Environmental Engineering Reference
In-Depth Information
Let us note that the schemes in Figure 13.1 represent microscopic physical
situations at nanoscale level. Only a homogenization process can transcribe these
phenomena on the REV scale.
The anisotropy of the soil structure reinforces the dispersion phenomenon. In
fractured rocks in which flow mainly occurs within the fracture network, actual flow
velocities also differ from the average velocity.
Particles in solution at times t=0
Particles in solution at times t=t
1
Particles in solution at times t=t
2
Figure 13.1.
Mechanical dispersion
Therefore, the pollutant undergoes a
mechanical dispersion
and simultaneous
advection. The dispersion flow (average or homogenized REV value) of a pollutant
is modeled by the diffusion law:
v
=− ∇
D
C
[13.7]
dispersion
where
D
is the second-order mechanical dispersion tensor. For an isotropic porous
medium it is orthotropic, with revolution symmetry in the flow local axes (Frenet's
triad) that is aligned with the flow velocity:
uu
⊗
(
)
DauI a a
=
+
−
[13.8]
T
L
T
u
