Phil. Trans. R. Soc. A (2011) 369, 2510–2518 doi:10.1098/rsta.2011.0073 Lattice Boltzmann simulations of incompressible liquid–gas systems on partial wetting surfaces BY CHING-HSIANG SHIH,CHENG-LONG WU,LI-CHEN CHANG AND CHAO-AN LIN* Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China A three-dimensional Lattice Boltzmann two-phase model capable of dealing with large liquid and gas density ratios and with a partial wetting surface is introduced. This is based on a high density ratio model combined with a partial wetting boundary method. The predicted three-dimensional droplets at different partial wetting conditions at equilibrium are in good agreement with analytical solutions. Despite the large density ratio, the spurious velocity around the interface is not substantial, and is rather insensitive to the examined liquid and gas density and viscosity ratios. The influence of the gravitational force on the droplet shape is also examined through the variations of the Bond number, where the droplet shape migrates from spherical to flattened interface in tandem with the increase of the Bond number. The predicted interfaces under constant Bond number are also validated against measurements with good agreements. Keywords: two-phase Lattice Boltzmann method; high density ratio; wetting boundary condition 1. Introduction The Lattice Boltzmann method (LBM) [1] has achieved considerable success in simulating hydrodynamic problems, and its major advantages are that it is explicit, easy to implement and natural to parallelize. Thus, it is natural to extend the LBM to simulate multi-phase flows [2–4], and there are many multi-phase industrial applications, for example, bio-chip [5] and electro-wetting [6] based tunable micro lens system [7]. The correct simulation of these devices depends on the LBM’s capability to tackle high-phase density ratios and wetting boundaries. The pseudo-potential by Shan & Chen [2], for example, has been widely employed to compute two-phase flows owing to its simplicity in implementation. However, its undesirable feature is the generation of spurious velocity along the phase interface and the limitation of the simulated density ratio. Both of these deficiencies can be alleviated by adopting different equation of states [8] or by adopting an extended pseudo-potential method [9]. *Author for correspondence (calin@pme.nthu.edu.tw). One contribution of 25 to a Theme Issue ‘Discrete simulation of fluid dynamics: applications’. This journal is © 2011 The Royal Society 2510 Downloaded from https://royalsocietypublishing.org/ on 21 February 2022