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On the in-line motion of two spherical bubbles in a viscous fluid

Published online by Cambridge University Press:  26 April 2006

H. Yuan  and
A. Prosperetti
H. Yuan
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
A. Prosperetti
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

The motion of two equal spherical bubbles moving along their line of centres in a viscous liquid is studied numerically in bispherical coordinates. The unsteady Navier-Stokes equations are solved using a mixed spectral/finite-difference scheme for Reynolds numbers up to 200. Free-slip conditions at the bubble surfaces are imposed, while the normal stress condition is replaced by the sphericity constraint under the assumption of small Weber number. The vorticity shed by the upstream bubble affects the drag on the trailing bubble in a very complex fashion that appears to be quite beyond the power of existing asymptotic analyses. The separation between two equal bubbles rising in line under the action of buoyancy is predicted to reach an equilibrium value dependent on the Reynolds number. This result is at variance with experiment. The explanation offered of this difference casts further doubt on the feasibility of a simplified simulation of bubbly liquid dynamics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 325 - 349
Copyright
© 1994 Cambridge University Press

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