Phase-field Lattice Boltzmann model for liquid bridges and coalescence in wet granular media

Abstract

In this paper a phase-field based Lattice Boltzmann model is formulated to simulate the formation and coalescence of capillary bridges between spherical solid particles as well as the associated capillary forces. To capture the air–water interface, Allen–Cahn equation is coupled with two-phase Navier–Stokes equation through a surface tension term. The capillary force arising from the water interaction with a curved solid surface is formulated along with a numerical integration scheme. Two benchmark examples are considered to validate the proposed model, namely: the spreading of a drop on a spherical particle and capillary rise in a narrow tube. Then, the capillary forces due to isolated and coalesced liquid in two and three spherical particle configurations are computed to illustrate the pendular regime and its transition to the funicular regime. Numerical simulation results are found to be in good agreement with available experimental and numerical data for wetting in a doublet and a triplet of particles, respectively. The numerical results indicate that the proposed model provides a viable framework within which the complex capillary interface evolution during the wetting of a large assembly of particles could be captured. • The proposed model is used to simulate capillary bridges in an air–water system. • Transition of capillary bridges from pendular to funicular regimes is handled. • A numerical procedure is proposed to compute capillary forces. • Validation on small granular assemblies composed of two and three particles.