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Bifurcation analysis of bubble-induced convection in a horizontal liquid layer: role of forces on bubbles

Published online by Cambridge University Press:  27 July 2021

Kotaro Nakamura Open the ORCID record for Kotaro Nakamura [Opens in a new window] ,
Harunori N. Yoshikawa Open the ORCID record for Harunori N. Yoshikawa [Opens in a new window] ,
Yuji Tasaka Open the ORCID record for Yuji Tasaka [Opens in a new window]  and
Yuichi Murai Open the ORCID record for Yuichi Murai [Opens in a new window]
Kotaro Nakamura*
Affiliation:
Laboratory for Flow Control, Hokkaido University, Sapporo 060-8628, Japan
Harunori N. Yoshikawa
Affiliation:
Université Côte d'Azur, CNRS, Institut de Physique de Nice, 06100 Nice, France
Yuji Tasaka
Affiliation:
Laboratory for Flow Control, Hokkaido University, Sapporo 060-8628, Japan
Yuichi Murai
Affiliation:
Laboratory for Flow Control, Hokkaido University, Sapporo 060-8628, Japan
*
Email address for correspondence: kotaro@ube-k.ac.jp
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Abstract

We investigate with a two-fluid model the convections developing in a gas–liquid two-phase flow, which consists of a horizontal liquid layer subject to the injection of monodisperse gas bubbles at the bottom. The convections develop in either whole- or multi-layered modes, once the gas injection flux exceeds a critical value (Nakamura et al., Phys. Rev. E, vol. 102, 2020, 053102). We determine the nonlinear evolution of these modes of flows with varying injection flux and find that the whole- and multi-layered modes develop through subcritical and supercritical bifurcations, respectively. The formation of gas plumes is observed in both cases when the nonlinearity is significant. Examining energy transfer from base to perturbation flows, we show that the lift forces on bubbles play a key role in the bifurcations. While they impede the convections in both subcritical and supercritical bifurcations at weak nonlinearity, the lift forces turn to driving the convections in the subcritical bifurcation as nonlinearity increases.

JFM classification

Convection: Buoyancy-driven instability Multiphase and Particle-laden Flows: Gas/liquid flow Nonlinear Dynamical Systems: Bifurcation
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , R4
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

Present address: Department of Mechanical Engineering, National Institute of Technology, Ube College, Ube 755-8555, Japan.

References

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