Direct numerical simulation of side-by-side rising bubble coalescence behavior based on a Weber number criterion

Abstract

The coalescence dynamics of two bubbles rising side by side in quiescent water are investigated using direct numerical simulations based on the Volume of Fluid (VOF) method with adaptive mesh refinement (AMR), implemented on the Basilisk platform. To address the inherent issue of numerical coalescence in VOF simulations, a physically motivated criterion based on the Weber number is employed, enabling accurate distinction between coalescence and rebound events. The topology-based AMR algorithm allows resolution of micrometer-scale features of film drainage and interfacial deformation. Simulation results show excellent agreement with experimental data in terms of rise velocity, approach velocity, and collision outcomes. Three representative interaction regimes are analyzed in detail: direct-coalescence, rebound-coalescence, and rebound-separation. The results reveal that surface and wake vorticity play a central role in controlling bubble approach, deformation, and film drainage. Notably, the emergence of a double-spiral, counter-rotating vortex structure is found to induce bubble reorientation and retard film drainage, thereby governing the transition between rebound and coalescence. Energy budget analysis further indicates that rebound and separation following contact are closely linked to high bubble deformation and significant accumulation of surface energy during the approach phase. The conversion of surface energy back into kinetic energy drives the rebound and eventual separation. While viscous dissipation related to film drainage plays an important role in a direct-coalescence case, it is considerably small in the rebound and separation case, where the dissipation is mainly caused by shape oscillation and vorticity accumulation upon collision. A phase diagram is constructed to map collision outcomes as a function of bubble size and initial separation distance, highlighting the coupled effects of vortex dynamics and energy transfer and dissipation in bubble coalescence and rebound. These findings provide new insights into the hydrodynamic mechanisms underlying bubble interactions in multiphase flows and contribute to the development of more accurate coalescence models for practical and industrial applications.