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- Title
Exact solutions for the evolution of ellipsoidal inclusions in porous media.
- Authors
BUCHAK, PETER; CROWDY, DARREN
- Abstract
This paper derives exact mathematical solutions for the time-dependent evolution of a single ellipsoidal inclusion in a porous medium when a linear straining flow is active in the far field. This represents a two-phase free boundary problem. It is shown that the dynamics is such that an initially ellipsoidal inclusion remains ellipsoidal under evolution. The theory of ellipsoidal harmonics is used to determine the system of ordinary differential equations governing the geometrical parameters of the ellipsoidal inclusion.
- Subjects
BOUNDARY value problems; DIFFERENTIAL equations; DYNAMICS; LAME'S functions; POROUS materials
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2008, Vol 61, Issue 2, p161
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbn005