Theory of Decomposition Macrokinetics and Thermal Explosion of Volatile Explosives - Fast Reactions in Energetic Materials - page 149

F ( T ∗ )
F ( T ∗ ) ,

T 0cr = T ∗ −

α

S
V

= F ( T ∗ ) .

cr

Due to the inflection of the F ( T ) curve at T lim determined by the equation F ( T )= 0,
the system can attain the critical conditions for thermal explosion only if

< α

cr

α S

V

S
V

,

lim

α cr

S
V

= F ( T lim ) .

lim

> α V cr

At α V

lim only a single value of the liquid temperature corresponds to any
value of T 0 . The same restriction is applied to the ambient temperature. The critical
transition is feasible only if

F ( T lim )

T 0 < T cr

0 lim and T cr 0 lim = T lim −

F ( T lim ) .

This peculiar dependence of the stationary warm-up on the process parameters is
qualitatively illustrated by the diagram for a model liquid presented in Fig. 10.3.
The following inequalities correspond to curves 1-7:
0 = α

< α < α < α

S
V

S
V

S
V

S
V

1 2 3 4

= α

cr

< α < α < α

S
V

S
V

S
V

S
V

7 → ∞

.

lim 5 6

Fig. 10.3 Plot of the liquid
warm-up against the ambient
temperature at constant ambi-
ent pressure (see explanation
in the text)

R