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Two‐dimensional solute transport for periodic flow in isotropic porous media: an analytical solution
Author(s) -
Yadav R. R.,
Jaiswal Dilip Kumar
Publication year - 2012
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.8398
Subject(s) - laplace transform , dispersion (optics) , mathematical analysis , boundary value problem , porous medium , isotropy , flow (mathematics) , periodic boundary conditions , mathematics , retardation factor , mechanics , diffusion , physics , porosity , thermodynamics , geology , geotechnical engineering , optics , chemistry , column chromatography , organic chemistry
In this article, a mathematical model is presented for the dispersion problem in finite porous media in which the flow is two‐dimensional, the seepage flow velocity is periodic, and dispersion parameter is proportional to the flow velocity. In addition to these, first‐order decay and zero‐order production parameters have also been considered directly proportional to the velocity. Retardation factor is taken into account in the present problem. First‐type boundary condition of periodic nature is considered at the extreme end of the boundary. Mixed‐type boundary condition is assumed at the origin of the domain. A classical mathematical substitution transforms the original advection–dispersion equation into diffusion equation in terms of other dependent and independent variables, with constant coefficients. Laplace transform technique is used to obtain the analytical solution. Copyright © 2011 John Wiley & Sons, Ltd.