Summary: Europhys. Lett., 59 (3), pp. 370376 (2002)
EUROPHYSICS LETTERS 1 August 2002
Bubbles creeping in a viscous liquid
along a slightly inclined plane
P. Aussillous and D. QuŽerŽe
Laboratoire de Physique de la Mati`ere CondensŽee, URA 792 du CNRS
Coll`ege de France - 75231 Paris Cedex 05, France
(received 1 February 2002; accepted in final form 13 May 2002)
PACS. 47.15.Gf Low-Reynolds-number (creeping) flows.
PACS. 68.15.+e Liquid thin films.
PACS. 83.50.Lh Slip boundary effects (interfacial and free surface flows).
Abstract. We describe the upwards movement of an air bubble creeping along a slightly
inclined plane immersed in a viscous liquid which totally wets the solid. After characterizing
the shape of the static bubble under a horizontal plane, we tilt the plane and study the resulting
motion. The bubble reaches a steady velocity, which is described as a function of the bubble
size, the liquid viscosity and the tilting angle. We interpret our results by considering the
viscous dissipation in the so-called dynamic meniscus, which is the zone where a lubricating
Introduction. We consider a tank filled with a viscous liquid, in which a bubble is
introduced. If the upper boundary of the tank is tilted, the bubble creeps along this boundary