In this paper, we present a detailed numerical investigation of capillary bridge formation between solid grains using a multi-phase Lattice Boltzmann Method (LBM). Building upon our earlier work that coupled Discrete Element Method (DEM) with LBM to model unsaturated granular materials across scales ( Younes et al., 2023 ), the present study isolates the fluid dynamics at the microscale to explore in depth the equilibrium morphology of capillary bridges in the pendular regime. The model incorporates both the Navier–Stokes equations for incompressible fluid flow and the Allen–Cahn equation to capture interface dynamics within a phase-field framework. Simulations of air–water systems with high density contrast are conducted using an accurate cubic wetting boundary condition, efficiently implemented on Graphics Processing Units (GPUs). After validating the wetting behavior through standard 2D and 3D benchmarks, we simulate axisymmetric liquid bridges between two spherical grains at various separation distances. The results show excellent agreement with the Young–Laplace analytical solution and reproduce key physical features such as the mean curvature sign inversion. These findings demonstrate the ability of the proposed model to accurately resolve interface-level phenomena essential to the mechanical behavior of unsaturated soils. This study contributes to the multiscale modeling of geomechanics by providing insights into grain-scale interactions governed by capillarity.
Younes et al. (2026) studied this question.