Effect of Scale - Transport and Fate of Chemicals in Soils: Principles and Applications - page 118

the distance-dependent α, the concentration at the inlet is always at c 0 for
all times during pulse application (16 h). At early times, solute distribution
profiles appear similar for both types of α models. However, the two snap-
shots separated gradually over time. Generally, solute concentration profiles
exhibited a rapid decrease or sharp fronts when distance-dependent α was
used. In other words, distance-dependent α resulted in a steeper solute con-
centration profile than time-dependent α. At later times, the solute fronts
advanced further in the porous media when distance-dependent α was used.
Our results clearly demonstrate the differences between transport processes
in a medium with time-dependent and that with distance-dependent α.

4.3 Effects of Nonlinearity of the Dispersivity Model
The nonlinear dispersivity models (Equations 4.21 through 4.28) provide an
opportunity to investigate the effects of fractal dimension on solute BTCs.
For computational convenience, only 10-cm-long soil columns were consid-
ered in this section (Table 4.2). For time-dependent dispersivity, the BTCs for
different fractal dimension D fr are compared in Figure 4.3. From this figure,
we can see that the fractal dimension has significant influences on the overall
shape of the BTCs. As D fr increases, the initial arrival time becomes shorter
with lower peak concentrations. Moreover, the BTCs exhibited enhanced
tailing or increased spreading as D fr value approached 2.0.
Comparison of BTCs for distance-dependent α having different exponent
values is shown in Figure 4.4. For distance-dependent dispersivity, higher
values of D fr resulted in earlier arrival of BTC, a lower peak concentration,
and an enhanced tailing in the BTCs. However, our simulations clearly show
that the differences among BTCs for different D fr shown in Figure 4.4 are

TABLE 4.2
Parameters Used in Simulation to Examine the Effect of Exponents in the
Dispersivity Expressions of Equations 4.21 and 4.26

Parameter Time-Dependent α Distance-Dependent α

Moisture content (cm 3 /c m 3 ) 0.40 0.40

Column length (cm) 10.0 10.0

Water flux rate (cm/h) 5.0 5.0

Initial concentration (mg/L) 0.0 0.0

Concentration in input
pulse (mg/L)

10.0 10.0

Pulse duration (h) 2.0 2.0

Dispersivity α (cm)

x D fr

− , D fr = 1.25, 1.50, 1.75, 2.0

x D fr

− , D fr = 1.25, 1.50, 1.75, 2.0

0.5 0.5