Development of an immersed boundary-multiphase lattice Boltzmann flux solver with high density ratio for contact line dynamics

Abstract

Interaction between a two-phase fluid and a structure involving contact line dynamics is a common phenomenon. In this paper, we aim to develop a fluid–solid coupling model that can study contact line dynamics in the case of a high density ratio between the two fluids. The fluids are treated using a multiphase lattice Boltzmann flux solver (MLBFS) that uses the cell-centered finite volume method to obtain macroscopic flow variables, and the interface fluxes are reconstructed locally by the standard lattice Boltzmann method (LBM) solutions. This approach retains the advantages of the original LBM while being more flexible in handling nonuniform grids and external force terms. The immersed boundary method (IBM) is an effective method for processing structural information, and here, the implicit boundary-condition-enforced IBM is used to accurately satisfy the Dirichlet boundary condition (no-slip boundary). Moreover, the Neumann boundary condition is deemed to represent the contribution from the structure boundary flux and is incorporated into the IB-MLBFS. The developed IB-MLBFS is verified by several test cases, including contact line motion of a two-phase fluid along a circular cylinder and droplet spreading on a flat plate, where both equilibrium results and dynamic process are correctly reproduced for different density ratios and wettability conditions. Furthermore, based on the IB-MLBFS established here, the contact line dynamics of a two-phase fluid between two square cylinders or two circular cylinders is studied. The effects of distance, structure size, and wettability on the interface state and the contact angle are studied in detail. The robustness of the proposed model is verified.