An enhanced model for the capillary rise problem. (July 2020) - Gründing, Dirk
Highlights: Incorporating the full liquid volume in the capillary gives an exact prediction for the stationary rise height and a suitable regularization. The classical rise model is extended to incorporate Navier slip on the capillary walls. The ODE model has been validated against numerical solutions (ALE approach) of the full continuum mechanical problem. 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.