Numerical Study of Surfactant-Laden Drop-Drop Interactions
Jian-Jun Xu 1*, Zhilin Li 2, John Lowengrub 3, Hongkai Zhao 31 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
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.
Email: firstname.lastname@example.org (J. Xu), email@example.com (Z. Li), firstname.lastname@example.org (J. Lowengrub), email@example.com (H. Zhao)