An analytical solution of the advection dispersion equation in a bounded domain and its application to laboratory experiments. (English) Zbl 1285.76042

Summary: 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 \(\theta_3\) Function. The analytical solution here presented has been provided when the inlet (Dirac) and the boundary conditions (Dirichlet, Neumann, and mixed types) are fixed. The proposed solution was used to study experimental data acquired by using a noninvasive technique.


76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics
35B08 Entire solutions to PDEs
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