Theory of the Linear Pyrolysis of Condensed Materials - Fast Reactions in Energetic Materials - page 17

Table 1.1 Analytical expressions for the rate of linear pyrolysis in the limiting modes
Mode of linear pyrolysis

For zero-order reaction For first-order reaction

ak 0 R T S exp ak 0 R T S exp

⎧
⎨
⎩

⎫
⎬
⎭

⎧
⎨
⎩

⎫
⎬
⎭

1 / 2 1 / 2

“Fast” linear pyrolysis
4Bi
M 2

E
R T S

E
R T S

<< 1

− −

E ( T S − T ∞ )(1 − η g ) 2 E ( T ∞ − T S ) ln η g )

U = (1.50) U = (1.51)

Q
2 c (1

Q
2 c (1

− η g ) ∓ η g ± − η g + ln

“Slow” linear pyrolysis for:
a semi-infinite sample

k 0 R T S exp( k 0 R T S exp(

U = δ

− E / R T S )

U = δ

− E / R T S )

g ) √ Bi

(1.52)

g √ Bi

(1.53)

4Bi
M 2

>> 1

E ( T S − T ∞ )(1 − η E ( T S − T ∞ ) ln η

U = lk 0 R T S exp( − E / R T S )
E ( T S −

U = lk 0 R T S exp( − E / R T S )
E ( T ∞ −

a sample of a “finite” length
l << U
a

(1.54) (1.55)

T ∞ )(1 − η g ) T S ) ln η g