Non-unique bubble dynamics in a vertical capillary with an external flow

Abstract

We study bubble motion in a vertical capillary tube under an external flow. Bretherton (J. Fluid Mech., vol. 10, issue 2, 1961, pp. 166–188) has shown that, without external flow, a bubble can spontaneously rise when the Bond number (, thus suggesting non-unique, history-dependent solutions for the steady-state film thickness under the same external flow conditions. Furthermore, inertialess symmetry-breaking shape profiles at steady state are found as the bubble transits near the tipping points of the solution branches, which are shown in both experiments and three-dimensional numerical simulations.