An Arbitrary Lagrangian-Eulerian Method for the Direct Numerical Simulation of Wetting Processes

The process of wetting is present in virtually all technologies that involve liquids. Hence, the modeling and simulation of the involved physics is a key element in modern product design processes. To investigate the wetting process, an Arbitrary Lagrangian-Eulerian (ALE) method is developed in OpenFOAM. The extension includes new Navier and a free slip boundary conditions that are introduced into the framework. Furthermore, a flexible contact angle library is provided. The implementation allows to combine heuristic models on arbitrary contact line topologies. Various test cases ranging from simple channel flows, over oscillating droplets and even local surface geometries provide a sound verification basis. Special emphasis is given to the extension of available reference cases for moving contact lines, specifically, the case of a liquid rising in a capillary. For this purpose, an ordinary differential equation (ODE) is derived from the continuum mechanical description for free surface flows. This model incorporates a Navier slip boundary condition and outlines necessary assumptions for a comparison to a numerical solution of the associated continuum mechanical model. In addition, the derivation explains the origin of the singularity in the classical rise model that is closely related to a precise computation of the stationary height of the liquid column. Moreover, it is shown that a convective contribution is missing in standard rise models. An extensive code to code comparison between the extended ALE-imple\-mentation, a geometric as well as an algebraic Volume of Fluid code, and a level-set approach has been executed in a collaborative effort. This provides novel benchmark data for the capillary rise test case that allows for a comprehensive comparison to the considered class of ODE rise models. Furthermore, the influence of numerical slip and Navier slip boundary condition on the rise behavior are analyzed. Finally, an overview of different applications and a comparison to experimental results highlights the new capabilities of the implemented extensions