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Interaction between two spherical bubbles rising in a viscous liquid

Published online by Cambridge University Press:  02 March 2011

YANNICK HALLEZ  and
DOMINIQUE LEGENDRE
YANNICK HALLEZ
Affiliation:
Université de Toulouse, INPT, UPS, LGC (Laboratoire de Génie Chimique), 118 route de Narbonne, F-31062 Toulouse CEDEX 9, France
DOMINIQUE LEGENDRE*
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France CNRS, IMFT, F-31400 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier–Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalised by the bubble radius) and the angle θ (0° ≤ θ ≤ 90°) formed between the centreline and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0°) by Legendre, Magnaudet & Mougin (J. Fluid Mech., vol. 497, 2003, p. 133) and for two bubbles moving in line (θ = 90°) by Yuan & Prosperetti J. Fluid Mech., vol. 278, 1994, p. 325). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore's correction) and a significant wake effect observed on both the drag and the transverse forces of the second bubble when located in the wake of the first one.

JFM classification

Drops and Bubbles: Bubble dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 673 , 25 April 2011 , pp. 406 - 431
Copyright
Copyright © Cambridge University Press 2011

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