# Capillary Rise -- A Computational Benchmark for Wetting Processes

## TL;DR

This paper compares four numerical methods for simulating capillary rise between parallel plates, validating them against classical ODE models and providing benchmark data for future research.

## Contribution

It introduces a comprehensive comparison of diverse numerical approaches for capillary rise, including finite volume and discontinuous Galerkin methods, with validation against extended analytical models.

## Key findings

- Excellent agreement among numerical methods with minor deviations.
- Qualitative agreement with continuum models; quantitative differences increase with oscillations.
- Reducing slip length dampens oscillations, differing from ODE predictions.

## Abstract

Four different numerical approaches are compared for the rise of liquid between two parallel plates. These are an Arbitrary Lagrangian-Eulerian method (OpenFOAM solver interTrackFoam), a geometric volume of fluid code (FS3D), an algebraic volume of fluid method (OpenFOAM solver interFoam), and a level set approach (BoSSS). The first three approaches discretize the bulk equation using a finite volume method while the last one employs an extended discontinuous Galerkin discretization. The results are compared to ODE models which are the classical rise model and an extended model that incorporates a Navier slip boundary condition on the capillary walls and levels at a corrected stationary rise height. All physical parameters are based on common requirements for the initial conditions, short simulation time, and a non-dimensional parameter study. The comparison shows excellent agreement between the different implementations with minor quantitative deviations for the adapted interFoam implementation. While the qualitative agreement between the full solutions of the continuum mechanical approach and the reference model is good, the quantitative comparison is only reasonable, especially for cases with increasing oscillations. Furthermore, reducing the slip length changes the solution qualitatively as oscillations are completely damped in contrast to the solution of the ODE models. To provide reference data for a full continuum simulation of the capillary rise problem, all results are made available online.