剂在粗糙表面上的液体薄膜上扩散的模型，并提出了一种基于有限元的离散化方法。通过考虑表面粗糙度对膜高度和表面活性剂浓度的影响，首先增强了现有的表面活性剂扩散框架。在一种标准方法中，薄膜高度的四阶方程被分解成两个二阶系统。然而，与以前的方法不同，该方法还将地表和深度平均速度场近似为独立变量，从而产生耦合非线性方程的五场系统。基准计算表明，这种方法允许Δ t ~ h 2缩放，而不会损失牛顿算法的收敛性。与分析估计一致，表面活性剂滴滴在光滑基底上的薄液体膜上的模拟显示表面活性剂前缘的时间尺度为t1∕4，而恒定表面活性剂源的演化速度更快，并表现出t1∕2的尺度。最后，表面活性剂在极薄薄膜上扩散的模拟表明，指指不稳定性可以由薄膜高度或衬底粗糙度的扰动触发。
A model for the spreading of surfactants over thin liquid films on rough surfaces is presented, along with a novel finite element based discretization. An existing framework for surfactants spreading is first augmented by allowing for the influence of a non-trivial surface roughness on the film height and surfactant concentration. In a standard approach, the fourth order equation for the film height is then split into two second order systems. However, distinct from previous approaches, the proposed method also approximates the surface and depth-averaged velocity fields as independent variables, giving rise to a five-field system of coupled nonlinear equations. Benchmark calculations indicate that this approach allows for a Δ t∼ h 2 scaling without loss of convergence in the Newton algorithm. Consistent with analytical estimates, simulations of surfactant drops spreading over thin liquid films on smooth substrates exhibit a t 1∕ 4 temporal scaling for the surfactant leading edge, while constant surfactant sources show faster evolutions and exhibit a t 1∕ 2 scaling. Finally, simulations of surfactants spreading over extremely thin films demonstrate that fingering instabilities can be triggered by perturbations to either the film height or the substrate roughness.
影响因子：
4.6
作者：
Karapetsas, George;Craster, Richard V.;Matar, Omar K.
通讯作者：
Matar, Omar K.