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The effect of confinement on the motion of a single clean bubble

Published online by Cambridge University Press:  10 December 2008

B. FIGUEROA-ESPINOZA ,
R. ZENIT  and
D. LEGENDRE
B. FIGUEROA-ESPINOZA
Affiliation:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, 04510 México, D.F., México
R. ZENIT*
Affiliation:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, 04510 México, D.F., México
D. LEGENDRE
Affiliation:
Institut de Mécanique des Fluides de Toulouse, Alee du Prof. Soula, 31400 Toulouse, France
*
†Email address for correspondence: zenit@servidor.unam.mx
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Abstract

The effect of confining a gas bubble between two parallel walls was investigated for the inertia-dominated regime characterized by high Reynolds and low Weber numbers. Single bubble experiments were performed with non-polar liquids such that the bubble surface could be considered clean; hence, shear free. The drag coefficient was found to be the result of two main effects: the Reynolds number and the confinement. The total drag could be written as the product of the corresponding unconfined drag, which depended mainly on the Reynolds number, and a function F(s)=1 + κs3. The confinement parameter s was defined as the ratio of the bubble radius to the gap width. The value of the constant κ depended on the way in which the bubbles moved within the gap, which was found to be either in a rectilinear (κ≈8) or oscillatory trajectory (κ≈80). For Re < 70, and a range of values of the confinement parameter, the bubbles followed a rectilinear path. For this regime, numerical simulations were performed to obtain the drag force on the bubble directly; a reasonable agreement was found with experiments. Moreover, a comparison of these results with a potential-flow-based model indicated that the vorticity produced at the walls induced a significant part of the drag. For Re > 70, oscillations were observed in the bubble trajectory. In all cases, the oscillation occurred in a zigzag manner. Near the transition the bubbles oscillated but did not reach the walls; for larger Reynolds numbers, the bubbles collided repeatedly with the walls as they ascended. The instability, which is different from the well-known unconfined path instability, resulted from the reversal of sign of the wall-induced lift force: for low Reynolds number, the walls have a stabilizing effect because of the repulsive nature of the lift force between the walls and the bubble, while for high Reynolds number the lift is attractive and trajectories become unstable. Considering a model for the lift force of a bubble moving near a wall, the conditions for the transition were identified. A reasonable agreement between the model and experiments was found.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 616 , 10 December 2008 , pp. 419 - 443
Copyright
Copyright © Cambridge University Press 2008

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