We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details and an implementation of higher-order spatial and temporal discretisation of the underlying free boundary problem using the finite element method. The corresponding partial differential equation is based on a thermodynamic consistent energetic variational formulation of the problem using the free energy and viscous dissipation in the bulk, on the surface, and at the moving contact line. Model hierarchies for limits of strong and weak contact line dissipation are established, implemented and studied. We analyze the performance of the numerical algorithm and investigate the impact of the dynamic contact angle on the evolution of two benchmark problems: gravity-driven sliding droplets and the instability of a ridge.
翻译:我们为平面上的薄膜流体流动提供了一个数学和数字框架,包括动态接触角度,特别是,我们提供算法细节,并采用有限元素方法对基础自由边界问题进行较高顺序的空间和时间分解,相应的部分差异方程式基于热力持续动态动态,利用散装、表面和移动的接触线上的自由能量和粘度散变异形成问题。建立、实施和研究强弱接触线消散限度的模型等级。我们分析数字算法的性能,并调查动态接触角对两个基准问题演变的影响:重力驱动滑动滴和脊的不稳定。