Abstract Starting from the full continuum mechanical description of free surface flows, a model for the rise of a liquid in a capillary is derived. The derivation improves on several aspects: Firstly, the influence of a slip boundary condition on the capillary wall is added to the model. Secondly, the stationary rise height is corrected. Thirdly, a regularization is suggested that uses the mass in interface vicinity. Fourthly, the influence of the velocity field close to the contact line is added. Finally, a convection contribution arises as the analysis considers the capillary without a reservoir. To validate the model, an Arbitrary Lagrangian-Eulerian (ALE) approach is used to solve the full continuum mechanical model that serves as a reference solution. The correction for the stationary height shows excellent agreement with the continuum mechanical results, while the extended model generally improves the classical description. Increasing the viscous term to increase for additional dissipation effects leads to excellent agreement with the fully resolved validation cases. However, in the regime with rise height oscillations, the amplitudes are overestimated by the extended models.

中文翻译：

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毛细管上升问题的增强模型

摘要 从自由表面流动的完整连续介质力学描述出发，推导出毛细管中液体上升的模型。推导在几个方面进行了改进：首先，将滑动边界条件对毛细管壁的影响添加到模型中。其次，修正固定上升高度。第三，建议使用界面附近的质量进行正则化。第四，增加了靠近接触线的速度场的影响。最后，当分析考虑没有储层的毛细管时，会产生对流贡献。为了验证模型，使用任意拉格朗日-欧拉 (ALE) 方法来求解作为参考解决方案的完整连续介质力学模型。固定高度的修正与连续介质力学结果非常吻合，而扩展模型通常改进了经典描述。增加粘性项以增加额外的耗散效应导致与完全解决的验证案例非常一致。然而，在上升高度振荡的情况下，扩展模型高估了振幅。