Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios

Based on the recent work by Fakhari et al. (2017b), a three-dimensional phase-field lattice Boltzmann method was developed to investigate the rise of a Taylor bubble in a duct. The proposed approach couples the conservative phase-field equation with a velocity-based lattice Boltzmann scheme equipped with a weighted multiple-relaxation-time collision operator to enhance numerical stability. This makes the model ideal for numerical simulation of immiscible fluids at high density ratios and relatively high Reynolds numbers. Several benchmark problems, including the deformation of a droplet in a shear flow, the Rayleigh-Taylor instability, and the rise of a Taylor bubble through a quiescent fluid, were considered to asses the accuracy of the proposed solver. The Rayleigh-Taylor instability simulations were conducted for a configuration mimicking an air-water system, which has received little attention in the literature. After detailed verification and validation, the presented formulation was applied to study the flow field surrounding a Taylor bubble, for which numerical results were compared with the experimental work of Bugg and Saad (2002). The findings highlighted that the experimental bubble rise velocity, instantaneous flow field, and interface profile can be accurately captured by the presented model. In particular, the rise velocity of the present model indicated an improvement in accuracy when compared to the reference numerical solutions. The agreement between various numerical schemes, in some instances, indicated potential experimental difficulties in measuring the local flow field. Future application of the present model will facilitate detailed investigation of the pressure and flow profile surrounding Taylor bubbles evolving in co-current and counter-current flows.