Chemistry Reference
In-Depth Information
Here
g
is the part of the unreacted compound that leaves the pyrolysis surface
due to the physical process accompanying decomposition (for example disper-
sion, which includes processes such as dissociative sublimation and evaporation
that result in the partial loss of unreacted compound from the sample surface, or
sublimation).
The set of Eqs. (1.44)-(1.47) can be solved using methods similar to those ap-
plied to analyze linear pyrolysis in the case of zero-order reactions (Sects. 1.1-1.5)
under the standard assumptions made for the analysis of condensed system burning
accompanied by dispersion or sublimation [14, 15, 16, 17, 18].
After a number of mathematical manipulations (leading to bulky expressions
omitted for the sake of brevity), one can write final relationships for M correspond-
ing to two processes:
linear pyrolysis in the case of the zero-order reaction [
η
ϕ
(
η
)=1] accompanied
by dispersion,
⎧
⎨
⎫
⎬
1
/
2
2
R
T
S
k
0
exp(
δ
−
E
/
R
T
S
)
M =
1 +
1 + 4Bi
/
M
2
2
(1.48)
⎡
−
η
g
)
2
⎤
⎩
⎭
Q
2
c
(1
⎣
(
T
S
−
⎦
aE
T
∞
)
(1
−
η
g
)
∓
and linear pyrolysis in the case of the zero-order reaction [
ϕ
(
η
)=1
−
η
],
⎧
⎨
⎫
⎬
1
/
2
2
R
T
S
k
0
exp(
δ
−
E
/
R
T
S
)
M =
T
S
)
1 +
1 + 4Bi
/
M
2
2
.
(1.49)
⎡
g
)
2
⎤
⎩
⎭
Q
2
c
(1
⎣
(
T
∞
−
⎦
aE
ln
η
±
−
η
g
+ ln
η
g
Expressions for the linear pyrolysis rates for the two modes that differ in terms of
the conditions of outward heat exchange can easily be obtained from relationships
(1.48) and (1.49) (Table 1.1).
Joint analysis of the expressions for the linear pyrolysis rates (Table 1.1) allows
one to evaluate the dispersion contribution into an overall rate of linear decomposi-
tion for various volumetric reactions.
At
1 Eqs. (50), (51) as well as (52), (53) and (54), (55) are identical; in
other words, at significant dispersion (or at a very low burn-out in the surface layer)
the linear pyrolysis rate does not depend on the reaction order. At insignificant dis-
persion (
η
g
≈
η
g
<<
1) the effect of the unreacted compound loss on the linear pyrolysis
rate can be neglected for a zero-order reaction. In the case of first-order reaction (in
general at
n
= 0, where
n
is the reaction order), the burn-out markedly influences the
linear pyrolysis rate. Plots of the dimensionless rate of linear pyrolysis for zero-order
