Using Experimental Research for an Analysis of Sorption Term in Groundwater Contaminant Transport Equation - Experimental Methods in Hydraulic Research - page 135

desorption rate constant); and N adsorption constant characterizing geometric

shape of adsorption isotherm (in the local equilibrium conditions).
However, ( 2 ) describes a fully reversible adsorption mechanism, in which
the forward reaction is nonlinear and the backward desorption reaction is linear
(Seidel-Morgenstern 2004 ; Chiang 2005 ).
For the linear kinetic sorption model, when the value of N is unity, ( 2 ) reduces to
the reversible linear first-order kinetic sorption process described by the following
equation that is frequently used in practice:

¼

@ S m

r

t ¼

k 1 C k 2 S (3)

@

Equation ( 3 ) assumes that the rate of solute sorption by the soil matrix is related
to the difference between what can be adsorbed at some concentration and what has
already been adsorbed.
In the case of a local equilibrium-controlled state ( 0), ( 2 ) can be written

in relation to the nonlinear sorption kinetics in the form (Aniszewski 2009 ):

@ S =@ t ¼

k 1
k 2

m
r

C N C N S ¼ ¼ K 2 (4)

k 1
k 2

m

where K 2 is the constant nonlinear adsorption parameter.

Equation ( 4 ) is the Freundlich nonlinear isotherm, well known in literature and
often used in practice; it has been presented in relation to static equilibrium-
controlled sorption model for relatively large concentrations of moving contami-
nants in ground media (Seidel-Morgenstern 2004 ; Chiang 2005 ; Aniszewski 2009 ).
In turn, for the linear kinetic sorption model in the local equilibrium-controlled
state (

r ¼

@ S =@ t ¼ 0), ( 2 ) can be written in the form (Seidel-Morgenstern 2004 ; Chiang

2005 ):

k 1
k 2

m
r

S ¼ C ¼ k 1 C (5)

k 1
k 2

m

where K 1 is the constant linear adsorption parameter.

Equation ( 5 ) represents the Henry linear isotherm, well known in the literature and
often put into practice; it has also been presented in relation to static equilibrium-
controlled sorption model for relatively low concentrations of moving contaminants
in ground media (Seidel-Morgenstern 2004 ;Chiang 2005 ; Aniszewski 2009 ).
At the same time, it should be noted that for the great sorption rates this process
is an equilibrium-controlled one, and the concentration change of dissolved sub-
stance in liquid phase (

r ¼

t ) is directly proportional to the concentration change
of dissolved substance in solid phase (

@ C =@

@ S =@ t ) in the local equilibrium conditions

(Seidel-Morgenstern 2004 ).