Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 63

3

Transport

To describe the general equation dealing with the transport of solutes
present in the soil solution, a number of definitions must be given and
the continuity or mass balance equation for the solute must be derived.
One can assume that a heavy metal, or generally a solute species, may be
present in a dissolved form in the soil water, that is, the solution phase.
The amount of a dissolved species is expressed in terms of concentration
(mass per unit volume) in the solution phase. A solute species may also
be retained or sorbed by the soil matrix or be present in a precipitate or
coprecipitate form.
For a given bulk volume within the soil, the total amount of solute χ
(Μg cm -3 ) for a species i may be expressed as

χ Θρ =

C + S (3.1) i i

i

where S is the amount of solute retained by the soil (Μg per gram soil), C is
the solute concentration in solution (Μg cm -3 or mg L -1 ), Θ is the volumetric
soil water content (cm 3 cm -3 ), and ρ is the soil bulk density (g cm -3 ).

3.1 Continuity Equation
The continuity or mass balance equation for a solute species is a general rep-
resentation of solute transport in the soil system and accounts for changes
in solute concentration with time at any location in the soil. To derive the
continuity equation, let us examine the transport of a solute species through
a small volume element of a soil. For simplicity, we consider the volume ele-
ment to be a small rectangular parallepiped with dimensions Δ x , Δ y , and
Δ z as shown in Figure 3.1. Assume that J x is the flux or rate of movement of
solute species i in the x direction, that is, the mass of solute entering the face
ABCD of the volume element per unit area and time. Therefore, the solute
inflow rate, or total solute mass entering into ABCD per unit time, is

Solute inflowrate=J yz

(3.2)

x

63