Biomedical Engineering Reference
In-Depth Information
The adsorption occurs on the sites where the second last layer is covered ( q N 1 ) but not occu-
pied by the last layer, i.e. ( q N 1 q N ), whereas the desorption occurs only from the covered
last layer ( q N ). Eqn (9.50) can be reduced to
bðq N1 q N Þ¼q N
(9.57)
where
k N
k N p A ¼ . ¼
k i
k i p A ¼ b
(9.58)
where i
1. By imposing Eqn (9.58) , we have assumed that the interactions among
adsorbate e adsorbent e adsorbate are identical if the adsorbate is not adsorbed on the first
layer.
For the adsorption in the i -th layer (in the middle), the available sites for adsorption is the
covered sites by the lower layer ( q i 1 ) but not covered on the current layer, i.e. q i 1 q i . The
desorption can only occur on the sites that are covered by the current layer but not occupied
above. The coverage of the site on top of the current adsorbate molecule would be prevented
it from leaving. Therefore,
0
s
¼ r ad;i ¼ k i ðq i1 q i Þp A k i ðq i q iþ1 Þ
(9.59)
Since the adsorption and desorption are occurring on top of the adsorbed molecules (like
condensation), we have assumed that the adsorption and desorption rate constants are iden-
tical from layer to layer by imposing Eqn (9.58) .Eqn (9.53) leads to
q i q iþ1 ¼ bðq i1 q i Þ
(9.60)
and adsorption on the first layer or directly on the adsorbent surface,
0
¼ r ad;1 ¼ k ad;1 ð
1
q 1 Þp A k des;1 ðq 1 q 2 Þ
(9.61)
which is different from the rest of the layers on top of the first layer. The adsorption is on the
adsorbent surface, where the interaction between the adsorption site on the adsorbent and
the adsorbate molecule is different from the interaction between adsorbed molecule and
the adsorbate molecule. Still, the adsorption can only occur on the free sites (not occupied
by the adsorbate molecules), whereas the desorption can only occur to the adsorbed mole-
cules which are not covered from the top. Eqn (9.61) can be reduced to
cbð
1
q 1 Þ¼q 1 q 2
(9.62)
where
k ad;1
k des;1
k i
k i
c ¼
(9.63)
The total number of molecules adsorbed on the adsorbent surface is
n As;N ¼ n s1 X
N
1 q i
(9.64)
Search WWH ::




Custom Search