Three-dimensional numerical simulation of bubble rising in viscous liquids: A conservative phase-field lattice-Boltzmann study

Abstract

Simulating bubble rising in viscous liquids is challenging because of the large liquid-to-gas density ratio and complex topological evolution of the gas-liquid interface. In this study, a conservative phase-field model is employed to accurately track the interface during bubble rising, and the lattice Boltzmann model is used to determine the flow field driven by the buoyancy force and the surface tension force. To facilitate large-scale three-dimensional simulations, a parallel-adaptive mesh refinement algorithm is developed to reduce the computing overhead. The simulated bubble shapes under different configurations are compared with the shape chart through experiments [D. Bhaga and M. E. Weber, “Bubbles in viscous liquids: shapes, wakes, and velocities,” J. Fluid Mech. 105, 61–85 (1981)]. The influence of the numerical parameters (including domain size, surface tension, liquid viscosity, gravity, and density ratio) on the bubble dynamics is investigated, which demonstrates the capability of the current numerical scheme in simulating multiphase flow. Furthermore, complex topology changes including the bubble coalescence, splitting, and interplay with obstacles (i.e., squeeze deformation and bubble splitting) are simulated and compared in different cases, i.e., with different Reynolds, Eötvös, and Morton numbers. The effect of the initial bubble spacing on the coalescence of the two bubbles and the influence of boundary conditions on multiple bubble dynamics are investigated. When the bubbles can be completely blocked by the obstacle is quantified in terms of the obstacle width. Numerical results validate the robustness of the present numerical scheme in simulating multiphase flow.