Three-dimensional two-phase smoothed particle hydrodynamics simulation of bubble/droplet rise and coalescence at moderate Reynolds numbers

Bubble and droplet dynamics play pivotal roles in diverse industrial and scientific applications. This study presents an advanced three-dimensional (3D) Lagrangian framework for two-phase flow simulation that combines Smoothed Particle Hydrodynamics (SPH) with the Continuum Surface Force method to solve the Navier–Stokes equations. The developed model incorporates two key innovations: a density-independent formulation using Rusanov-flux-inspired artificial diffusion and an implicit 3D advection velocity correction scheme. The specialized simulator accurately captures bubble rise and coalescence dynamics across moderate Reynolds numbers (23≤Re≤135) and a broad range of Eötvös numbers (5≤Eo≤1000), while systematically evaluating critical numerical parameters, including particle resolution effects, boundary interactions, and density/viscosity ratio dependencies. Validation against experimental data and established numerical benchmarks confirms the model's precision in predicting both isolated bubble behavior and complex coalescence processes. The 3D SPH approach successfully reproduces diverse bubble morphologies, from oblate ellipsoids to skirted configurations, while maintaining numerical stability throughout all stages of coalescence, from initial approach to final interface rupture. Additionally, 3D streamline visualizations based on the velocity field reveal vortex dynamics and their influence on the wake structure and surrounding flow. These patterns highlight how vortex cores shift and evolve in response to changes in bubble morphology and proximity to sidewalls during rising and merging. Overall, the results demonstrate the robustness of the proposed framework for modeling complex interfacial flow phenomena, with strong potential for both fundamental research and industrial applications involving multiphase systems.