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The axisymmetric rise of a spherical bubble at the exit of an orifice in the presence of a stagnant cap of insoluble surfactants

Published online by Cambridge University Press:  21 April 2006

Zeev Dagan ,
Zong-Yi Yan  and
Huixian Shen
Zeev Dagan
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031, USA
Zong-Yi Yan
Affiliation:
Department of Mechanics, Peking University, Beijing, China
Huixian Shen
Affiliation:
Department of Mathematics, The Affiliated College of Peking University, Beijing, China
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Abstract

The motion of a spherical droplet in unbounded exterior phase in the presence of a stagnant cap of adsorbed insoluble surfactants has been recently presented by Sadhal & Johnson (1983). The present study considers the axisymmetric motion of a gas bubble at the exit of a circular orifice in the presence of a similar stagnant cap.

The solution procedure utilizes the boundary integral representation in order to obtain the drag correction factor for a bubble translating away from the orifice in otherwise quiescent fluid, and for a fixed bubble exposed to Sampson's flow towards the orifice. It is demonstrated that the presence of the confining orifice boundaries substantially increases the drag acting on the bubble, and the solution approaches the exact result of Sadhal and Johnson as the distance between the bubble and the orifice is increased. Furthermore, it is shown that for a fixed amount of surfactants on the bubble surface the cap angle increases with distance from the orifice due to the diminishing hydrodynamic interaction. Hence, the quasi-steady terminal velocity of a bubble rising from an orifice is reduced by the viscous boundary interaction, and by the growing immobile cap size.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 299 - 319
Copyright
© 1988 Cambridge University Press

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