Environmental Engineering Reference
In-Depth Information
rate of diffusive flux between two points is positively related to the differ-
ence in concentration and inversely related to the distance between the two
points. The basic equation used to describe
chemical diffusion
is
Fick's law:
C
2
)
(
x
1
(
C
1
J
D
x
2
)
where the
diffusion flux
(
J
, the amount of a compound diffusing per unit
area per unit time) is a function of the
diffusion coefficient
(
D
, the intrin-
sic rate of diffusion independent of concentration and distance), the dif-
ference in concentration (
C
), and the distance (
x
) between points 1 and 2.
The rate is greatest with large concentration gradients (difference between
C
1
and
C
2
) and small distances (
x
1
-
x
2
). Figure 3.2 provides a visual repre-
sentation of this equation. The diffusion coefficient is a function of the
fluid, size of the diffusing molecule (larger molecules diffuse more slowly),
temperature, obstruction of diffusion by pore structure in sediments or
other materials, and the rate of mixing of water. Fick's law can be applied
to many biological problems related to diffusion, such as calculating the
rate of spread of pollutants (Example 3.1).
Thermal movement of molecules
(Brownian motion)
causes them to
mix randomly throughout the fluid and leads to
molecular diffusion
. The
importance of Brownian motion is related inversely to spatial scale. For ex-
ample, many molecules randomly collide with a human swimmer from all
sides, but because of the size of the human body relative to water mole-
cules, the force is the same from all directions. A bacterium is small enough
that more molecules probably will collide with it from one side than an-
other at any particular time, and thus it jiggles under a microscope. The
smaller the particle or ion, the more it is influenced by collisions with wa-
ter molecules. Molecular diffusion is more rapid for smaller molecules (i.e.,
C
1
C
2
J
x
1
- x
2
FIGURE 3.2
Schematic illustrating diffusion between two flat surfaces at different concen-
trations (
C
1
and
C
2
). The rate of diffusion (
J
) is described by Fick's law (see text). The con-
centration at
C
1
is greater than at
C
2
, so the net diffusion is toward
C
2
. Diffusion is less rapid
as distance (
x
1
x
2
) between the two planes increases and as the difference between the con-
centrations at the two planes (
C
1
C
2
) decreases.
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