Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-19T23:55:09.184Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  11 July 2002

FUMIO TAKEMURA
Affiliation:
Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
SHU TAKAGI
Affiliation:
Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan
JACQUES MAGNAUDET
Affiliation:
Institut de Mecanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, 2, Avenue Camille Soula, 31400 Toulouse, France
YOICHIRO MATSUMOTO
Affiliation:
Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan

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.

Type
Research Article
Copyright
© 2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)