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6. Dispersivity under Partially-Saturated Conditions
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decreases, the pore-water velocity decreases and the geometry of the liquid
phase in water-conducting pores changes with less opportunity for mixing and
increased tortuosity.
6.1.2 Experimental works and modeling studies
Compared to studies done on saturated dispersion, there is much less research
conducted on dispersion under unsaturated conditions. De Smedt et al. [1986]
observed a substantial increase in dispersivity (by a factor of about 80) when
changing from saturated to unsaturated conditions. They have attributed this
behavior to the broader distribution of microscopic pore-water velocities encountered
under unsaturated conditions. A possible cause for increase in dispersion
could also be the existence of mobile and immobile water zones as the
soil becomes unsaturated. Results of their modeling showed that, on the average,
64% of the water in the sand column could be considered mobile and 36%
immobile, for almost all experiments.
To capture the effect of saturation on solute transport, Krupp and Elrick [1968]
performed a series of miscible displacement experiments in an unsaturated column
packed with glass beads, all at a constant average velocity. The earliest
appearance of tracer in the effluent was observed at an intermediate saturation
in the range of 0.54 to 0.56. They attributed this behavior to the large degree
of disorder in the water distribution. Presence of filled and partially filled pores
and pore sequences cause mixing to be related to saturation in a complex way.
At higher water content, flow in filled pores was dominant, whereas at lower
water content, flow in partially filled pores and films dominated the displacement.
Although dispersivity increases non-linearly with the decrease in saturation, a
major observation is that the relation is not monotonic and dispersivity reaches
a maximum value, α max , at an intermediate saturation [Bunsri et al., 2008,
Toride et al., 2003]. We refer to this as the “critical saturation”, S cr . At saturations
lower than the critical saturation (i.e., S w < S cr ) the magnitude of
dispersivity reduces with further decrease in saturation.
Similar results were found by Bunsri et al. [2008], who performed experiments
on sand (with mean particle size of 250 µm) and soil columns (which contained
soil particle sizes up to 2.00 mm). They also performed numerical modeling
to simulate the experimental data. The simulation results showed that
the magnitude of dispersivity under unsaturated conditions was larger than
its value under saturated conditions. They found that the dispersivity in the
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