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Electrical Response of Flow, Diffusion, and Advection in a Laboratory Sand Box

^a Institut de Physique du Globe de Strasbourg, CNRS–Université Louis Pasteur, 5 rue Descartes, 67000 Strasbourg, France
^b Institut de Mécanique des Fluides et des Solides de Strasbourg, CNRS–Université Louis Pasteur, 2 rue Boussingault, 67000 Strasbourg, France

View larger version (39K): [in a new window]   Fig. 1. Experimental setup. (a) Annex system. The recharge reservoirs supply fluid to the upstream reservoir of the tank. The overflow system of the primary recharge reservoir connected to the secondary recharge reservoir allows the inflow rate to be constant. The secondary reservoir feeds the primary reservoir continuously due to pumping. Fluid flowing out of the sand box is collected by the recovery reservoir. The recovered fluid is reinjected in the secondary recharge reservoir, so the entire system constitutes a closed hydraulic circuit. (b) Seepage configuration. The levels of the upstream and downstream reservoirs are maintained at fixed values using the upstream clamp and the downstream overflow system. The water level difference generates a two-dimensional flow field through the porous medium, in which the measurements electrodes are planted. (c) Darcy configuration. The tank is tilted, and the levels of the upstream and downstream reservoirs are maintained at the same value. Flow through the porous medium is hence one-dimensional.

View larger version (14K): [in a new window]   Fig. 2. Schematic copper–copper sulfate electrode. A copper wire is inserted into a thin glass capillary containing saturated copper sulfate solution. Contact with the external medium is ensured by mean of a porous ceramic. The upper end is closed using a paraffin wax.

View larger version (15K): [in a new window]   Fig. 3. Location of the electrodes. (a) Top view (x,y plane); (b) transverse lateral view (x,z plane). Three lines of four measurement electrodes were used. The first line was located at 5 cm from the bottom (x = 6 cm), the second at 8 cm (x = 0), and the third at 11 cm (x = –6 cm). The electrodes along each line were located at 5, 12, 19, and 26 cm (y coordinate) from the upstream reservoir, respectively. The reference electrode was placed in the upstream reservoir, at z = 8.4 cm.

View larger version (25K): [in a new window]   Fig. 4. Example of electrokinetic electric potential difference for an increasing water table and deionized water. (a) Evolution of the upstream and downstream water levels. The upstream level was maintained at 20 cm; the downstream started at 5 cm and was increased by 3-cm steps until there was no flow. (b) Corresponding electric potential difference between the electrode located at (x,y,z) = (–6, 12, 5 cm) and the reference electrode located in the upstream reservoir (see Fig. 3).

View larger version (23K): [in a new window]   Fig. 5. Example of electrokinetic electric potential difference for a decreasing water table and deionized water. (a) Evolution of the upstream and downstream water levels. The upstream level was maintained at 20 cm; the downstream started at 20 cm (i.e., no flow) and was decreased by 3-cm steps until 5 cm. (b) Corresponding electric potential difference between the electrode located at (x,y,z) = (–6, 12, 5 cm) and the reference electrode located in the upstream reservoir (see Fig. 3).

View larger version (35K): [in a new window]   Fig. 6. Results of the NaCl diffusion experiment (no flow, salt added to the upstream reservoir). (a) Room temperature; (b) Conductivity in the upstream reservoir, exponentially decreasing with time due to diffusion of salt to the sand; (c) electric potential differences between the electrodes located at 5 cm from the upstream reservoir and the reference (see Fig. 3). The fact that results depend on the depth suggests a density effect. (d, e, f) same as (c) for the electrodes located at 12, 19, and 26 cm from the upstream reservoir, respectively.

View larger version (30K): [in a new window]   Fig. 7. Results of the NaCl advection experiment for the seepage configuration (upstream level at 20 cm, downstream at 10 cm). (a) Upstream reservoir conductivity, exponentially decreasing due to advection of salt to the sand and dilution with fluid from the recharge reservoir; (b) electric potential differences between the z = 5 cm electrodes and the reference (see Fig. 3). All electric potential differences decrease as soon as salt is added and return to positive values after the salt front passes the electrode. (c, d) same as (b) for lines z = 8 and z = 11 cm.

View larger version (40K): [in a new window]   Fig. 8. Results of the NaCl advection experiment for the Darcy configuration (reservoir levels at 20 cm, hydraulic gradient 7.72%). (a) upstream reservoir conductivity, exponentially decreasing due to advection of salt to the sand and dilution with fluid from the recharge reservoir; (b) downstream reservoir conductivity; (c) electric potential differences between the z = 5 cm electrodes and the reference (see Fig. 3). All electric potential differences decrease as soon as salt is added and return to positive values after the salt front passes the electrode. The vertical lines correspond to the injection time (I), the theoretical travel times between the upstream reservoir and the electrodes located at 5, 12, 19, and 26 cm from the upstream reservoir (5, 12, 19, 26), and the theoretical travel time between the upstream and downstream reservoir (A). (d) Corresponding local electric potential differences (i.e., between adjacent electrodes).

View larger version (39K): [in a new window]   Fig. 9. Results of the KCl advection experiment for the Darcy configuration (reservoir levels at 20 cm, hydraulic gradient 7.72%). (a) Upstream reservoir conductivity, exponentially decreasing due to advection of salt to the sand and dilution with fluid from the recharge reservoir; (b) downstream reservoir conductivity; (c) electric potential difference between the z = 11 cm electrodes and the reference (see Fig. 3). All electric potential differences decrease as soon as salt is added, and become positive after the salt front passes the electrode. The vertical lines correspond to the injection time (I), the theoretical travel times between the upstream reservoir and the electrodes located at 5, 12, 19, and 26 cm from the upstream reservoir (5, 12, 19, 26), and the theoretical travel time between the upstream and downstream reservoir (A). (d) Corresponding local electric potential differences (i.e., between adjacent electrodes).

View larger version (17K): [in a new window]   Fig. 10. Computed free surface and piezometric head profile for an upstream level of 20 cm and a downstream level of 10 cm, using the Baiocchi method. The iso-curves of piezometric head are spaced of 1 cm.

View larger version (16K): [in a new window]   Fig. 11. Measured electric potential difference values vs. computed hydraulic potential difference for deionized water and measurement electrode located at (x,y,z) = (–6, 12, 5 cm) (see Fig. 3). The slope of the straight line gives the electrokinetic coupling coefficient.

View larger version (37K): [in a new window]   Fig. 12. Local electric potential differences (i.e., between adjacent electrodes) for the NaCl diffusion experiment. (a) Measurements at z = 5 cm; (b) measurements at z = 11 cm (see Fig. 3); (c) one-dimensional modeling for an effective diffusion coefficient equal to twice the molecular diffusion coefficient; (d) One-dimensional modeling for an effective diffusion coefficient equal to the molecular diffusion coefficient.

View larger version (36K): [in a new window]   Fig. 13. One-dimensional modeling of the NaCl advection experiment for the Darcy configuration. (a) Electrokinetic potential differences for the electrodes located at 5, 12, 19, and 26 cm from the upstream reservoir (see Fig. 3); (b) junction potential differences; (c) sum of the electrokinetic and junction signals; (d) same as (c) but between adjacent electrodes.