The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell

Christopher Green, Christopher Lustri, Scott W. McCue

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry
    Original languageEnglish
    Article number20170050
    Pages (from-to)1-20
    Number of pages20
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume473
    Issue number2201
    DOIs
    Publication statusPublished - 31 May 2017

    Keywords

    • selection problem
    • surface tension
    • bubbles
    • Hele-Shaw cell
    • conformal map
    • complex potential

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