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We consider an energy-based boundary condition to impose an equilibriumwetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model onvoxel-set-type computational domains. These domains typically stem from themicro-CT imaging of porous rock and approximate a (on {\mu}m scale) smoothdomain with a certain resolution. Planar surfaces that are perpendicular to themain axes are naturally approximated by a layer of voxels. However, planarsurfaces in any other directions and curved surfaces yield a jagged/roughsurface 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 onthe contact angle. However, a prescribed contact angle smaller or larger than90 degrees on jagged voxel surfaces is amplified in either direction. As aremedy, we propose the introduction of surface energy correction factors foreach fluid-solid voxel face that counterbalance the difference of the voxel-setsurface area with the underlying smooth one. The discretization of the modelequations is performed with the discontinuous Galerkin method, however, thepresented semi-analytical approach of correcting the surface energy is equallyapplicable to other direct numerical methods such as finite elements, finitevolumes, or finite differences, since the correction factors appear in thestrong formulation of the model.

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