Investigation of Lattice Boltzmann wetting boundary conditions for capillaries with irregular polygonal cross-section

We have investigated the performance of an alternative wetting boundary condition for complex geometries in a phase field Lattice Boltzmann scheme, which is an alternative to the commonly used formulation by Yeomans and coworkers. Though our boundary condition is much simpler in its implementation, all investigated schemes show proper droplet spreading behaviour following the Cox–Voinov law. Still, numerical artefacts like spurious velocities or chequer board effects in the pressure field can be significantly reduced by the use of a two-relaxation-time (TRT) scheme, likewise recent studies by the Yeomans group. The outstanding property of our implementation is the presence of an (artificial) thin wetting layer, which influences the relation between the saturation (_Sw$S_w$) and capillary pressure _pcap$p_{cap}$ in channels with irregular polygonal cross section. The _pcap(_Sw)$p_{cap}\left(S_w\right)$ relation from our simulation follows the shifted-Young–Laplace (sYL) law, showing that the physics of this wetting layer is similar to precursor films due to Van der Waals forces. With the knowledge of the thickness of the wetting layer, simulation results can be translated back to realistic pore configurations with thinner wetting layers.