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

Yu A. Semenov, L. J. Cummings

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)607-631
Number of pages25
JournalEuropean Journal of Applied Mathematics
Issue number5
StatePublished - Oct 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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