Dilip Kumar Jaiswal

Solute Transport along Temporally and Spatially Dependent Flows through Horizontal Semi-Infinite Media: Dispersion Proportional to Square of Velocity

According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a power n of the velocity; the power ranges between 1 and 2. Based on the value n=1, analytical solutions of the dispersion problems along temporally dependent flow domains were obtained in previous works. In the present work, two dispersion problems are addressed for n=2. Using the Laplace transform technique, analytical solutions are obtained for two-dimensional advection-diffusion equations describing the dispersion of pulse-type point source along temporally and spatially dependent flow domains, respectively, through a semi-infinite horizontal isotropic medium. Point sources of a uniform and varying nature are considered. The inhomogeneity of the medium is demonstrated by the linearly interpolated velocity in the space variable. Introduction of new space variables enable one to reduce the advection-diffusion equation in both problems to a one-dimensional equation with constant coefficients. The solutions are...

Three-dimensional temporally dependent dispersion through porous media: analytical solution

A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model also account for a uniform flow field, first-order decay which is inversely proportional to the dispersion coefficient and retardation factor. Porous media with semi-infinite domain is considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse-type input source conditions. The governing solute transport equation is solved analytically by employing Laplace transformation technique (LTT). The solutions are illustrated and the behavior of solute transport may be observed for different values of retardation factor, for which simpler models that account for solute adsorption through a retardation factor may yield a misleading assessment of solute transport in ‘‘hydrologically sensitive’’ subsurface environments.

Analytical solutions for temporally dependent dispersion through homogeneous porous media

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.

One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Abstract One-dimensional solute transport, originating from a continuous uniform point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Velocity is considered as directly proportional to the linear spatially-dependent function that defines the heterogeneity. It is also assumed temporally dependent. It is expressed in both the independent variables in degenerate form. The dispersion parameter is considered to be proportional to square of the velocity. Certain new independent variables are introduced through separate transformations to reduce the variable coefficients of the advection–diffusion equation to constant coefficients. The Laplace Transformation Technique (LTT) is used to obtain the desired solution. The effects of heterogeneity and unsteadiness on the solute transport are investigated. Editor D. Koutsoyiannis; Associate editor F.F. Hattermann Citation Kumar, A., Jaiswal, D.K., and Kumar, N., 2012. One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrological Sciences Journal, 57 (6), 1223–1230.

Analytical Solutions of One-Dimensional Temporally Dependent Advection-Diffusion Equation along Longitudinal Semi-Infinite Homogeneous Porous Domain for Uniform Flow

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional to the dispersion coefficient. Retardation factor is also considered in present paper. Analytical solutions are obtained for two cases: former one is for uniform input point source and latter case is for increasing input point source where the solute transport is considered initially solute free. The Laplace transformation technique is used. New space and time variables are introduced to get the analytical solutions. The solutions in all possible combinations of increasing or decreasing temporally dependence dispersion are compared with each other with the help of graph. It is observed that the concentration attenuation with position and time is the fastest in case of

Temporally Dependent Solute Dispersion in One-Dimensional Porous Media

Analytical solutions are obtained for temporally dependent dispersion along a uniform flow velocity in a one-dimensional semi-infinite domain by using Laplace integral transform technique. Initially the domain is not solute free. It is combination of exponentially increasing function of space variable and ratio of zero order production and first decay which are inversely proportional to dispersion coefficient. Retardation factor is also considered. The solutions are obtained for two cases, first one for uniform and second for increasing input source. The variable coefficients in the advection–dispersion equation are reduced into constant coefficients by introducing new space and time variables. Illustrations are given with different graphs.