Bubbles creeping in a viscous liquid along a slightly inclined plane

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 film forms.