Modeling of co-axial bubbles coalescence under moderate Reynolds regimes: A Bi-phase SPH approach

Edgar Andres Patino Narino*, Andres Felipe Galvis Rodriguez, Renato Pavanello, Mario Gongora

*Corresponding author for this work

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Phenomena involving bubble flow play a significant role in numerous industrial, natural, and scientific systems. Thus, liquid–gas interfaces must be considered the influence of surface tension and buoyancy. This work analyzes a complete numerical study for bi-fluid flow problems in the deformation evolution of two bubbles coalescing in a viscous liquid. This study discusses diverse configurations of the coalescence bubbles process and their effect on the displacement of the center of mass, velocity, streamlines, and evolution of the morphologies’ deformation. The resulting simulations revealed the process of the coalescence bubbles regarding three stages: approaching, drainage, and rupture of the interface. These steps reach different morphologies, defined as oblate ellipsoid, prolate ellipsoid, and ellipsoidal cap shapes between the trailing, leading, and merging bubbles. Likewise, an approximated bi-phase 2D methodology using the Navier–Stokes equations with Smoothed Particle Hydrodynamics (SPH) method and associated with the Continuous Surface Force (CSF) method was employed to approach the interaction between the bubbles, the surrounding liquid, and cavity walls. This approach with SPH and CSF for fused bubbles and their liquid interaction are validated employing numerical benchmarks in situations with high and moderate regimes of the Reynolds (Re) and Eötvös (Eo) numbers, and different sizes of diameter between coalescence bubbles. Correspondingly, examples of bubbles merging around a liquid owing to gravitational are rarely treated in the literature of mesh-free methods, especially to characterize different viscosity, density and surface tension regimes at the bubble–liquid interface, the effect of the method precision (distance between particles, 𝛥𝑥), the size of the surrounding liquid cavity and the initial distance between lighter domains. According to the bubbles deformation, during the coalescence is observed significant influence of 𝛥𝑥 resolution and the cavity size, there are instances of instabilities, such as lateral tails, droplets inside the lighter domain, break-up, and satellite bubble formation. Finally, it is provided a robust numerical study of the coalescence process with a bi-phase SPH for different surfaces tension regimes (5 ≤ Eo ≤ 200), viscosity and density ratios (5 ≤ 𝜆, Φ ≤ 100) and initial conditions in merging bubbles problems with moderates Reynolds numbers (5 ≤ Re ≤ 50).
Original languageEnglish
Article number104355
Number of pages35
JournalInternational Journal of Multiphase Flow
Early online date16 Feb 2023
Publication statusPublished - 1 May 2023


  • Bubble morphology
  • Bubbles merging
  • Bi-phase model
  • Smoothed particle hydrodynamics

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