Page 217 - Soil and water contamination, 2nd edition

204 Soil and Water Contamination

Then, calculate the chloride loads of the effluent and the stream just upstream from the
effluent outfall:
3 -1
3
(CQ) = 180 g m × 0.040 m s = 7.2 g s -1
effluent
-3
3 -1
(CQ) = 20 g m × 0.36 m s = 7.2 g s -1
stream
-1
The total chloride load is 7.2 + 7.2 = 14.4 g s ; the total discharge is 0.040 + 0.36 =
3 -1
0.40 m s . The chloride concentration downstream from the outfall is
(CQ) (CQ) 2 . 7 2 . 7 14 4 .
C downstream effluent stream 36 mg l -1
Q Q . 0 04 . 0 36 4 . 0
effluent stream
11.3 DIFFUSION AND DISPERSION
11.3.1 Molecular diffusion

Molecules move randomly through water due to so-called Brownian motion. Even if water
seems to be entirely quiescent, chemicals move from regions of high concentrations to
regions of low concentrations. This process results in increase of entropy and is known as
molecular diffusion . In nature, molecular diffusion occurs primarily through thin, laminar
boundary layers, at, for instance, air–water or sediment –water interfaces or in stagnant
pore water. In the mid-19th century, Fick determined that the mass transfer by molecular
diffusion was linearly related to the cross-sectional area over which the transfer takes place
and the concentration gradient. Accordingly, Fick’s first law describes the flux density of mass
transport as follows:
dC
J D (11.18)
dx
-1
-2
-1
2
where J = the flux density [M L T ], D = molecular diffusion coefficient [L T ], C = the
-3
chemical concentration [M L ], and x = the distance over which the change in concentration
is considered. The negative sign reflects that the direction of the mass transfer is in the
same direction as the concentration gradient, i.e. opposite to the direction of positive
change in concentration. The mass transfer continues until equilibrium is reached, i.e. the
concentration gradient is zero everywhere.
The diffusion coefficient D depends on the chemical and thermodynamic properties of
the substance under consideration and the water temperature . Molecular diffusion increases
in magnitude with increasing temperatures and with decreasing size of the molecules. At
environmental temperatures, the molecular diffusion coefficients of most chemicals are in the
-1
-9
2
order of 10 m s , indicating a very slow transport process. Except for transport through
stagnant boundary layers (e.g. water–air interface) and in quiescent sediment pore waters,
molecular diffusion is generally not a relevant transport process in natural waters.
11.3.2 Turbulent diffusion and mechanical dispersion
Besides moving through molecular diffusion , molecules in surface water also move due to
constantly changing swirls or eddies of different sizes depending on the flow regime. The

random mixing caused by this type of turbulence is called turbulent diffusion or eddy
diffusion. In fact, this mixing process is a differential advective process at the microscale.
The mass transfer due to turbulent diffusion is several orders in magnitude larger than the
mass transfer due to molecular diffusion, and contributes significantly to mixing in rivers and

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