"flash and sound" mixture is an example of this type of danger-the composition will depend on the nature of the oxidizer ous composition.
and fuel, as well as on a variety of other factors. "Rate"
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Chemistry o f Pyrotechnics
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113
can be expressed in two ways - mass reacting per unit time or The fuel also plays an important role in determining the rate length burned per unit time. The loading pressure used, and of combustion. Metal fuels, with their highly exothermic heats the resulting density of the composition, will determine the re-of combustion, tend to increase the rate of burning. The pres-lationship between these two rate expressions.
ence of low-melting, volatile fuels (sulfur, for example) tends to Reaction velocity is primarily determined by the selection of retard the burning rate. Heat is used up in melting and vapor-the oxidizer and fuel. The rate-determining step in many high-izing these materials rather than going into raising the tempera-energy reactions appears to be an endothermic process, with de-ture of the adjacent layers of unreacted mixture and thereby ac-composition of the oxidizer frequently the key step. The higher celerating the reaction rate. The presence of moisture can greatly the decomposition temperature of the oxidizer, and the more en-retard the burning rate by absorbing substantial quantities of dothermic the decomposition, the slower the burning rate will be heat through vaporization. The heat of vaporization of water -
(with all other factors held constant).
540 calories/gram at 100°C - is one of the largest values found Shimizu reports the following reactivity sequence for the most-for liquids. Benzene, C 6H 6 , as an example, has a heat of vapor-common of the fireworks oxidizers [8]
ization of only 94 calories/gram at its boiling point, 80°C.
KC1O
The higher the ignition temperature of a fuel, the slower is 3 > NH,,C1O,, > KC1O q > KNO 3
the burning rate of compositions containing the material, again Shimizu notes that potassium nitrate is not slow when used in with all other factors equal. Shidlovskiy notes that aluminum black powder and metal-containing compositions in which a "hot"
compositions are slower burning than corresponding magnesium fuel is present. Sodium nitrate is quite similar to potassium ni-mixtures due to this phenomenon [1] .
trate in reactivity.
The transfer of heat from the burning zone to the adjacent Shidlovskiy has gathered data on burning rates for some of layers of unreacted composition is also critical to the combustion the common oxidizers [1]. Table 5.5 contains data for oxidizers process. Metal fuels aid greatly here, due to their high thermal with a variety of fuels. Again, note the high reactivity of potas-conductivity. For binary mixtures of oxidizer and fuel, combus-sium chlorate.
tion rate increases as the metal percentage increases, well past the stoichiometric point. For magnesium mixtures, this effect is observed up to 60-70% magnesium by weight. This behavior reTABLE 5.5 Burning Rates of Stoichiometric Binary sults from the increasing thermal conductivity of the composition Mixturesa
with increasing metal percentage, and from the reaction of excess magnesium, vaporized by the heat evolved from the pyrotechnic Linear burning rate, mm/secb
process, with oxygen from the atmosphere [1].
Stoichiometric mixtures or those with an excess of a metallic Oxidizer
fuel are typically the fastest burners. Sometimes it is difficult Fuel
KC1O 3
KNO 3
NaNO 3
Ba(NO3)2
to predict exactly what the stoichiometric reaction(s) will be at the high reaction temperatures encountered with these systems, Sulfur
2
Xc
X
so a trial-and-error approach is often advisable. A series of mixtures should be prepared - varying the fuel percentage Charcoal
6
2
1
0.3
while keeping everything else constant. The percentage yield-Sugar
2.5
1
0.5
0.1
ing the maximum burning rate is then experimentally determined.
Variation in loading density, achieved by varying the pressure Shellac
1
1
1
0.8
used to consolidate the composition in a tube, can also affect the burning rate. A "typical" high-energy reaction evolves a sub-aReference 1.
stantial quantity of gaseous products and a significant portion of bCompositions were pressed in cardboard tubes of the actual combustion reaction occurs in the vapor phase. For 16 mm diameter.
these reactions, the combustion rate (measured in grams con-cX indicates that the mixture did not burn.
sumed/second) will increase as the loading density decreases.
A loose powder should burn the fastest, perhaps reaching an
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Chemistry of Pyrotechnics
Ignition and Propagation
115
explosive velocity, while a highly-consolidated mixture, loaded TABLE 5.6 Predicted Burning Rates for Black Powder under considerable pressure, will burn much more slowly. The at Various External Pressures
combustion front in such mixtures is carried along by hot gaseous products.
The more porous the composition is, the faster the re-External pres-
External pres-
Linear burning
action should be. The "ideal" fast composition is one that has sure, atm
sure, p.s.i.
rate, cm/sec
been granulated to achieve a high degree of homogeneity within each particle but yet consists of small grains of powder with high 1
14.7
1.21
surface area. Burning will accelerate rapidly through a loose collection of such particles.
2
29.4
1.43
The exception to this "loading pressure rule" is the category 5
73.5
of "gasless" compositions.
1.78
Here, burning is believed to propa-
gate through the mixture without the involvement of the vapor 10
147
2.10
phase, and an increase in loading pressure should lead to an in-15
221
2.32
crease in burning rate, due to more efficient heat transfer via tightly compacted solid and liquid particles.
Thermal conductiv-
20
294
2.48
ity is quite important in the burning rate of these compositions.
30
441
2.71
Table 4.6 illustrates the effect of loading pressure for the "gasless" barium chromate/boron system.
Note:
The Shidlovskiy equation is valid for the pressure range 2-30 atmospheres.
Effect of External Pressure
The gas pressure (if any) generated by the combustion products, combined with the prevailing atmospheric pressure, will also affect the burning rate. The general rule here predicts that an increase in burning rate will occur as the external pressure increases.
This factor can be especially important when oxygen For the ferric oxide/aluminum (Fe 20 3 /Al), manganese dioxide/
is a significant component of the gaseous phase. The magnitude aluminum (MnO 2 /Al), and chromic oxide/magnesium (Cr 2O 3 / Mg) of the external pressure effect indicates the extent to which the systems, slight gas phase involvement is indicated by the 3-4
vapor phase is involved in the combustion reaction.
fold rate increase observed as the external pressure is raised The effect of external pressure on the burning rate of black from 1 to 150 atm. The chromic oxide /aluminum system, how-powder has been quantitatively studied. Shidlovskiy reports ever, reportedly burns at exactly the same rate - 2.4 millime-the experimental empirical equation for the combustion of black ters /sec - at 1 and 100 atm ; suggesting that it is a true "gas-powder to be
less" system [1].
P(0.24)
Data for the burning rate of a delay system as a function of burning rate = 1.21