Chemistry Reference
In-Depth Information
thermal explosions of Tetryl and DINA (see Sect. 10.5), both flameless flashes and
flashes with glow were observed. In the case of insignificant evaporation at rela-
tively low temperatures
T
0
, the transition from low degrees of warm-up (
R
T
0
/
E
)
∼
to high ones (
T
st
=
T
st
-
T
0
) is determined by the condensed-phase reaction. The
critical conditions for this process can be obtained by using standard expressions
from thermal explosion theory that does not take the explosive volatility into ac-
count. It is interesting that, in the case of a flameless process taking place in the
region above the explosion initiation limit, the stationary warm-up,
Δ
Δ
T
st
, decreases
with increasing
T
0
(at
T
changes sign.
Upon increasing
T
0
still further, the process occurs with underheating, and the tem-
perature of the liquid approaches the theoretical boiling point.
α
S
/
V
= const). As soon as
T
0
reaches
T
ad
,
Δ
10.4 Estimation of the Critical Conditions for Thermal
Explosion of a Volatile Explosive
Let us consider the critical conditions for the thermal explosion of a liquid volatile
explosive. If at
T
0
the pressure of the original liquid vapor is significantly lower than
the ambient pressure:
P
sv
(
T
0
)
<<
P
∞
,
(10.12)
T
∗
=
T
∗
-
T
0
) can be estimated by
using a simplified expression for the heat evolution rate,
Qk
0
exp
then the explosion limit maximum warm-up (
Δ
1
E
R
T
L
Q
b
a
P
0
exp(
−
L
/
R
T
)
−
−
P
∞
−
P
0
exp(
−
L
/
R
T
)
Qk
0
exp
1
.
E
R
T
L
Q
b
a
P
0
exp(
L
/
R
T
)
P
∞
−
≈
−
−
After performing the corresponding substitution in Eq. (10.9), differentiating both
parts, and solving the set of two equations using the Semenov approach (equality of
the heat emission and heat evolution functions and their derivatives at the contact
point for the heat evolution and heat emission curves), one obtains
1
−
1
T
0
=
R
T
∗
2
E
L
2
QE
L
/
R
T
∗
)
P
∞
b
a
P
0
exp(
−
T
∗
=
T
∗
−
Δ
−
.
After transforming this equation using the Frank-Kamenetsky approach (expansion
of exp(
L
/
RT
) around
T
=
T
0
+
RT
0
/
E
), one obtains
−
1 +
L
/
R
T
b
)
exp
.
T
∗
=
R
T
0
E
L
2
b
exp(
L
/
E
)
QEa
exp(
L
R
T
0
Δ
−
(10.13)
−
Taking into account condition (10.12), one can obtain an expression for the critical
condition from Eq. (10.13):
