Agriculture Reference
In-Depth Information
7.4.2.2 Diffusive Solute Transport
Diffusion is the process of moving fluids from higher concentration to lower
concentration. Ionic and molecular species in solute move from areas of higher con-
centration to lower concentration. Transfer of mass of a chemical species is caused
by gradient in concentration. Molecular diffusion in solutions is controlled by Fick's
first and second laws. It is assumed that the rate of transfer of solute by diffusion
through a unit area of a section of soil is proportional to the gradient in concentra-
tion normal to the section. The diffusive mass flux of solute through a unit area is
D
c
∂
C
∂
q
d
=−
θ
(7.2)
x
where
diffusive flux of solute (kg/m
2
/s)
q
d
=
total volumetric water content of soil (m
3
water/m
3
soil)
θ
=
chemical diffusion coefficient of solute in pure water (m
2
/s)
D
c
=
concentration of solute in water (kg/m
3
of water)
C
=
The negative sign in the equation arises because diffusion occurs in the direction
opposite to that of increasing concentration.
Fick's first law
: Steady state flux of solute is given by
D
∂
C
∂
F
=−
(7.3)
x
where
F
=
flux of solute under steady state (mass/area/time)
10
-9
to 2
10
-9
m
2
/s)
D
=
Diffusivity coefficient (1
×
×
C
=
Solute concentration (mass/volume)
∂
C
∂
x
=
Concentration gradient
Fick's second law
: Rate of change of solute concentration over time is given by
2
C
∂
∂
C
∂
D
∂
t
=
(7.4)
x
2
where
∂
C
∂
t
=
Change of solute concentration with time
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