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On the lateral migration of a slightly deformed bubble rising near a vertical plane wall

Published online by Cambridge University Press:  18 August 2010

KAZUYASU SUGIYAMA  and
FUMIO TAKEMURA
KAZUYASU SUGIYAMA*
Affiliation:
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
FUMIO TAKEMURA
Affiliation:
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan National Institute of Advanced Industrial Science and Technology, 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, Japan
*
†Email address for correspondence: sugiyama@fel.t.u-tokyo.ac.jp
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Abstract

Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance c between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxén mirror image technique for a/(a + c) ≪ 1 (here a is the bubble radius), when the clearance parameter ϵ(=c/a) is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing ϵ. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble–wall gap. The numerical and lubrication analyses consistently demonstrate that when ϵ ≤ 1, the lubrication effect makes the migration velocity asymptotically μVB12/(25ϵγ) (here, VB1, μ and γ denote the rising velocity, the dynamic viscosity of liquid and the surface tension, respectively).

JFM classification

Drops and Bubbles: Drops and Bubbles Low-Reynolds-number flows: Lubrication theory Low-Reynolds-number flows: Stokesian dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 209 - 231
Copyright
Copyright © Cambridge University Press 2010

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