Sorption Kinetics - Transport and Fate of Chemicals in Soils: Principles and Applications - page 42

where k f to k b are the associated rate coefficients ( h ) and S the total amount
of solute retained by the soil matrix. As a result, the rate of solute retention
may be expressed as:

ρ ∂
∂

S
t

= k θφ −ρ C S

k

f b

or

(2.6)

ρ ∂

S
t ∂ =θ−−ρ

( SSC ) S

k k

f T b

where S T (μg/g soil) represents the total amount of total sorption sites.
Figure 2.6 shows the results of second-order simulations of Cu isotherm at
different times during adsorption.
It is obvious that, as the sites become occupied by the retained solute, the
number of vacant sites approaches zero (ϕ → 0) and the amount of solute
retained by the soil approaches that of the total capacity of sites, that is, S → .
Vacant specific sites are not strictly vacant. They are assumed occupied by
hydrogen, hydroxyl, or other specifically sorbed species. As t → ∞ ; that is,
when the reaction achieves local equilibrium, the rate of retention becomes:

S
C =

θ
ρ

k
k

kCkS 0, θφ −ρ= or

f

= ω

(2.7)

f b

φ

b

400

Sorption Isotherms
McLaren soil

350

300

250

2 h
4
12

200

150

100

196

50

0

0 20 40 60 80

Cu Concentration (mg/L)

FIGURE 2.6
Adsorption isotherms for copper on McLaren soil at different retention times.