Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity

Su, Ninghu, Sander, G.C., Liu, Fawang, Anh, Vo, and Barry, D.A. (2005) Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity. Applied Mathematical Modelling, 29 (9). pp. 852-870.

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Abstract

A specific form of the Fokker–Planck equation with a time- and scale-dependent dispersivity is presented for modelling solute transport in saturated heterogeneous porous media. By taking a dispersivity in the form of separable power-law dependence on both time and scale, we are able to show the existence of similarity solutions. Explicit closed-form solutions are then derived for an instantaneous point-source (Dirac delta function) input, and for constant concentration and constant flux boundary conditions on a semi-infinite domain. The solutions have realistic behaviour when compared to tracer breakthrough curves observed under both field and laboratory conditions. Direct comparison with the experimental laboratory data of Pang and Hunt [J. Contam. Hydrol. 53 (2001) 21] shows good agreement between the source solutions and the measured breakthrough curves.

Item ID: 1739
Item Type: Article (Refereed Research - C1)
Keywords: time- and scale-dependent dispersivity; similarity solutions; fractal; heterogeneity
ISSN: 1872-8480
Date Deposited: 16 Oct 2007
FoR Codes: 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010406 Stochastic Analysis and Modelling @ 0%
01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics @ 0%
01 MATHEMATICAL SCIENCES @ 0%
04 EARTH SCIENCES @ 0%
01 MATHEMATICAL SCIENCES @ 0%
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