Chemistry Reference
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is plotted over time for
k
1
=
10
3
and
k
1
=
0
(no binding case). The time interval is
chosen to be
because during this time the concentration front passes the
characteristic depth. The graph shows that the average gain lines are slightly inclined
downwards and do not intersect for different
k
1
. We see clear difference between the
two cases. Therefore, the graph showing the average gain function at particular time
will be representative for comparison of the effect of different values of
k
1
. The aver-
age gain at any time point is defined as the mean value between the two apexes of the
gain function adjacent to this point.
On Figure 5 the average gain of free, bound, and total solute mass uptake by the
gel at time
[
]
′
t
=
0,0.2
1
the graphs for free and total
solute coincides because the concentration of bounded solute is orders of magnitude
less than free solute concentration. Note, that different
k
1
can represent different reac-
tion rate or different frequency. In the last case the time variable
′
0.2
is plotted as a function of
k
1
. For
k
1
≤
t
=
t
will correspond
to different real time. This must be taken into account when comparing the effect of
frequency on mass transport at particular time moment. Also it is important to empha-
size that for non binding case (
k
1
=
′
0) the gain will be close to the gain for total solute
uptake when
k
1
0, which means that bene¿ cial effect of binding is seen for free
solute or for bound solute alone. The same tendency is seen when other parameters
(
R
g
,
>
N
,
ε
0
) are varied.
′
FIGURE 3
Percent gain of free, bound, and total solute mass uptake by the gel relative to the
free diffusion case as a function of dimensionless time (
R
g
1
,
k
k
1
= 10
−3
,
k
1
= 10
3
).
100
,
ε
0
= 0.05
,
=
N
′
=
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