Page 226 - Soil and water contamination, 2nd edition

Substance transport 213

a b

Concentration Concentration

Depth Depth

t = 0
t = 10
t = 20
t = 40
t = 80
6642 t = 160

Figure 11.9 Vertical dispersion in soil with a) a constant dispersion coefficient over the vertical soil profile and b) a
decreasing dispersion coefficient with soil depth.

of a layer of contaminated sediment , for example after flooding, the initial sharp boundary
between the uncontaminated soil and the fresh contaminated sediment becomes blurred in
the course of time, as shown in Figure 11.9a. Note that in this example advective transport
does not take place and the dispersion coefficient is constant throughout the soil profile . Just
as in the groundwater example, the depth profiles of the contaminant concentrations follow a
Gaussian cumulative distribution function. Under natural conditions, however, the biological
activity responsible for the dispersion process tends to diminish with depth (Middelkoop
1997). Accordingly, the mixing decreases with depth and results in the contamination
moving more slowly deeper in the soil profile (Figure 11.9b).
11.3.4 Transverse dispersion

Transverse dispersion is the process of mixing perpendicular to the average flow direction.
When mass spreads in two or three dimensions, the distribution of mass sampled
perpendicular to the direction of flow is also normally distributed with a standard deviation
that increases proportionally to t 2 (compare Equation 11.27). The two-dimensional
dispersal of a substance in a unidirectional flow field therefore leads to an elliptically shaped
distribution of the concentration. Typical transverse dispersion coefficients are smaller than

longitudinal dispersion coefficient s. In unconfined or semi-confined groundwater systems,
transverse dispersion results in a reduction of concentration everywhere beyond the advective
front, while longitudinal dispersion only does so at the front of the plume (Figure 11.10). In
general, in groundwater dispersion does not occur through the confining layers and in rivers
it does not occur through the river banks. In rivers, the transverse dispersion results in lateral
mixing when a substance has entered the river from the river bank.
Similar to the estimation of the longitudinal dispersion coefficient , the transverse
dispersion coefficient can be estimated by fitting a Gaussian curve on a graph of
concentration versus distance perpendicular to the main flow direction. Furthermore, based

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