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124 CHAPTER 3. TERRESTRIAL SYSTEMS
3.1.3 Fingered Flow Through Initially Dry Porous Hele-Shaw cell
Participating scientist Fereidoun Rezanezhad, Hans-Jörg Vogel, Kurt Roth
Abstract Fingered flow is an instability that occurs during infiltration into dry, coarse-textured,
and uniform porous media. We study the dynamics of such fingers in porous Hele-Shaw cells with
dimensions 1.6 × 0.6 × 0.003 [m]. High-resolution measurements of the water saturation are obtained
from light transmission images that have been calibrated by X-ray transmission.
Background Unstable flow of water during infiltration
into unsaturated porous media belongs
to the class of preferential flow. It has been studied
for many years and we have a quite complete
description of the general phenomena. Glass and
Nicholl (1996) reviewed the classical understanding
and DiCarlo (2004) summarizes the newer
developments which focus on the nature of the
saturation overshoot in the finger tip. Fingered
flow is important for some practical issues, e.g.,
for rapid contaminant transport with irrigation in
many arid regions. However, it also illuminates
our very understanding of the physics of multiphase
flow in porous media. Indeed, the current
theory – Richards equation – cannot explain the
existence of such fingers.
Funding DFG RO 1080/9-1&2
Methods and Results The key to understanding
fingered flow are rapid high-resolution measurements
of the water saturation. To facilitate
this, we work with Hele-Shaw cells – two parallel
glass plates separated by a few millimeters –
that are filled with sand. Light transmission is
the used as a proxy for water saturation. A simple
digital camera then yields the required rapid measurements.
Since the relation between transmission
and saturation is nonlinear, it is calibrated
with X-ray transmission which is accurate but too
slow and also too expensive for routine measurements.
In our experiments, fingers are initiated
at the transition from a fine-textured layer, where
the flow is very uniform, to a coarse-textured
Figure 3.3: Experimental setup for X-ray and
light transmission measurements. The front
view shows the highly localized flow paths that
originate from the flow instability in the uniform
part of the medium.
layer. They eventually disappear into the simulated
groundwater at the lower end of the cell. At
different stages, a dye tracer is added to the flow in
order to study the flow field behind the finger tip.
Finally, pressure sensors are installed to monitor
the potential energy of the water.
First, a number of experimental findings of
other groups were reproduced. These are in particular
(i) the maximum saturation that occurs in
the finger tip, (ii) the stability of the resulting flow
channel on short time scales and its diffusive decay
on very long time scales, and (iii) the existence of a
mobile core and an immobile fringe. Some newer
findings include (i) the demonstration that flow
channels are destroyed when they encounter heterogeneous
layers, (ii) the detection of pressure
drops in the overlaying fine-textured layer upon
initialization of a new finger, and (iii) the detection
of correlated intermittency between different
fingers.
Outlook/Future Work The future work will
concentrate on the theoretical understanding of
the experiments. This necessitates a still higher
spatial resolution, however, which in turn requires
a more detailed representation of the light transmission
through the porous medium. Measurements
of the point spread function in the nearinfrared
as well as in the visible region are under
way (project 3.1.4). On another route, a microscope
was installed that allows the resolution of
the pore space and the detailed observation of the
water phase during the passage of a finger tip.