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Time-dependent motion of a confined bubble in a tube: transition between two steady states

Published online by Cambridge University Press:  29 October 2018

Yingxian Estella Yu Open the ORCID record for Yingxian Estella Yu [Opens in a new window] ,
Lailai Zhu Open the ORCID record for Lailai Zhu [Opens in a new window] ,
Suin Shim ,
Jens Eggers Open the ORCID record for Jens Eggers [Opens in a new window]  and
Howard A. Stone
Yingxian Estella Yu
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Lailai Zhu
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Linné Flow Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, SE 10044 Stockholm, Sweden
Suin Shim
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Jens Eggers*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

When a confined bubble translates steadily in a cylindrical capillary tube, without the consideration of gravity effects, a uniform thin film of liquid separates the bubble surface and the tube wall. In this work, we investigate how this steady state is established by considering the transitional motion of the bubble as it adjusts its film thickness profile between two steady states, characterized by two different bubble speeds. During the transition, two uniform film regions coexist, separated by a step-like transitional region. The transitional motion also requires modification of the film solution near the rear of the bubble, which depends on the ratio of the two capillary numbers. These theoretical results are verified by experiments and numerical simulations.

JFM classification

Drops and Bubbles: Bubble dynamics Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , R4
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Copyright
© 2018 Cambridge University Press 

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