On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity

Antoine Sellier

doi:10.1016/j.crme.2004.10.004

On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity

Presented by: Sébastien Candel

Antoine Sellier ¹

¹ LadHyX, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 111-116.

Abstract
Résumé

The slow migration of N spherical bubbles under combined buoyancy and thermocapillarity effects is investigated by appealing solely to $3 N + 1$ boundary-integral equations. In addition to the theory and the associated implementation strategy, preliminary numerical results are both presented and discussed for a few clusters involving 2, 3, 4 or 5 bubbles with a special attention paid to the case of rigid configurations.

On détermine la migration de N bulles sphériques sous l'action combinée de la pesanteur et d'effets thermocapillaires par la seule résolution de $3 N + 1$ équations de frontière. Outre la théorie et sa mise en oeuvre numérique on présente les premiers résultats obtenus pour quelques situations à 2, 3, 4 ou 5 bulles avec une attention particulière pour les configurations rigides.

Received: 2004-08-11
Accepted: 2004-10-11
Published online: 2004-11-20

DOI: 10.1016/j.crme.2004.10.004

Keywords: Fluid mechanics, Buoyancy, Thermocapillarity, Boundary-integral equations
Mots-clés : Mécanique des fluides, Sédimentation, Thermocapillarité, Équations de frontière

Author's affiliations:

Antoine Sellier ¹

¹ LadHyX, École polytechnique, 91128 Palaiseau cedex, France

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Antoine Sellier. On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity. Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 111-116. doi : 10.1016/j.crme.2004.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.10.004/

References
Cited by

[1] N.O. Young; J.S. Goldstein; M.J. Block The motion of bubbles in a vertical temperature gradient, J. Fluid Mech., Volume 197 (1959), pp. 350-356

[2] R.M. Merritt; D.S. Morton; R.S. Subramanian Flow structure in bubble migration under the combined action of buoyancy and thermocapillarity, J. Colloid Interf. Sci., Volume 155 (1993), pp. 200-209

[3] H. Wei; R.S. Subramanian Migration of a pair of bubbles under the combined action of gravity and thermocapillarity, J. Colloid Interf. Sci., Volume 172 (1995), pp. 395-406

[4] A. Sellier On the capillary motion of arbitrary clusters of spherical bubbles. Part 1. General theory, J. Fluid Mech., Volume 197 (2004), pp. 391-401

[5] M. Meyyappan; W. Wilcox; R.S. Subramanian The slow axisymmetric motion of two bubbles in a thermal gradient, J. Colloid Interf. Sci., Volume 94 (1983), pp. 243-257

[6] V.S. Satrape Interactions and collisions of bubbles in thermocapillary motion, Phys. Fluids A, Volume 4 (1992), pp. 1883-1900

[7] C. Pozrikidis Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, 1992

[8] M. Bonnet Boundary Integral Equation Methods for Solids and Fluids, Wiley, 1999

[9] D.D. Joseph; Y.Y. Renardy Fundamentals of Two-Fluid Dynamics. Part I: Mathematical Theory and Applications, Springer-Verlag, 1991

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