Agriculture Reference
In-Depth Information
7.4.2.3 Dispersive Solute Transport
In porous media, solute dispersion is caused by two mechanisms: (i) molecular dif-
fusion and (ii) hydrodynamic dispersion. Hydrodynamic dispersion is explained
by the tortuous nature of the convective stream lines resulting from microscopic
fluctuation of the advection velocity.
The size and shape of the pores in soil differ, which cause variations in the veloc-
ity of water through the pores. Also, the velocity is faster at the center of a pore than
near the periphery. The complexity of the pore system causes mixing of the soil solu-
tion along the direction of flow, and hence dispersion of the solute. Dispersion is a
velocity- dependent process. It occurs only during the flow of water. Sometimes it is
termed mechanical dispersion. The mechanical dispersion is described in a similar
way as chemical diffusion using Fick's law as
D
m
∂
C
∂
q
m
=−
θ
(7.5)
x
where
dispersive flux of solute (kg/m
2
/s)
q
m
=
total volumetric water content of soil (m
3
water/m
3
soil)
θ
=
mechanical dispersion coefficient of solute in pure water (m
2
/s)
D
m
=
concentration of solute in water (kg/m
3
of water)
C
=
The transport of solutes in a porous medium is governed by the combined
effect of convection (the average solute particle velocity), diffusion, and dispersion.
Due to similarity between the chemical diffusion and mechanical dispersion, the
coefficients D
c
and D
m
are assumed to be additive. Thus,
D
=
D
c
+
D
m
where
D
is the longitudinal hydrodynamic dispersion coefficient (m
2
/s)
Usually,
D
is simply referred to as the dispersion coefficient. It is also termed as
apparent diffusion coefficient or the diffusion-dispersion coefficient.
The average solute particle velocity defines the centroid of the solute plume at
a given time or the average arrival time of solutes at a given depth. For a homoge-
neous porous medium, steady-state water flow and an inert (nonreactive) solute,
the average solute particle velocity equals
q
/
. The solute dispersion quantifies
the dispersion of the solute plume around the centroid at a certain time or the
dispersion of the solute breakthrough around the average arrival time at a certain
depth.
θ
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