Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid

Abstract

The two components of the force acting on a clean almost spherical bubble rising near a plane vertical wall in a quiescent liquid are determined experimentally. This is achieved by using an apparatus in which a CCD camera and a microscope follow the rising bubble. This apparatus allows us to measure accurately the bubble radius, rise speed and distance between the bubble and the wall. Thereby the drag and lift components of the hydrodynamic force are determined for Reynolds numbers Re (based on bubble diameter, rise velocity U, and kinematic viscosity ν) less than 40. The results show the existence of two different regimes, according to the value of the dimensionless separation L* defined as the ratio between the distance from the bubble centre to the wall and the viscous length scale ν/U. When L* is O(1) or more, experimental results corresponding to Reynolds numbers up to unity are found to be in good agreement with an analytical solution obtained in the Oseen approximation by adapting the calculation of Vasseur & Cox (1977) to the case of an inviscid bubble. When L* is o(1), higher-order effects not taken into account in previous analytical investigations become important and measurements show that the deformation of the bubble is significant when the viscosity of the surrounding liquid is large enough. In this regime, experimental results for the drag force and shape of the bubble are found to agree well with recent theoretical predictions obtained by Magnaudet, Takagi & Legendre (2002) but the measured lift force tends to exceed the prediction as the separation decreases.