Chemistry Reference
In-Depth Information
Since the rate of linear steady propagation of the reaction front always equals the
product of the reaction layer thickness and the rate constant of the volumetric reac-
tion at the characteristic temperature, one obtains expression (1.40).
Noting that, by definition
U
=
d
l
/
d
t
for linear pyrolysis under quasi-steady
conditions, one can integrate relationship (1.40) and obtain the expression for the
time dependence of the sample thickness:
l
=
l
0
exp
−
,
t
t
0
−
(1.42)
where
l
0
is the initial thickness of the sample and
t
0
=
E
(
T
S
−
T
∞
)
R
T
S
k
0
E
R
T
S
.
exp
(1.43)
Thus, despite the complicated nature of the experimental technique, the use of the
linear pyrolysis-based experimental approach in combination with the analysis of
the results using Eqs. (1.40)-(1.42) allows one to obtain data on the kinetics of the
volumetric reaction without the need for data on the thermophysical characteris-
tics of the material in the high-temperature region. These data are almost always
unavailable. In addition, the limiting stage of the decomposition reaction (if the pro-
cess occurs in the volume or on the surface) can be directly identified. In the latter
case (evaporation, dissociative sublimation, etc.), the rate of linear pyrolysis does
not decrease with decreasing sample thickness.
1.6 Effect of Conversion Degree on the Linear Pyrolysis Rate
In order to take burn-out during linear pyrolysis into account, one may write
exp
d
2
T
dx
2
+
M
δ
dT
dx
±
Qk
0
ϕ
(
η
)
E
R
T
Bi
δ
−
−
2
(
T
−
T
∞
)=0
,
(1.44)
ac
) exp
= 0
U
d
dx
+
k
0
ϕ
E
R
T
(
η
−
(1.45)
with the boundary conditions (1.3)-(1.4) and
η
|
x
=0
= 1
−
η
g
,
(1.46)
η
|
x
→
∞
= 0
.
(1.47)
For the linear pyrolysis of a “finite” length sample, the boundary conditions for the
cold end (
x
=
l
)are
T
|
x
=
l
=
T
∞
,
η
|
x
=
l
= 0
.
