Retarded motion of bubbles in Hele–Shaw cells

Abstract

The motion of bubbles in a Hele–Shaw cell driven by a surrounding fluid or by gravity has been studied. Assuming that the surrounding fluid wets the solid wall and that the bubble surface is rigid due to the surfactant influence, the translational velocity of an elliptic bubble is estimated. The result indicates that the bubble velocity can decrease by an order of magnitude compared to the prediction of Taylor and Saffman [Q. J. Mech. Appl. Math. 12, 265 (1959)] due to the surfactant influence. The retarded bubble velocity is apparently in reasonable agreement with the experimental observations of Kopf-Sill and Homsy [Phys. Fluids 31, 18 (1988)], suggesting that the puzzling observations by them are likely to be due to the surface active contaminants.