Numerical Investigation of Two In-Line Two-Dimensional Bubbles Rising in a Two-Dimensional Quiescent Ambient Liquid by a Conservative Phase-Field Lattice Boltzmann Method

Abstract

The coalescence and interaction of two in-line two-dimensional bubbles rising in viscous ambient liquids were studied using two-dimensional simulations. A mass-conserving lattice Boltzmann model that was combined by the phase-field lattice Boltzmann equation (LBE) and the pressure-evolution lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision operator was used to solve the Navier–Stokes equations for multiphase flow. Starting from the circle shape, the interfaces of bubbles during the rising processes are captured by the calculation of the conservative phase-field LBE. The influence of liquid viscosity and interface tension on the coalescence and interaction of bubbles was studied by varying the Archimedes numbers (Ar) from 1 to 300 and several Bond numbers (Bo) from 5 to 200. It was found that the bubble–bubble interaction is enhanced with the decrease of the liquid viscosity, and the outcome of the coalescence is promoted by the two vortex rings (liquid circulations) around the two bubbles. A comprehensive map of the coalescence regime was obtained. Four distinct coalescence regimes (namely, Central I, Central II, Edge, and Hug) were identified, and three critical Ar that can distinguish the above four regimes were defined. Moreover, the effects of Ar and Bo on the coalescence time and the relative velocity between the two bubbles were also investigated. The current work enhances the understanding of the coalescence and interaction of bubbles.