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Free boundary Darcy flows with surface tension: Analytical and numerical study

Published online by Cambridge University Press:  08 February 2007

Yu. A. SEMENOV  and
L. J. CUMMINGS
Yu. A. SEMENOV
Affiliation:
Institute of Hydromechanics of the NAS of Ukraine, Zhelyabov str. 8/4, 03057, Kiev, Ukraine email: [email protected]
L. J. CUMMINGS
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
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Abstract

We study surface tension effects for two-dimensional Darcy flow with a free boundary in a corner between two non-parallel walls. The analytic solution is based on two governing expressions constructed in an auxiliary parameter domain, namely a complex velocity and a derivative of the complex potential. These expressions admit a general solution for the problem in a corner geometry for the flow generated by a source/sink at the corner vertex or at infinity. We derive an integral equation in terms of the velocity modulus and angle at the free surface, determined by the dynamic boundary condition. A numerical procedure, used to solve the obtained system of equations, and numerical results concerning the effect of surface tension on the time evolution of the free boundary, are discussed.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 17 , Issue 5 , October 2006 , pp. 607 - 631
Copyright
2007 Cambridge University Press

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