Journal of Applied Mathematics
Volume 2011 (2011), Article ID 493014, 14 pages
doi:10.1155/2011/493014
Research Article

An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to Laboratory Experiments

1CIMA Research Foundation, Via Magliotto 2, 17100 Savona, Italy
2Department of Engineering Production, Thermoenergetic and Mathematical Models, DIPTEM, University of Genoa, Piazzale Kennedy, Pad. D, 16129 Genoa, Italy
3Department of Communication Computer and System Sciences, DIST, University of Genoa, Via Opera Pia 13, 16145 Genoa, Italy

Received 6 September 2010; Accepted 1 November 2010

Academic Editor: Juergen Geiser

Copyright © 2011 M. Massabó et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain in order to simulate an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the advection dispersion equation in a porous medium was obtained by utilizing the Jacobi 𝜃 3 Function. The analytical solution here presented has been provided when the inlet (Dirac) and the boundary conditions (Dirichelet, Neumann, and mixed types) are fixed. The proposed solution was used to study experimental data acquired by using a noninvasive technique.