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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.

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

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