Simulating wetting phenomenon with large density ratios based on weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann model

Abstract

The wetting phenomenon is widespread in nature and industry, but simulating it with large density ratios remains challenging. In this study, a modified two-dimensional weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann (WMRT-PLB) model is extended to simulate the wetting phenomenon at large density ratios. A simple formula describing the contact angle and interaction force is derived, and an alternative geometrical formulation scheme based on the interaction force is proposed to model the contact angle. First, theoretical analysis shows that the continuum form of the alternative geometrical formulation scheme is mathematically equivalent to that of the geometrical formulation scheme based on the pseudopotential. In contrast, the discrete forms of the two schemes are different in implementation. Then, four classical benchmark cases (static droplet on a wall, static droplet under gravity, droplet spreading on a wall and capillary intrusion) under a large density ratio (ρl/ρg=857.7) are performed to verify and evaluate the performance of the WMRT-PLB model coupled with the alternative geometrical formulation scheme. The numerical results show that in the framework of the WMRT-PLB model, compared with the two conventional geometrical formulation schemes, the alternative geometrical formulation scheme is superior in numerical stability, especially under low surface tension, and achieves comparable numerical accuracy within a large range of surface tensions and contact angles.