Commun. Comput. Phys., 10 (2011), pp. 453-473.


Numerical Study of Surfactant-Laden Drop-Drop Interactions

Jian-Jun Xu 1*, Zhilin Li 2, John Lowengrub 3, Hongkai Zhao 3

1 School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China.
2 Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA.
3 Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA.

Received 9 March 2010; Accepted (in revised version) 2 June 2010
Available online 28 April 2011
doi:10.4208/cicp.090310.020610a

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.


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PACS: 47.55.D-, 47.55.dk, 47.55.N-
Key words: Surfactants, drops, coalescence, surface tension, Marangoni effect, level-set method, immersed interface method, Stokes flow.

*Corresponding author.
Email: jjxu21@xtu.edu.cn (J. Xu), zhilin@math.ncsu.edu (Z. Li), lowengrb@math.uci.edu (J. Lowengrub), zhao@math.uci.edu (H. Zhao)
 

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