Michael E. Brown,Steven J. Taylor and Michael J. Tribelhorn- Fuel-Oxidant Particle Contact in Binary...

Summary

The number of points of contact between particles of fuel andparticles of oxidant in various pyrotechnic mixtures have been cal-culated on the assumption that the fuel and oxidant powders consist ofuniform spherical particles of different sizes. The calculated numbersof contact points are compared with the experimental burning rates ofthese mixtures. In spite of the severe approximations made, there is aqualitative connection between the calculated numbers of contactpoints, NR, and the measured burning rates, v, of those pyrotechniccompositions which are presumed to burn mainly via solid-solidreactions.

1. Introduction

Hao and Tanaka(1) have shown that in a binary mixture of

solids A and B, if the particles of A and B are assumed to be

uniformly spherical with radii, rA and rB, and molar den-

sities (mol m73), rA and rB, respectively, and if the initial

amounts of A and B (in moles) are mAO and mBO, the total

number of contact points between the two kinds of spheres,

for this speci®ed amount of mixture, is

NR � XY yZ

where

X � �3�1ÿ EA�mAOy�prAr3A��

Y � ��1� Rr � 2y�2f2Rr � �1� Rr�yg2�Z � ��1� y��Rr � y�2f3�Rr � y�2 � �1� y��R2

r � y�g�and EA � the surface porosity(2) of the spherical packing,

Rr � rByrA; Rr � rByrA; Rm � mB0ymA0;

and y � R3r RryRm:

A contact point is de®ned(3,4) as a small connection pipe

with ®nite area and thickness.

Examples of one of the many classes of practically

important binary mixtures of solid particles are the solid

fuel=solid oxidant mixtures extensively used in pyrotechnic

applications. The initial interactions of such mixtures are

generally assumed to be exothermic solid-solid reactions of

the type:

aA�s� � bB�s� ! products

The temperature, however, rises rapidly and melting, vapor-

ization, decompositions of oxidants, and solid-gas reactions

may participate. Experimentally determined burning rates

have been reported for numerous binary fuel=oxidant com-

binations. Table 1 gives a list of a selection of pyrotechnic

systems for which a considerable amount of experimental

information is available and summarizes the main character-

istics of these systems. More details of the fuel and oxidant

samples used are given in Table 2.

Fuel±Oxidant Particle Contact in Binary Pyrotechnic Reactions

Michael E. Brown(*), Steven J. Taylor, and Michael J. Tribelhorn

Chemistry Department, Rhodes University, Grahamstown, 6140 (South Africa)

Kontaktstellen zwischen den Brennstoff- und den Oxidator-Par-tikeln bei binaÈren pyrotechnischen Reaktionen

Die Zahl der BeruÈhrungspunkte zwischen den Brennstoff- und denOxidator-Partikeln in verschiedenartigen pyrotechnischen Mischungenwurde berechnet unter der Annahme, daû die Brennstoff- und Oxi-datorpulver aus einheitlichen kugeligen Teilchen von unterschied-licher KorngroÈûe bestehen. Die berechnete Zahl der Kontakstellenwird verglichen mit den experimentellen Abbrandgeschwindigkeitendieser Mischungen. Trotz der gemachten NaÈherungen gibt es einenqualitativen Zusammenhang zwischen der berechneten Anzahl anKontaktpynkten NR und den gemessenen Abbrandgeschwindigkeiten vsolcher pyrotechnischer Mischungen, die vermutlich bevorzugt uÈberFeststoff-Feststoffreaktionen abbrennen.

Points de contact entre particules combustibles et oxydantes lorsde reÂactions pyrotechniques binaires

On a calculeÂ le nombre de points de contact entre les particulescombustibles et les particules oxydantes dans diffeÂrents meÂlangespyrotechniques en supposant que les poudres combustibles et oxy-dantes sont composeÂes de particules spheÂriques uniformes de granu-lomeÂtrie diffeÂrente. Le nombre de points de contact calculeÂ estcompareÂ aux vitesses de combustion expeÂrimentales de ces meÂlanges.En deÂpit des approximations faites, il y a une correÂlation qualitativeentre le nombre calculeÂ de points de contact NR et les vitesses decombustion mesureÂes v de ces meÂlanges pyrotechniques, dont onsuppose que la combustion est principalement le fait de reÂactionssolides=solides.

(*)To whom correspondence should be addressed,(E-mail: [email protected])

Table 1. Main Characteristics of the Binary Pyrotechnic Systems

SYSTEM Range of Burning Composition Referencecompositions rates at Vmax

(mass % fuel) (mm s71) (% fuel)

Sb=KMnO4 30±70 2±28 60 5±8Fe=BaO2 15±50 6±42 30 23Fe=SrO2 20±55 4±9 25, 45 23Mn=BaO2 15±65 1.7±11.7 20 19±22Mn=SrO2 20±80 4.5±12.3 75 19±22Mo=BaO2 20±70 2.7±10.1 45 19±22Mo=SrO2 40±45 2.2±2.3 40 19±22Si=SnO2 20±55 5±17 40 14,15,17,18Si=Fe2O3 20±40 2.3±4.5 40 14,15,17,18Si=KNO3 30±85 2±35 85 14,16±18Si=Sb2O3 20±50 1.6±8.7 40 14,16±18W=K2Cr2O7 30±85 1.0±25 70 9±12Si=Pb3O4 5±50 40±257 15 13

# WILEY-VCH Verlag GmbH, D-69451 Weinheim, 1998 0721-3115/98/0306±0320 $17.50�:50=0

320 Propellants, Explosives, Pyrotechnics 23, 320±327 (1998)

In this paper, the assumption of uniform spherical parti-

cles of both fuel and oxidant is used to calculate the num-

bers of contact points between fuel and oxidant particles,

NR, in each case based on 1.00 g of the speci®ed composi-

tion, for the systems listed in Table 1. The results of com-

parison of the values of NR obtained and the experimental

burning rates, v, are given for each individual system,

below. (The value of the surface porosity, EA, used was

0.35(1) and was assumed constant for all compositions of all

the systems examined.)

2. Results

Antimony=Potassium Permanganate

The SbyKMnO4 system has been widely used in com-

mercial delays and has been extensively studied(5±8).

Results for three samples with different average fuel particle-

sizes were available. Table 3 lists the calculated contact

points and experimental burning rates for these three sam-

ples.

For a sample of ®xed rSb (e.g., sample (1) in Table 3), the

variations of NR and of v with composition are shown

(suitably scaled) in Figure 1. The similarity of the two

curves and the close coincidence of their maxima suggest a

dependence of v upon the value of NR. Burning fails at a

higher value of NR on the fuel-rich side of the curve.

Both NR and v increase with decreasing rSb as shown in

Figure 2. The maximum value of NR shifts to lower %Sb as

Table 3. Calculated Contact points* (NR) and Experimental Burning Rates (v) for the Sb=KMnO4 System(5±8)

KMnO4 r� 13mmSb sample (1) Sb sample (3) Sb sample (4)

r� 13mm r� 9 mm r� 3mmrfuel=roxidant 1.0 0.69 0.23

%Sb v NR v NR v NR

(mm s71) (�107) (mm s71) (�107) (mm s71) (�107)

10 ± 1.6 ± 3.4 ± 5020 ± 3.1 ± 6.4 ± 8630 2.0 4.3 2.5 8.8 6.5 10535 2.5 4.3 8.440 5.5 5.3 7.0 10.6 12.5 11150 10.0 6.0 11.5 11.6 19.0 10660 11.0 6.3 11.0 11.8 20.5 9470 9.5 6.1 11.0 10.9 22.5 7780 ± 5.2 ± 8.8 ± 5490 ± 3.3 ± 5.3 ± 29

*based on 1.00 g of the speci®ed composition.

Figure 1. Variation of the calculated number of contact points, NR,and the experimental burning rate, v, with composition of theSb=KMnO4 system.

Table 2. Characteristics of the Fuels and the Oxidants

FUELS Meltingpoint (�C)

Sample r(g cm73) r(mm)

Sb 631 (1) 6.68 13(2) 14(3) 9(4) 3.0(5) 2.0

Fe 1535 7.86 2.6Mo 2610 (1) 10.2 32.0

(2) 17.2(3) 6.9

Mn 1244 (1) 7.2 56.5(2) 8.4

Si 1410 (1)&(C) 2.33 2.5(2)&(B) 2.0(3) 1.7(4) 1.3(5)&(A) 1.0

W 3410 19.25 0.40

OXIDANTS Decomposition temperature (�C) r(g cm73) r(mm)

KMnO4 290 exo, 520 endo 2.70 13.0BaO2 500 endo 4.96 5.1SrO2 390 endo, 525 endo 4.56 1.75Fe2O3 melts 1565 5.24 0.30SnO2 melts 1630 6.95 0.45Sb2O3 melts 656, sublimes 5.5 1.2KNO3 melts 334, d 400 exo 2.11 6.7K2Cr2O7 melts 398, d 500 2.68 3.0Pb3O4 d 500 9.1 2.5

Propellants, Explosives, Pyrotechnics 23, 320±327 (1998) Fuel±Oxidant Particle Contact in Binary Pyrotechnic Reactions 321

Figure 2. Variation of the calculated number of contact points, NR,and the experimental burning rate v, with fuel particle-size of the 40%Sb=KMnO4 system.

Table 4. Calculated Contact Points* (NR) and Experimental BurningRates (v) for the W=K2Cr2O7 System(9±12)

W (0.40 mm) K2Cr2O7 (3.0mm)rfuel : roxidant� 1 : 7.5

%W v NR

(mm s71) (�109)

10 ± 7420 ± 14130 1.43 18440 8.0 20250 14.4 20160 19.7 18370 25.2 15280 18.8 11085 15.090 ± 59


Figure 3. Variation of the calculated number of contact points, NR,and the experimental burning rate, v, with composition of theW=K2Cr2O7 system.

Figure 4. Variation of the calculated number of contact points, NR,and the experimental burning rate, v, with composition of theSi=Pb3O4 system. Si radius: (a) 1.0mm; (b) 2.0 mm; and (c) 2.5 mm.

322 M. Brown, S. Taylor, and M. Tribelhorn Propellants, Explosives, Pyrotechnics 23, 320±327 (1998)

rSb decreases (see Table 3), but vmax remains at high pro-

portions of Sb, suggesting incomplete reaction.

Tungsten=Potassium Dichromate

Another extensively studied system is WyK2Cr2O7,

which has been very carefully characterized by Boddington,

Laye and co-workers(9±12) at Leeds University. Values of

NR calculated for one of their systems are compared in

Table 4 with reported burning rates.

The variations of NR and of v with composition are shown

(suitably scaled) in Figure 3. NR values are at a maximum at

40% W, but vmax occurs at about 70% W. The values cal-

culated for NR are approximately 100 times those calculated

for the Sb�4�yKMnO4 system above, although vmax values

for the two systems are similar (25 and 21 mm s71,

respectively).

Silicon=Oxidant Systems

Silicon=lead oxide systems

Silicon=lead oxide systems are of considerable com-

mercial importance for use as short-period delays, i.e. their

burning rates are relatively fast, and they have been

extensively studied. Data published by Al-Kasraji and

Rees(13) have been used to calculate values of NR for the

SiyPb3O4 system. These values are compared with the

reported burning rates in Table 5.

The variations of NR and of v with composition are shown

(suitably scaled) in Figures 4 (a)±(c). NR values for the

smallest Si particles (A) are at a maximum at very low % Si,

increasing to about 10% Si for the larger particles (B) and

(C), but vmax occurs at higher proportions of Si (about 15%

(A) to 30% (B) and (C). Values of vmax and of NR are plotted

against particle size in Figure 5.

Silicon=other oxidants

A detailed study has been reported(14±18) of silicon as the

fuel in binary combination with a variety of oxidants other

than the lead oxides (see above). Values of NR calculated

for each of the systems are compared in Table 6 with the

reported burning rates, and illustrated in Figures 6 (a)±(d).

Figure 5. Variation of the calculated number of contact points, NR,and the maximum experimental burning rate, vmax, with fuel particle-size of the Si=Pb3O4 system.

Table 5. Calculated Contact Points* (NR) and Experimental Burning Rates (v) for the Si=Pb3O4 System(13,25)

Pb3O4 r� 2.5 mmSi sample (A) Si sample (B) Si sample (C)

r� 1.0 mm r� 2.0mm r� 2.5mmrfuel : roxidant 1 : 2.5 1 : 1.3 1 : 1

%Si v NR v NR v NR

(mm s71) (�109) (mm s71) (�109) (mm s71) (�109)

5 108.9 18.3 46.1 4.3 42.4 2.810 222.2 26.6 94.4 7.0 64.6 4.815 257.4 30.2 100.6 8.7 71.5 6.120 249.9 31.7 108.7 9.8 79.9 6.925 138.8 31.8 134.3 10.3 98.7 7.430 139.0 31.1 163.0 10.5 114.8 7.735 127.1 29.9 116.6 10.4 86.6 7.740 114.7 28.4 89.4 10.2 72.3 7.645 94.4 26.6 69.2 9.7 53.2 7.350 59.3 24.6 38.8 9.2 7.055 22.5 8.5 6.560 20.2 7.8 6.065 17.9 7.0 5.470 15.5 6.1 4.775 13.0 5.2 4.080 10.5 4.2 3.385 7.9 3.2 2.590 5.3 2.2 1.795 2.7 1.1 0.9



Table 6. Calculated Contact Points* (NR) and Experimental Burning Rates (v) for Si=oxidant Systems(14±18)

Si sample (3) rfuel� 1.7mmSi=SnO2 Si=Fe2O3 Si=Sb2O3 Si=KNO3

rfuel=roxidant 3.8 5.7 1.4 0.25

%Si v NR v NR v NR v NR

(mm s71) (�1010) (mm s71) (�1010) (mm s71) (�1010) (mm s71) (�1010)

10 ± 11.6 ± 23.5 ± 2.68 ± 0.70415 ± 16.9 ± 34.7 ± 3.69 ± 0.90720 5.25 21.7 2.33 45.5 1.56 4.50 ± 1.0325 7.54 26.0 3.67 55.8 3.25 5.13 ± 1.1030 11.6 29.8 3.82 65.6 6.30 5.58 1.65 1.1335 14.8 33.0 3.60 74.7 8.71 5.8940 17.1 35.6 4.54 83.1 8.52 6.05 2.78 1.1045 15.7 37.6 ± 90.5 8.73 6.0850 12.8 38.8 ± 96.9 7.25 5.98 4.96 0.99555 9.11 39.2 ± 102 ± 5.7860 ± 38.7 ± 105 ± 5.46 8.43 0.84465 ± 37.3 ± 107 ± 5.0670 ± 35.0 ± 106 ± 4.56 10.7 0.66175 ± 31.5 ± 102 ± 3.98 17.1 0.56080 ± 27.0 ± 93.7 ± 3.32 20.6 0.45585 ± 21.4 ± 80.1 ± 2.58 34.5 0.34690 ± 14.8 ± 59.8 ± 1.78 ± 0.234


Figure 6. Variation of the calculated number of contact points, NR, and the experimental burning rate, v, with composition of the: (a) Si=SnO2

system (b) Si=Fe2O3 system (c) Si=Sb2O3 system (d) Si=KNO3 system.


Metal=Alkaline-Earth Metal Peroxide Systems

The contact points and burning rates of systems with

either barium or strontium peroxide as the oxidant and

manganese, molybdenum(19±22), or iron(23) as the fuel are

listed in Table 7, and illustrated in Figures 7 (a)±(e). Note

that the curve for the MoySrO2 system is not illustrated

because only two compositions burned.

3. Conclusions

Dodds(24) has discussed porosity and contact points in

multicomponent random sphere packings. The major

assumption made is that each sphere touches its neighbour.

This allows the simpli®cation that, by joining the centres of

the spheres through their contact points, the packing space is

divided up into tetrahedral subunits. The geometries of these

tetrahedra are completely described by the radii of the four

spheres from which they are formed. For an idealized binary

packing of two different size spheres, A and B, there are ®ve

different tetrahedral subunits: AAAA, AAAB, AABB,

ABBB and BBBB. The model is limited to size ratios of less

than 1 : 6.46, and the packing can be described in terms of

the relative numbers of the different tetrahedra present.

The real pyrotechnic systems, described above, are very

different from this idealized situation. Average radii for fuel

and oxidant particles have been used in the calculations

without allowance for the range of particle-sizes of each.

Particles have also been assumed to be approximately

spherical, which is not very realistic for most of the oxi-

dants considered. It is thus of interest that for many of the

pyrotechnic systems the trends in experimental burning

rates, v, qualitatively parallel the trends in number of

contact points (per 1.00 g of composition). However, as

shown in Table 8 and Figure 8 (where the highest values of

both variables have been omitted to avoid compression of

the data in the neighbourhood of the origin), there is no

direct relationship between burning rate and number of

contact points over all the systems considered. Such a direct

relationship would not be expected since chemical and=or

diffusion factors speci®c to each system must control

reaction through the contact point.

Several features arise on surveying the systems listed in

Table 2. Most of the oxidants, except Fe2O3, Sb2O3 and

SnO2 decompose with some release of O2(g) at tempera-

tures (Table 1) often well below the recorded values of

Tmax. Sb2O3 melts and vaporizes, KNO3 melts and decom-

poses, and K2Cr2O7 melts. The melting points of the fuels

(Table 1) are high (excluding Sb). Substitution of SrO2 for

the apparently chemically similar oxidant, BaO2, does not

affect the burning rate of Mn=peroxide compositions (Table

2) as much as it affects the Mo=peroxide compositions.

Thus variation of the constituents of the binary mixtures

listed can result in burning rates of from 2 to 115 mm s71.

This range is also, the maximum variation observed with

change of composition (20 to 70% fuel) of the ®xed binary

combination (Fe=KMnO4). The Sb=KMnO4 and Si=KNO3

systems also show above average ranges of burning rates

with varying composition.

Variation of the particle-size of the fuel in the

Sb=KMnO4 system from a radius of 14 to 2.0 mm changed

the burning rate (Table 5) from 2 to 8 mm s71 compared to

the range of 2 to 28 mm s71 with change in composition

(Table 2). Decreasing the particle-radius of Mo from 17.2 to

6.9 mm produced faster burning Mo=peroxide mixtures

(Table 5) than were possible by varying the composition of

the mixtures with the larger Mo particles (Table 2).

Table 7. Calculated Contact points* (NR) and Experimental Burning Rates (v) for Metal=Peroxide Systems(19±23)

Mn rfuel� 8.4mm Mo rfuel� 17.2 mm Fe rfuel� 2.6 mm

Mn=BaO2 Mn=SrO2 Mo=BaO2 Mo=SrO2 Fe=BaO2 Fe=SrO2

rfuel=roxidant 1.6 4.8 3.4 9.8 0.51 1.5

%fuel v NR v NR v NR v NR v NR v NR

(mm s71) (�107) (mm s71) (�107) (mm s71) (�107) (mm s71) (�107) (mm s71) �108) (mm s71) (�108)

10 ± 9.76 ± 48.5 ± 2.26 ± 14.0 ± 9.1 ± 26.615 6.4 14.3 ± 72.3 ± 3.37 ± 21.0 8.7 12.8 ± 39.020 11.7 3.61 4.5 95.8 2.8 4.45 ± 27.9 12.9 16.0 3.6 50.725 9.7 3.82 5.1 119 4.1 5.52 ± 34.8 17.1 18.6 6.9 61.630 9.5 3.89 6.6 142 4.5 6.56 ± 41.7 35.7 20.6 7.4 71.735 7.2 3.87 4.8 164 4.9 7.56 ± 48.5 25.5 22.2 5.9 80.740 6.7 3.76 7.5 185 4.7 8.53 2.3 55.3 11.6 23.1 8.3 88.745 6.6 3.60 7.1 206 10.1 9.45 2.2 62.0 6.2 23.6 6.5 95.450 9.2 3.39 6.8 225 6.0 10.3 ± 68.6 6.7 23.6 6.5 10155 7.8 3.15 8.3 244 6.2 11.1 ± 75.2 ± 23.1 6.2 10460 3.3 2.87 10.1 260 6.8 11.8 ± 81.5 ± 22.1 ± 10665 1.8 2.57 9.5 274 5.5 12.3 ± 87.7 ± 20.7 ± 10670 ± 2.24 12.0 285 4.8 12.7 ± 93.5 ± 18.8 ± 10375 ± 1.90 12.3 291 ± 12.9 ± 98.8 ± 16.6 ± 96.980 ± 1.54 7.2 289 ± 12.6 ± 103 ± 14.0 ± 87.585 ± 1.17 ± 276 ± 11.8 ± 106 ± 11.0 ± 74.190 ± 0.79 ± 240 ± 10.0 ± 105 ± 7.7 ± 55.7



Figure 7. Variation of the calculated number of contact points, NR, and the experimental burning rate, v, with composition of the: (a) Fe=BaO2

system (b) Fe=SrO2 system (c) Mn=BaO2 system (d) Mn=SrO2 system (e) Mo=BaO2 system. Note that the curve for the Mo=SrO2 system is notillustrated because only two compositions burned.


In spite of the severe approximations made, there is a

qualitative connection between the calculated numbers of

contact points, NR, and the measured burning rates, v, of

those pyrotechnic compositions which are presumed to burn

mainly via solid-solid reactions. Further aspects of inter-

particle contact need to be examined, including the effects

of particle-size distribution and the role of inert additives in

decreasing fuel=oxidant contact.

4. References

(1) Y-J. Hao and T. Tanaka, `̀ Role of the Contact Points betweenParticles on the Reactivity of Solids'', Can. J. Chem. Eng. 66,761±766 (1988).

(2) N. Ouchiyama and T. Tanaka, `̀ Estimation of the AverageNumber of Contacts between Randomly Mixed Solid Particles'',Ind. Eng. Chem. Fundam. 19, 338±340 (1980).

(3) A. Shimizu and J. Saitou, `̀ Effect of Contact Points betweenParticles on the Reaction Rate in the Fe2O3-V2O5 System'', SolidState Ionics 38, 261±269 (1990).

(4) Y-J. Hao and T. Tanaka, `̀ A New Experimental Method toSpecify the Diffusing Component in a Reacting ParticulatePacking'', Can. J. Chem. Eng. 68, 81±88 (1990).

(5) M. W. Beck and M. E. Brown, `̀ Thermal Analysis of Anti-mony=Potassium Permanganate Pyrotechnic Compositions'',Thermochim. Acta 65, 197±212 (1983).

(6) M. W. Beck and M. E. Brown, `̀ Thermochemistry and ReactionKinetics of the Antimony=Potassium Permanganate PyrotechnicSystems'', Proceedings of the 10th International PyrotechnicSeminar, `̀ Pyrotechnics'', Fraunhofer-Institut, fuÈr Treib- undExplosivstoffe, 1985, paper 14.

(7) M. W. Beck and M. E. Brown, `̀ Burning of Antimony=PotassiumPermanganate Pyrotechnic Compositions in Closed Systems'',Comb. Flame 65, 263±271 (1986).

(8) M. W. Beck and M. E. Brown, `̀ Modi®cation of the BurningRates of Pyrotechnic Compositions'', Comb. Flame 66, 67±75(1986).

(9) T. Boddington, P. G. Laye, J. R. G. Pude, and J. Tipping,`̀ Temperature Pro®le Analysis of Pyrotechnic Systems'', Comb.Flame 47, 235±254 (1982).

(10) T. Boddington, P. G. Laye, J. Tipping, and D. Whalley, `̀ KineticAnalysis of Temperature Pro®les of Pyrotechnic Systems'',Comb. Flame 63, 359±368 (1986).

(11) T. Boddington, A. Cottrell, and P. G. Laye, `̀ A Numerical Modelof Combustion in Gasless Pyrotechnic Systems'', Comb. Flame76, 63±69 (1989).

(12) T. Boddington, A. Cottrell, and P. G. Laye, `̀ CombustionTransfer in Gasless Pyrotechnics'', Comb. Flame 79, 234±241(1990).

(13) J. A. C. Good®eld and G. J. Rees, `̀ Pyrotechnic Reaction of LeadMonoxide and Silicon: Measurement of Reaction Temperature'',Fuel 60, 151±154 (1981).

(14) R. A. Rugunanan and M. E. Brown, `̀ Reactions of PowderedSilicon with some Pyrotechnic Oxidants'', J. Thermal Anal. 37,1193±1211 (1991).

(15) R. A. Rugunanan and M. E. Brown, `̀ Combustion of Binary andTernary Silicon=Oxidant Pyrotechnic Systems. Part I: Fe2O3 andSnO2 as Oxidants'', Comb. Sci. Technol. 95, 61±83 (1994).

(16) R. A. Rugunanan and M. E. Brown, `̀ Combustion of Binary andTernary Silicon=Oxidant Pyrotechnic Systems. Part II: Sb2O3 andKNO3 as Oxidants'', Comb. Sci. Technol. 95, 85±99 (1994).

(17) R. A. Rugunanan and M. E. Brown, `̀ Combustion of Binary andTernary Silicon=Oxidant Pyrotechnic Systems. Part III: TernarySystems', Comb. Sci. Technol. 95, 101±115 (1994).

(18) R. A. Rugunanan and M. E. Brown, `̀ Combustion of Binary andTernary Silicon=Oxidant Pyrotechnic Systems. Part IV: KineticAspects'', Comb. Sci. Technol. 95, 117±138 (1994).

(19) M. E. Brown and R. L. Drennan, `̀ A Thermal Study of theManganese=Barium Peroxide Pyrotechnic System'', Proceedingsof the 14th International Pyrotechnic Seminar, Jersey, (1989), pp.423±432.

(20) R. L. Drennan and M. E. Brown, `̀ Binary and Ternary Pyro-technic Systems of Mn and=or Mo and BaO2 and=or SrO2. Part I:Thermal Analysis'', Thermochim. Acta 208, 201±221 (1992).

(21) R. L. Drennan and M. E. Brown, `̀ Binary and Ternary Pyro-technic Systems of Mn and=or Mo and BaO2 and=or SrO2. PartII: Combustion Studies'', Thermochim. Acta 208, 223±246(1992).

(22) R. L. Drennan and M. E. Brown, `̀ Binary and Ternary Pyro-technic Systems of Mn and=or Mo and BaO2 and=or SrO2. PartIII: Kinetic Aspects'', Thermochim. Acta 208, 247±259 (1992).

(23) M. E. Brown, M. J. Tribelhorn, and M. G. Blenkinsop, `̀ Use ofThermomagnetometry in the Study of Iron-Containing Pyro-technic Systems'', J. Thermal. Anal. 40, 1123±1130 (1993).

(24) J. A. Dodds, `̀ The Porosity and Contact Points in Multi-component Random Sphere Packings Calculated by a SimpleStatistical Geometric Model'', J. Colloid Interface Sci. 77, 317±327 (1980).

(25) S. S. Al-Kazraji and G. J. Rees, `̀ The Fast Pyrotechnic Reactionof Silicon and Red Lead: Heats of Reaction and Rates of Burn-ing'', Fuel 58, 139±143 (1979).

AcknowledgementThe authors are grateful to AECI Explosives Ltd for ®nancial

support.

(Received April 4, 1997; Ms 23=97)

Table 8. Comparison of Calculated Contact Points* (NR) andMaximum Experimental Burning Rates (vmax)

SYSTEM vmax NR at vmax

(mm s71) (�109 per 1.00 g)

Sb(1)=KMnO4 11.0 0.063Sb(3)=KMnO4 11.5 0.116Sb(4)=KMnO4 22.5 0.77Fe=BaO2 35.7 2.06Fe=SrO2 8.3 8.87Mn=BaO2 11.7 0.036Mn=SrO2 12.3 2.91Mo=BaO2 10.1 0.0945Mo=SrO2 2.3 0.553Si(3)=SnO2 17.1 356Si(3)=Fe2O3 4.54 831Si(3)=KNO3 34.5 3.46Si(3)=Sb2O3 8.73 60.8W=K2Cr2O7 25.2 152Si(A)=Pb3O4 257 30.2Si(B)=Pb3O4 163 10.5Si(C)=Pb3O4 115 7.7

Figure 8. Plot of the calculated MAXIMUM number of contactpoints, NR, against the experimental MAXIMUM burning rates, vmax,for the pyrotechnic systems in Table 8. (The highest values of bothvariables have been omitted.)


Michael E. Brown,Steven J. Taylor and Michael J. Tribelhorn- Fuel-Oxidant Particle Contact in Binary...

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