Longitudinal and lateral dispersion in an isotropic porous medium

Abstract

Coefficients of longitudinal and lateral dispersion were measured for steady uniform laminar flow through an isotropic porous medium. A unique experimental method for measuring lateral dispersion is described. It is found that the ratio of the coefficient of longitudinal dispersion D1 to the coefficient of lateral dispersion D2 is given by $\frac {D_1}{D_2} = \lambda \Re ^n$ where λ and n are dimensionless coefficients dependent upon the pore-system geometry, and [real ] is the Reynolds number based on the seepage velocity, the average grain diameter, and the kinematic viscosity.

Colloid particle size‐dependent dispersivity

“…Numerous laboratory and field-scale studies have focused on estimation of either the longitudinal dispersion coefficient [Harleman and Rumer, 1963;Pickens and Grisak, 1981;Koch and Brady, 1985;Han et al, 1985;Chrysikopoulos et al, 1990;Delgado, 2006] or the transverse dispersion coefficient [Delgado and Guedes de Carvalho, 2000;Cirpka et al, 2006;Acharya et al, 2007;Olsson and Grathwohl, 2007]. Transverse dispersion is increasingly recognized as a controlling mass transfer mechanism for contaminant plume migration and NAPL dissolution in aquifers [Chrysikopoulos et al, 1994;Chrysikopoulos and Kim, 2000;Chrysikopoulos et al, 2003;Rahman et al, 2005;Cirpka et al, 2006;Acharya et al, 2007;Rolle et al, 2010].…”

Analytical Solution to the One-Dimensional Advection-Diffusion Equation with Temporally Dependent Coefficients

“…As evident from Equation (15) the solution in Equation (29) cannot be traced for 2 but the solutions in Equations (30-31) can be used to trace this case (the figure is not drawn). From Figures (1-3) it may be observed that at a particular position rs)…”

“…For example the analytical solution of the advectiondiffusion equation with constant coefficients in an initially solute free semi-infinite domain for a continuous uniform input point source 0 at the origin has been reported by Ogata and Banks [1], Harleman and Rumer [2], Guvanasen and Volker [3], Marshall et al [4], by using the transformations in Equation (2), as…”

Observations of 3-D transverse dispersion and dilution in natural consolidated rock by X-ray tomography

“…Tracer tests are most common and based on three principle techniques: (1) an annular core device with a uniform solute injected into the core region and concentration measurements of the effluent [6,27,22], (2) a device equally divided into two sides with a uniform solute injected at one-side and concentration measured using X-ray light attenuation [24], at probe locations along the core [25,26] or of the effluent [35], and (3) a device for point source injection of a solute of uniform concentration and concentration measurements taken at several points along the center line of the column [39,32]. Benekos et al [2] proposed a different technique with 70 a helix and a cochlea device.…”

“…Furthermore, most of the experiments were carried out using sand [6,21,30,15,22] or bead packs [26,27,25,39,43,2,22], besides Grane [24] who determined the transverse dispersion coefficient in a Berea sandstone that is known to have homogeneous flow and transport characteristics [4].…”