Commun. Comput. Phys., 8 (2010), pp. 735-757.


Numerical Simulation of Moving Contact Lines with Surfactant by Immersed Boundary Method

Ming-Chih Lai 1*, Yu-Hau Tseng 1, Huaxiong Huang 2

1 Center of Mathematical Modeling and Scientific Computing Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan.
2 Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada.

Received 28 October 2009; Accepted (in revised version) 12 February 2010
Available online 17 May 2010
doi:10.4208/cicp.281009.120210a

Abstract

In this paper, we present an immersed boundary method for simulating moving contact lines with surfactant. The governing equations are the incompressible Navier-Stokes equations with the usual mixture of Eulerian fluid variables and Lagrangian interfacial markers. The immersed boundary force has two components: one from the nonhomogeneous surface tension determined by the distribution of surfactant along the fluid interface, and the other from unbalanced Young's force at the moving contact lines. An artificial tangential velocity has been added to the Lagrangian markers to ensure that the markers are uniformly distributed at all times. The corresponding modified surfactant equation is solved in a way such that the total surfactant mass is conserved. Numerical experiments including convergence analysis are carefully conducted. The effect of the surfactant on the motion of hydrophilic and hydrophobic drops are investigated in detail.

AMS subject classifications: 65M06, 76D45

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Key words: Immersed boundary method, interfacial flow, Navier-Stokes equations, surfactant, moving contact line, hydrophilic drop, hydrophobic drop, wetting.

*Corresponding author.
Email: mclai@math.nctu.edu.tw (M.-C. Lai), yhtseng@math.nctu.edu.tw (Y.-H. Tseng), hhuang@yorku.ca (H. Huang)
 

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