Entropic multiple-relaxation-time multirange pseudopotential lattice Boltzmann model for two-phase flow

Abstract

An entropic multiple-relaxation-time lattice Boltzmann approach is coupled to a multirange Shan-Chen pseudopotential model to study the two-phase flow. Compared with previous multiple-relaxation-time multiphase models, this model is stable and accurate for the simulation of a two-phase flow in a much wider range of viscosity and surface tension at a high liquid-vapor density ratio. A stationary droplet surrounded by equilibrium vapor is first simulated to validate this model using the coexistence curve and Laplace’s law. Then, two series of droplet impact behavior, on a liquid film and a flat surface, are simulated in comparison with theoretical or experimental results. Droplet impact on a liquid film is simulated for different Reynolds numbers at high Weber numbers. With the increase of the Sommerfeld parameter, onset of splashing is observed and multiple secondary droplets occur. The droplet spreading ratio agrees well with the square root of time law and is found to be independent of Reynolds number. Moreover, shapes of simulated droplets impacting hydrophilic and superhydrophobic flat surfaces show good agreement with experimental observations through the entire dynamic process. The maximum spreading ratio of a droplet impacting the superhydrophobic flat surface is studied for a large range of Weber numbers. Results show that the rescaled maximum spreading ratios are in good agreement with a universal scaling law. This series of simulations demonstrates that the proposed model accurately captures the complex fluid-fluid and fluid-solid interfacial physical processes for a wide range of Reynolds and Weber numbers at high density ratios.