Advective transport from a penny-shaped crack in a porous medium and an associated uniqueness theorem |
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Authors: | A P S Selvadurai |
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Institution: | Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6 |
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Abstract: | This paper examines the problem of the advective transport of a contaminant from sources in the shape of either a penny-shaped crack or an elongated needle-shaped cavity located in a porous medium of infinite extent. The advective transport is induced by Darcy flow in the porous medium, where the internal boundary is maintained at a constant potential. The paper presents an approximate analytical solution to this problem, which is deduced from a formulation that models a cavity in the shape of either an oblate or a prolate spheroid. The results also represent one of the few spatially three-dimensional exact analytical solutions for the, albeit linear, hyperbolic problem governing the contaminant transport problem. The paper also presents a canonical proof of uniqueness for advective contaminant transport problems associated with media of infinite extent. Copyright © 2004 John Wiley & Sons, Ltd. |
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Keywords: | advective transport transport from a penny-shaped cavity transport from an elongated cavity uniqueness theorem for advective transport |
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