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Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

Published online by Cambridge University Press:  14 December 2007

M. HAMEED ,
M. SIEGEL ,
Y.-N. YOUNG ,
J. LI ,
M. R. BOOTY  and
D. T. PAPAGEORGIOU
M. HAMEED
Affiliation:
Division of Mathematics and Computer Science, Unversity of South Carolina Upstate, Spartanburg, SC 29303, USA
M. SIEGEL
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Newark, NJ 07102, USA
Y.-N. YOUNG
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Newark, NJ 07102, USA
J. LI
Affiliation:
Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK
M. R. BOOTY
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Newark, NJ 07102, USA
D. T. PAPAGEORGIOU
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Newark, NJ 07102, USA
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Abstract

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit.

The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure.

The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 307 - 340
Copyright
Copyright © Cambridge University Press 2008

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