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Numerical Study of Surfactant-Laden Drop-Drop Interactions

Published online by Cambridge University Press:  20 August 2015

Jian-Jun Xu ,
Zhilin Li ,
John Lowengrub  and
Hongkai Zhao
Jian-Jun Xu*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China
Zhilin Li*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA
John Lowengrub*
Affiliation:
Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA
Hongkai Zhao*
Affiliation:
Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

In this paper, we numerically investigate the effects of surfactant on drop-drop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in (Xu et al., J. Comput. Phys., 212 (2006), 590-616). We find that surfactant plays a critical and nontrivial role in drop-drop interactions. In particular, we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number. This non-monotonic behavior, which does not occur for clean drops, is found to be due to the presence of Marangoni forces along the drop interfaces. This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops, as observed in recent experiments of Leal and co-workers. Although our study is two-dimensional, we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

Keywords

47.55.D-47.55.dk47.55.N-Surfactantsdropscoalescencesurface tensionMarangoni effectlevel-set methodimmersed interface methodStokes flow
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 453 - 473
Copyright
Copyright © Global Science Press Limited 2011

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