Competitive Sorption and Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 194

TABLE 7.1
Competitive Equilibrium and Kinetic Retention Models

Model Formulation

n i − 1

l

∑

SKC = α C

Sheindorf-Rebhun-Sheintuch (SRS) equilibium model

i i i i j , j

j = 1

n − 1

i

l

∂ () S

t

θ
ρ

∑

1 i

= kC α C − k () S

Sheindorf-Rebhun-Sheintuch (SRS) kinetic model

1, i i ij , j 2, i 1 i

∂

j = 1

S KC

KC

i i i

=

Competitive Langmuir equilibium model

S 1 +∑

max j j j

l

∂

∂ =λ θ

S
t

∑

i

() CS − S

−λ

() S

Competitive Langmuir kinetic model

fi i max j bi i

ρ

i = 1

()

ν j

ν j

*

( ζ

ζ

)

a
a

i

j

v

=

Vanselow ion exchange K

ij

()

ν i

( )

ν i

*

j

j

vi

ν j

ν i

= (

γ
γ

)

s
C

s
C

j i j

Gaines and Thomas ion exchange

G

K ij

( )

ν j

i j

i

n

ν
ν

j ν

ν

j

()
()

()
()

s
s

c
c

i i

Rothmund-Kornfeld ion exchange =

R

K

ij

i i

j j

∂
∂

S
t

i − BS i

= ae

Elovich ion exchange

i =κ β

Factional power model St

S
S

4 Dt

r

Dt
r

i
eq

m m

= −

Parabolic diffusion model

2 2

() π

i

7.2 Equilibrium Ion Exchange
One of the earliest concepts of competition among the various ions in the
soil solution and those retained on matrix surfaces is that of ion exchange.
Here one assumes that a positive (or negative) ion in solution can exchange
with another ion retained on charged surfaces (Sparks, 2003). Ion exchange is
commonly considered an instantaneous process representing (nonspecific)
sorption mechanisms and as a fully reversible reaction between heavy metal
ions in the soil solution and those retained on charged surfaces of the soil