The following pictures were developed by Dr. Silliman and an undergraduate student (taking part in Notre Dame's REU program). They are intended to demonstrate qualitatively the potential for horizontal flow in the capillary fringe (CF), the interaction of the CF with the overlying vadose zone when there is active flow in the region below the water table, and the potential for heterogeneity to lead to interesting transport patterns within the CF and the area immediately below the water table. This work is an outgrowth of discussion between Dr. Silliman and Drs. Brian Berkowitz and Harvey Scher of the Weizmann Institute of Science in Rehovot, Israel.
Comments and/or questions are welcome. {Dr. Silliman can be reached at Silliman.1@nd.edu}
Series One
These photographs show the active horizontal flow that can occur within the CF when there is active flow below the water table. The water table can be estimated in these photos by locating the pink water in the left and right reservoirs. The water table can be approximated as the straight line connecting the water levels on the right and left sides of the sand. The horizontal dimension here is on the order of one meter.
After flow was established, five dots of green dye were released along a vertical profile on the right portion of the tank (see photo labeled "0 Minutes". The lowest point is below the water table, the next point is approximately at the water table, the next point is within the CF (the Cf is the darker sand and its upper surface is labeled with the lower dotted line). the forth point is approximately at the upper limit of the CF and upper most point is above the CF.
As expected, the dye below and at the water table moved in the direction of the regional gradient. Interestingly, the dye released in the CF is moving in the same direction at a similar rate (the moisture content is high enough such that the unsat conductivity is nearly equal to that below the water table). Even more significantly, the dye release at the upper level of the CF moves horizontally and follows the upper boundary of the CF. This dye will track all the way to the outflow boundary where it will show a radical change in direction to exit within the saturated zone at the outflow boundary. The approximate route can be seen in the red dye in the photos at 0 and 15 minutes - this red dye is the remainder from a previous experiment.
It is noted that this horizontal flow in the CF can be predicted with standard numerical solutions of the equations of fluid flow in variably saturated media. These solutions demonstrate that the thickness of the horizontal flow is a function of the properties of the porous medium. An interesting interplay also exists between the horizontal gradient below the water table and the rate of infiltration through the vadose zone.
Series Two
The role of the upper portion of the CF on flow coming from the vadose zone is illustrated more dramatically in the photographs above. This is the same sand as in the previous experiments. In this case, horizontal flow was maintained in the saturated poriton of the flow field. In addition, artificial infiltration was added to the upper surface of the sand. A red dye tracer was then added as a slug in an isolated portion of the surface.
As shown in the upper left photo, the dye behaves as we would expect in the upper portion of the vadose zone. It fingers and spreads vertically in response to slight local heterogeneities.
However, when this dye reaches the upper portion of the CF, the vertical spread actually decreases as the dye begins to travel a relatively narrow flow line along the surface of the CF. Once again, the dye will follow a path along the upper surface of the CF until the downstream boundary condition causes the flow line to curve towards the saturated zone.
Series Three
This example shows the impact of heterogeneity above the water table (i.e., in the CF). In this case, a coarse sand has been added in a continuous layer approximately 2 cm above the water table (The height of water in the right reservoir is indicated by the black line in the last image. The water table was lowered to its present position, such that the distribution of water above the water table represents a drainage pattern (this is important as shown below). In this case, red dye is introduced at the right. The dye rapidly moves up into the CF and is transported along the coarse sand (the sand remains at 100% saturation due to the fine sand above it). The result is that the dye move more rapidly in the CF than in the region below the water table. Further, a portion of the dye is carried into the upper region of fine sand (still within the CF) such that a relatively complex distribution of dye is obtained at late time (last image and image below).
As shown below, the use of drainage conditions was critical. When the water table was initially well below the coarse layer and was then raised to a similar position as in the set of images above, the coarse zone did not become saturated. Hence, the relative permeability in the coarse zone was low. Instead of acting as a conduit for transport of the dye, the coarse zone acted, in this case, as a barrier to flow. The result is shown below in a comparison of the results of the drainage experiment (upper image) and the imbibition experiment (lower image).
Series Four
The impact of heterogeneity can lead to unusual distributions of tracer in both the CF and the region below the water table. In the image above, a coarse layer has been added to the system that starts and ends below the water table (a linear approximation to the water table is shown with the red line), but passes into the CF in between. Flow is once again left to right (the images are in reversed order, however, with early time at the top right and late time at the lower left). The red dye remains from a previous experiment and is slowly flushing through the region below the water table.
When the green dye is added to the inflow reservior, it moves in a pattern similar to that seen in the earlier photographs (i.e., a portion moves through the region below the water table and a portion enters the CF at the boundary. In addition, however, a substantial amount of dye moves through the coarse sand layer, thus up into the CF and finally back down below the water table to the outflow. It is noted that this coarse layers represents a source of tracer to the fine sand in the CF. Further, the presence of this coarse layer leads to the new (green) dye "leap frogging" past the older (red) dye remaining below the water table (note that the green dye is already in the outflow reservoir at 25 minutes).
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