Viscous froth model applied to the dynamic simulation of bubbles flowing in a channel: three-bubble case

C. Torres-Ulloa, P. Grassia

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
14 Downloads (Pure)


A two-dimensional foam system comprised of three bubbles is studied via simulations with the viscous froth model. Bubbles are arranged in a so called staircase configuration and move along a channel due to imposed driving back pressure. This flowing three-bubble system has been studied previously on the basis that it interpolates between a simpler staircase structure (a simple lens, which breaks up via so called topological transformations if driven at high pressure) and an infinite staircase (which sustains arbitrarily large driving pressure without breaking). Depending on bubble size relative to channel size, different solution branches for the three-bubble system were found: certain branches terminate (as for the simple lens) in topological transformations and others reach (as for an infinite staircase) a geometrically invariant migrating state. The methodology used previously was however a purely steady state one, and hence did not interrogate stability of the various branches, nor the role of imposing different driving pressures upon topological transformation type. To address this, unsteady state three-bubble simulations are realized here. Stable solution branches without topological transformation exist for comparatively low driving pressures. For sufficiently high imposed back pressures however, topological transformations occur, albeit with imposed pressure now influencing the transformation type.
Original languageEnglish
Article number20220487
Number of pages24
JournalProceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences
Issue number2267
Publication statusPublished - 16 Nov 2022


  • viscous froth model
  • physics of bubbles
  • foam rheology


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