Finite element simulation of dynamic wetting flows as an interface formation process
Finite element simulation of dynamic wetting flows as an interface formation process
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DOI：
10.1016/j.jcp.2012.07.018
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
J. Sprittles;Y. Shikhmurzaev
中科院分区：
文献类型：
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作者：
J. Sprittles;Y. Shikhmurzaev
一个数学上具有挑战性的模型的动态润湿的界面形成的过程中，第一次，完全纳入一个数值代码的基础上的有限元方法和应用，作为一个测试案例，毛细上升的问题。这项工作的动机来自于这样一个事实，即十多年前的实验发现，动态润湿流的关键变量-动态接触角-不仅取决于三相接触线的速度，而且取决于整个流场/几何形状。因此，为了描述这种效应，有必要使用具有这种依赖性作为其组成部分的数学模型。一个新的物理效应，被称为“流体动力学抵抗动态润湿”，发现毛细管的半径的动态接触角的影响，因此对全球流动，计算。数值框架的能力，然后证明通过比较的结果与实验上的非稳态毛细上升，其中获得了良好的协议。提供了一组给定的无量纲相似性参数的数值方案所需的空间分辨率的实际建议，并在有限的情况下，渐近结果的比较证实，代码收敛到正确的解决方案。附录给出了一个用户友好的分步指南，详细说明了整个实现，并允许读者轻松复制所有呈现的结果，包括基准计算。
A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows — the dynamic contact angle — depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the ‘hydrodynamic resist to dynamic wetting’, is discovered where the influence of the capillary’s radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a user-friendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations.