Conservative phase-field-based lattice Boltzmann equation for gas-liquid-solid flow

In this paper, a conservative phase-field based lattice Boltzmann equation (LBE) is developed to simulate gas-liquid-solid flows with large fluid density contrasts. In this model, the gas-liquid interface is captured by the conservative Allen-Cahn equation (CACE), where an additional source term is incorporated to realize the wettability of solid structure. Subsequently, a LBE is designed to solve this modified CACE (MCACE), while the two-phase flow field is resolved by using another classical incompressible LBE, and the fluid-solid interaction force is calculated by smoothed-profile method (SPM). Several classical simulations are conducted to demonstrate the capability of the present MCACE-LBE-SPM for simulating gas-liquid-solid flows, including a droplet spreading on a static wettable cylinder, a wettable cylinder floating on the gas-liquid interface without gravity, capillary interactions between two wettable cylinders under gravity, and multiple horizontal cylinders in gas-liquid channel flow. Numerical results indicate that the predictions by present MCACE-LBE-SPM are in good agreement with the theoretical or previous numerical results. © 2025 American Physical Society.