An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods

TL;DR

This paper introduces an energy-based boundary condition correction for phase-field models on jagged voxel surfaces to accurately impose equilibrium contact angles, addressing artifacts caused by voxel approximation of curved surfaces.

Contribution

It proposes surface energy correction factors for voxel faces to maintain prescribed contact angles on jagged surfaces in phase-field simulations.

Findings

Correction factors effectively restore desired contact angles.

Method applicable to various numerical discretization techniques.

Enhances accuracy of wetting simulations on voxel-based geometries.

Abstract

We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from the micro-CT imaging of porous rock and approximate a (on {\mu}m scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90 degrees, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90 degrees on jagged voxel surfaces is amplified in either direction. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method, however, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model.