TY - JOUR
T1 - Non-unique bubble dynamics in a vertical capillary with an external flow
AU - Yu, Yingxian Estella
AU - Magnini, Mirco
AU - Zhu, Lailai
AU - Shim, Suin
AU - Stone, Howard A.
N1 - Funding Information:
We thank the NSF for the support via grant CBET-1804863. M.M. acknowledges the use of Athena at HPC Midlands+, which was funded by the EPSRC grant EP/P020232/1, as part of the HPC Midlands+ consortium. L.Z. acknowledges the start-up grant R-265-000-696-133 given by the National University of Singapore.
Publisher Copyright:
©
PY - 2021
Y1 - 2021
N2 - 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 is above the critical value, where is the liquid density, the gravitational acceleration, the tube radius and the surface tension. It was then shown by Magnini et al. (Phys. Rev. Fluids, vol. 4, issue 2, 2019, 023601) that the presence of an imposed liquid flow, in the same (upward) direction as buoyancy, accelerates the bubble and thickens the liquid film around it. In this work we carry out a systematic study of the bubble motion under a wide range of upward and downward external flows, focusing on the inertialess regime with Bond numbers above the critical value. We show that a rich variety of bubble dynamics occurs when an external downward flow is applied, opposing the buoyancy-driven rise of the bubble. We reveal the existence of a critical capillary number of the external downward flow (, where is the fluid viscosity and is the mean liquid speed) at which the bubble arrests and changes its translational direction. Depending on the relative direction of gravity and the external flow, the thickness of the film separating the bubble surface and the tube inner wall follows two distinct solution branches. The results from theory, experiments and numerical simulations confirm the existence of the two solution branches and reveal that the two branches overlap over a finite range of, 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.
AB - 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 is above the critical value, where is the liquid density, the gravitational acceleration, the tube radius and the surface tension. It was then shown by Magnini et al. (Phys. Rev. Fluids, vol. 4, issue 2, 2019, 023601) that the presence of an imposed liquid flow, in the same (upward) direction as buoyancy, accelerates the bubble and thickens the liquid film around it. In this work we carry out a systematic study of the bubble motion under a wide range of upward and downward external flows, focusing on the inertialess regime with Bond numbers above the critical value. We show that a rich variety of bubble dynamics occurs when an external downward flow is applied, opposing the buoyancy-driven rise of the bubble. We reveal the existence of a critical capillary number of the external downward flow (, where is the fluid viscosity and is the mean liquid speed) at which the bubble arrests and changes its translational direction. Depending on the relative direction of gravity and the external flow, the thickness of the film separating the bubble surface and the tube inner wall follows two distinct solution branches. The results from theory, experiments and numerical simulations confirm the existence of the two solution branches and reveal that the two branches overlap over a finite range of, 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.
KW - Key words bubble dynamics
KW - lubrication theory
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U2 - 10.1017/jfm.2020.1027
DO - 10.1017/jfm.2020.1027
M3 - Article
AN - SCOPUS:85106421092
SN - 0022-1120
VL - 911
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A34
ER -