A mathematical and numerical study of incompressible flows with a surfactant monolayer

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March 2010, 28(1): 181-197. doi: 10.3934/dcds.2010.28.181

A mathematical and numerical study of incompressible flows with a surfactant monolayer

Yuen-Yick Kwan ^1, , Jinhae Park ^2, and Jie Shen ^3,

1.	Center for Computational Science, Tulane University, New Orleans, LA 70118, United States
2.	Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067
3.	Department of Mathematics, Purdue University, West Lafayette, IN 47907

Received March 2010 Revised March 2010 Published April 2010

Abstract
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We consider in this paper a mathematical model for the incompressible flows with a surfactant monolayer. The presence of surfactant gives rise to coupling surface terms which make the analysis and simulation challenging. We study the well-posedness of this coupled system of PDEs with physically relevant boundary conditions, as well as the stability of a numerical scheme. We also preform numerical simulations by a fast-spectral method and use it to study the effect of surfactant concentration on the motion of an incompressible fluid in a cylinder.

Keywords: Spectral-Galerkin method, Surfactant, Pressure-correction, Weak solution., Navier-Stokes, Instabilities, Existence.

Mathematics Subject Classification: Primary: 76B03, 65M70; Secondary: 76R99, 35K5.

Citation: Yuen-Yick Kwan, Jinhae Park, Jie Shen. A mathematical and numerical study of incompressible flows with a surfactant monolayer. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 181-197. doi: 10.3934/dcds.2010.28.181

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