Geoscience Reference
In-Depth Information
Hence, we can write the relationship:
@
C
@
t
¼
m
@
S
(6)
@
t
Taking into consideration (
6
), (
2
) can be presented in the form:
m
r
@
C
@
m
r
C
N
t
¼
k
1
k
2
S
(7)
and after transformation and using the auxiliary expression (
a
0
¼ r=
m
), in the
form:
@
C
@
C
N
t
¼
k
1
þ
k
2
a
0
S
(8)
One can say that the sorption kinetics as a first-order kinetically controlled process,
being described by the reversible nonlinear (
2
) or linear (
3
) equations, defines the
mechanismof gradually reaching the equilibrium-controlled state. In the final phase of
this mechanism, the kinetic process changes into a static one (instantaneous equilib-
rium sorption models), taking advantage of the reversible Freundlich nonlinear or
the Henry linear isotherms represented by (
4
)or(
5
), respectively, which are most
often used in practice and are simple in mathematical description (Letcher
2004
;
Seidel-Morgenstern
2004
; Aniszewski
2009
).
The further part of this chapter addresses an attempt of practical determining of
the rate constants of adsorption (
k
1
) and desorption (
k
2
), based on the nonlinear (
2
)
and the linear (
3
) model of the sorption kinetics and using at the same time the static
experimental research with immobile groundwater carried out by the author of this
chapter. Generally, during the author's laboratory research (performed in the
special closed vessels), the constant volumes (
V
) of the examined contaminant
solutes (with the known initial concentrations
C
0
) were inundated and mixed with
the ground samples with known, but varying masses
m
0
. After appropriate mixing
time, in the local equilibrium conditions, the final stabilized concentrations
C
of
the examined solutes in the particular samples were reached (in aqueous phase).
Using the measured differences between these initial (
C
0
) and final stabilized (
C
)
concentrations as well as the constant volumes of solutes (
V
), the masses of the
examined solutes (
S
) adsorbed on the ground sample grains were calculated based
on (9) as ratios to these ground sample masses (
m
0
) (in solid phase).
So, using in these static experimental research the final equilibrium state, the
dimensionless mass balance of the moving contaminants (as adsorbate) can be
written as:
V
ð
C
0
C
Þ
S
¼
(9)
m
0
