Title: Analytical solutions for temporally dependent dispersion through homogeneous porous media

Authors: R.R. Yadav; Dilip Kumar Jaiswal; Hareesh Kumar Yadav; Gulrana

Addresses: Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, India. ' Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, India. ' Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, India. ' Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, India

Abstract: Analytical solutions are obtained for advection-dispersion equation in two-dimensional horizontal semi-infinite porous domains. The solute dispersion parameter is considered temporally dependent along uniform flow. The two main characteristic of the porous medium: desorption and reaction, both always some attenuation in solute concentration in liquid phase, are considered by retardation factor and first order decay term, respectively. The solutions are obtained for uniform and increasing input sources. New space and time variables are introduced to reduce the variable coefficients of the advection-dispersion equation into constant coefficients and Laplace transform technique is used to obtain the analytical solutions. The solution of the present problem is also derived in one and three-dimension. Physical significance of the problems is illustrated by different graphs.

Keywords: advection; dispersion; groundwater; aquifer; water pollution; retardation; first order decay; point source; sorption; porous media; desorption; reaction.

DOI: 10.1504/IJHST.2012.045941

International Journal of Hydrology Science and Technology, 2012 Vol.2 No.1, pp.101 - 115

Published online: 16 Aug 2014 *

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