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Journal article
Two-layer flow during extraction through a point sink in a porous medium: Two-layer flow during extraction through a point sink
Journal of engineering mathematics, Vol.159(6)
2026
Abstract
Withdrawal into a point sink in a porous medium of a fluid that is layered in density, where both fluid layers are drawn into the outlet, is examined. The porous medium has finite vertical extent, but is infinite horizontally. These problems present a complex mathematical challenge due to the unknown interface shape and the singularity at the sink. By employing a spectral method, it is possible to remove the singularity and obtain numerical solutions, including two exact solutions: one where the sink is positioned at the initial interface height, and another in the limit of large flow rates. For all other flow rates, numerical solutions are obtained. Our results show that as the sink moves away from the initial height of the interface, the critical flow rate required to induce coning, and hence two-layer flow, increases significantly, aligning with the behaviour observed in single-layer, non-porous media flow dynamics.
Details
- Title
- Two-layer flow during extraction through a point sink in a porous medium
- Authors/Creators
- J. Jose - Murdoch UniversityG. C. Hocking - Murdoch UniversityD. E. Farrow - Murdoch University, School of Mathematics, Statistics, Chemistry and Physics
- Publication Details
- Journal of engineering mathematics, Vol.159(6)
- Publisher
- Springer Netherlands; DORDRECHT
- Number of pages
- 15
- Grant note
- Murdoch University
- Identifiers
- 991005902121607891
- Copyright
- © The Author(s) 2026
- Murdoch Affiliation
- School of Mathematics, Statistics, Chemistry and Physics
- Language
- English
- Resource Type
- Journal article
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