Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study

Mohammad Vahabi, Hamidreza Hadavandmirzaei, Babak Kamkari, Hesameddin Safari

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this paper, the interaction between two initially circular in-line bubbles during their rise in a viscoelastic liquid under gravity is numerically simulated by weakly compressible smoothed particle hydrodynamics (WC-SPH). The background fluid is assumed to obey Oldroyd-B rheological model and the surface tension between two phases is evaluated by continuum surface tension (CST) method. First, it is shown that the obtained results for two benchmark problems, including two rising bubbles in a Newtonian fluid and a single rising bubble in a viscoelastic fluid, are in good agreement with previously published results. Then, together ascending of two unequal in-line bubbles in an Oldroyd-B viscoelastic liquid is simulated. Two different configurations are considered for the position of larger bubble and the center-of-mass of the bubbles and its velocity are presented for each case. Also, the differences of velocity and stress distributions in the background liquid are evaluated for two configurations. Based on the obtained results, it could be said that when the larger bubble is placed above the smaller one, merging does not occurred and the upper bubble has a dual cusped trailing edge. In addition, the effects of Deborah number, polymer concentration, density and viscosity ratios, Reynolds number, and Bond number are investigated on rising bubbles. To the best of authors’ knowledge, it is the first time the simultaneous rising of two bubbles in Oldroyd-B fluids is investigated.

Original languageEnglish
Pages (from-to)413-429
Number of pages17
JournalEuropean Journal of Mechanics, B/Fluids
Early online date12 Nov 2020
Publication statusPublished (in print/issue) - 28 Feb 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Masson SAS


  • Continuum surface tension
  • Interaction of rising bubbles
  • Meshless method
  • Smoothed particle hydrodynamics
  • Viscoelastic fluid


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