One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

Abstract

The one-dimensional linear advection-diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection-diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

“…To account the mixing caused by velocity fluctuations, dispersion coefficient was considered as a function of both space and time variables in the porous media in a theoretical and experimental work by Sternberg et al (1996). On the basis of this paper, the dispersion parameter has been expressed in both the independent variables but in degenerate form (Su et al 2005;Yadav et al 2011). To accommodate the effects of winds upon solute transport in open tidal fjords channel, the velocity has been considered as function of depth variable and sinusoidally varying time variable (Wang et al 1977).…”

Seepage Migration Process of Soluble Contaminants in Porous Medium considering Adsorption History

“…Te adsorption mechanism of soil is complicated for its complex nature [4,5], and it also has specifc characteristics for desorption. Previous studies have shown that the adsorption capacity of porous media does not change after the initial adsorption [6][7][8], but in practice, the residue of pollutants in porous media will weaken its adsorption capacity [9][10][11]. Diverse soil conditions will result in complex adsorption-desorption processes, which in turn afect the migration of pollutants.…”

“…Cui et al [23] considered that the attenuation of soil adsorption performance is afected by its adsorption historical and temperature efect and conducted a sensitivity analysis on relevant parameters [24]. Some researchers [9,25,26], based on the hydrodynamic dispersion coefcient and fow velocity under unstable conditions, established their pollutant transport equations in semi-infnite space concerning space-time changes and obtained the analytical solution under the action of the Gaussian pulse pollution source. Cui et al [22] proposed a short-time pulse pollution source by studying pollution sources, established a pollutant migration model, and calculated the migration and deposition characteristics of pollutants in porous media.…”

Analytical solution for solute transport from a pulse point source along a medium having concave/convex spatial dispersivity within fractal and Euclidean framework

“…Analytical solutions of the ADE in one, two and three dimensions were derived in semi-infinite media for describing the solute transport in heterogeneous media with a linearly increasing distance-dependent dispersion coefficient and uniform/steady/unsteady velocity (Yates 1990;Huang et al 1996;Hunt 1998Hunt , 2002Pang and Hunt 2001;Chen et al 2008;Gao et al 2010). Kumar et al (2009) and Yadav et al (2011) have studied the one-dimensional solute through heterogeneous media originating from the uniform continuous source and pulse-type source, respectively, by using spatial-and temporal-dependent coefficients of the ADE. You and Zhan (2013) derived the two semi-analytical solutions for solute transport in a finite column with linear asymptotic and exponential distance-dependent dispersivities and timedependent sources along a uniform flow.…”