Wetting boundary condition for phase-field lattice Boltzmann method with singular mobility

A simplified wetting boundary condition is implemented for the phase-field lattice Boltzmann model with singular mobility [Bao and Guo, Phys.Rev.E 109, 025302 (2024)]. In this approach, the solid–liquid interfacial free-energy is incorporated into the chemical potential. As a result, only no-flux schemes for the order parameter and chemical potential need to be applied on solid surfaces, avoiding complex interpolation on irregular geometries. The proposed model is validated by several numerical tests, including droplets resting on the flat and cylindrical surfaces, droplets passing through pore-throat structures, and forced imbibition in a pore doublet model. The results for droplet resting demonstrate that the proposed model can accurately predict contact angles and effectively suppresses the spontaneous disappearance of droplets on wetting surfaces. Compared with the original model, the present model accurately captures the small droplet in pore-throat structures under hydrophilic conditions, and enables droplet transport with mass conservation under hydrophobic conditions. Moreover, the present model accurately reproduces the imbibition process across a range of capillary numbers, showing excellent agreement with theoretical solutions.