Biomedical Engineering Reference
In-Depth Information
where r s , s /c 1 is -1 is the rate of s-oligomer decomposing into all the lesser oligomers (and
monomers). Thus,
r s;s /c 1is1 ¼ðs
1
Þk H C s
(9.181)
2 X
N
X
N
k E
r s ¼
k H C n þ
n q n ðs
1
Þk H C s
(9.182)
n¼s
n¼sþ
1
for s
1. Comparing with the hydrolysis reaction alone, Eqn (6.85), there is one additional
term appeared in Eqn (9.182) due to the production of s-oligomer from the solid material.
Cleavage of xylo-oligomers from the woody biomass when the condensation reactions are
neglected is obtained as:
>
P
N
r qm ¼r qm;qm /c q0qiqm1 þ
r qm;qn / qm
n¼mþ
1
(9.183)
P
N
k E
n q n
¼k E q m þ
n¼mþ
1
The reaction is near the zeroth order with respect to xylan content initially and near the first
order near complete dissolution of xylan from woody biomass.
For all the accessible oligomers on the solid surface, the rate of extract can also be
expressed in terms of the total number of monomeric units extractable as
X
mr qm ¼k E X
X
m X
N
N
N
N
k E
n q n
r E ¼
mq m þ
(9.184)
1
1
1
n¼mþ
1
where r E is the rate of formation of oligomers on the solid phase in terms of the number of
monomer units. Eqn (9.184) can be rewritten as
r E ¼k E X
N
m þ
1
q m
(9.185)
2
1
Let,
X
N
P S ¼
mq m
(9.186)
1
be the concentration of total monomer units in extractable oligomers and the degree of poly-
merization for the extractable oligomers in the solid phase be given by
P 1 m q m
P m¼1 q m
DP
¼
(9.187)
then, the rate of extraction can be written as
1
P S
k E
2
1
DP
r E ¼
þ
(9.188)
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