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The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number

  • FUMIO TAKEMURA (a1) and JACQUES MAGNAUDET (a2)

Abstract

The transverse migration of both clean and fully contaminated spherical bubbles rising near a plane vertical wall in a quiescent viscous liquid is studied experimentally using an optical technique. Knowing the bubble radius $R$, rising speed $U$ and separation distance $L$ between the bubble centre and the wall as a function of time, the transverse or lift component of the hydrodynamic force is determined as a function of $L/R$ for Reynolds numbers $Re\,{=}\,2 UR/\nu $ less than 100 ($\nu $ is the kinematic viscosity). At low Reynolds number, the lift force is directed away from the wall for both clean and contaminated bubbles and its magnitude is found to be in good agreement with available analytical solutions. For $Re\,{>}\,1$, contaminated bubbles are still repelled from the wall, but the magnitude of the lift force is always larger than predicted by the low-$Re$ theory, the difference being an increasing function of $Re$. The behaviour of clean bubbles is markedly different as the experiments reveal that the lift force is directed away from the wall for $Re\,{<}\,35$ and toward it for higher $Re$. The differences found in the evolution of the lift force for clean and contaminated bubbles are analysed by considering the relative strength of two hydrodynamical mechanisms of wall interaction, one being due to the vorticity generated at the bubble surface while the other is due to the irrotational dipole associated with the bubble. Empirical correlations based on the strength of these two mechanisms are derived to obtain practical expressions of the lift force as a function of $Re$ and $L/R$. At high enough $Re$, clean bubbles rising sufficiently close to the wall are found to bounce very close to it. Based on present and past experimental results, we suggest that this bouncing process is essentially due to the competition between inertial and viscous effects, rather than to bubble deformation as previously believed, and we propose that observations may be explained by considering the effect of the vorticity present in the wall boundary layer. Evaluation of the various contributions involved in the lateral force balance of bouncing bubbles reveals the central role of history effects due to unsteady diffusion of vorticity from the bubble surface.

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The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number

  • FUMIO TAKEMURA (a1) and JACQUES MAGNAUDET (a2)

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