Combustion of solid oxidant-fuel systems: Thermodynamic and kinetic criteria leading to amplification of the combustion rate

C O M B U S T I O N A N D F L A M E 45:235-250 (1982)

235

Combustion of Sofid Oxidant-Fuel Systems: Thermodynamic and Kinetic Criteria Leading to Amplification of the Combustion Rate D. M. SPEROS and J. R. DEBESIS*

Lighting Research Laboratory, General Electric Company, Nela Park, Cleveland, OH 44112

The concept that combustion of solid oxidant-fuelsystems is governed by thermodynamicallypredictableoxidant dissociation pressures and measurablekinetics of oxygen evolution is shown to be consistent with the experimental results reported here. Selection criteria and a model based on this concept show that systems thus formulated necessarily

exhibit an amplificationof the combustion rate, i.e., an enhancement of the speed of combustion. This is due to (1) oxidant-fuel coupling or synergy associated with the familiar exponential increase in the combusion rate with temperatureand (2) sequential oxidantsyuergyin systems, such as Zr/C0304, BaCrO4,Fe203, containingoxidants dissociating at sequentiallyincreasingtemperaturesand rates. The net effect is that of a "kineticstepladder."These effectswereexperimentallyconfirmedand are appliedin commercialpractice.

L INTRODUCTION The purpose of this work was to explore the fundamental thermodynamic and kinetic factors which govern the combustion of solid oxidantsolid fuel systems. The practical objective was to develop criteria for oxidant selection which could lead to formulation of systems of optimal composition for specific applications. These systems are widely applied in metallurgy, ceramics, propellants, and other fields. Of particular interest here are processes resulting in light production. The problems of modeling and measurement in the simplest case of metal combustion, that of a single particle in gaseous oxygen, have proven to be severe [1]. These problems are compounded in the systems of interest here, consisting of large numbers of metallic particles dispersed among the particles of a solid oxidant, and seem to become intractable when the system involves a blend or mixture of several oxidants of different physical and chemical properties. * Presently at Xerox Corp., Rochester, NY 14644. Copyright © 1982 by The Combustion Institute Published by ElsevierScience Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

After a brief description of the physical state of the combustion system and its apparent changes during ignition and burning, we proceed to a working hypothesis based on the thermodynamics and kinetics of the thermal dissociation of the oxidants. This leads directly to the proposal of a combustion model. Although the model is intended to describe only the broad aspects of the combustion process, it predicts what may be termed "combustion rate amplification" due to coupling or synergy between the components of the system. This phenomenon is confirmed experimentally and applied in commercial practice. Finally, refinement of the model by means of computer simulation is discussed. H. PHYSICAL STATE O F C O M B U S T I O N SYSTEMS The specific system employed consisted of powder mixtures of zirconium with solid oxides, such as C o 3 0 4, BaCrO 4, etc. (Table 1), of particle sizes from 1 to 40 #. The sample weight covered the range between a fraction of a milligram to ~ 100 mg. The samples were formulated by mixing the

0010-2180/82/030235+16502.75

D. M. SPEROS and J. R. DEBESIS

236 o

o

g

O

Z

O 4-I

+I

(~I

O

O O e~

O

O

~2 0

0

0

0

8 0 0

o

°

li

8 "

SOLID OXIDANT-FUEL SYSTEM COMBUSTION

237

~i4~_/i

25CM

'~--2CM"-~"

Fig. 1. Experimentalcombustion cell: (1) powder oxidant-fuel mixture; (2) spark electrode or flash-lampigniter; (3) ceramic conduit for electric leads; (4) O rings; (5) set screws; (6) glass cover slip (optional); (7) glass microscope slide; (8) gas inlet tube (optional). dry component powders on glass plaques and standard precautions were taken to avoid injury in case of "spontaneous" ignition. The cell of Fig. 1 was used for all experiments reported here. The samples after mixing were poured from glass vials into the cavity of the cell where they assumed a roughly conical shape. Ignition was accomplished by the igniter device employed in flash lamps. This consists of 0.5 mg of a composition such as D in Table 1A, but containing a large excess of Zr, compacted in a small (0.6-mm i.d.) glass cylinder incorporating two electrodes; these are connected to a piezoelectric spark generator. The time of combustion of the igniter is a fraction of 1 msec. Observations and measurements were performed by means of high-speed photography, photometry, and spectroscopy. At the earlier stages of the work, measurements of temperature as a function of time relied on the method of"blue to red" ratio at two wavelengths of the spectral continuum [1]; subsequently these were supplemented by measurements of the ratio of spectral lines obtained by seeding the samples with Na tracers, as will be illustrated in Section IV in connection with thermally induced electronic excitation processes. High-speed photography showed that the igniter initiates the combustion of the sample by spraying burning Zr particles over its surface. Because of the

rapid (msec) combustion, and the high, heterogeneous brightness of these light-producing systems, it is difficult to obtain a quantitative measure of sample expansion as a function of time after ignition. Using high-speed photography in conjunction with photometric measurements it was estimated that, in general, the sample does not expand by more than a factor of approximately 1.5 until well after peak light intensity is reached. This apparent coherence of reactants and products during combustion is consistent with the considerations in the following section and the proposed combustion model in Section IV.

HI. THERMODYNAMIC AND KINETIC CONSIDERATIONS The above observations, and preliminary experiments employing a variety of oxidants, led to the hypothesis that the combustion is governed by the production of gaseous oxygen from the thermal dissociation of the solid oxidants. Thermal dissociation can be expressed quantitatively in terms of 1. The temperature range at which each oxidant dissociates to produce oxygen at a given pressure. This range can be predicted thermodynamically.

238 2. The kinetics of oxygen evolution at that temperature range. These can be measured independently. These considerations led to two of the criteria of oxidant selection for the formulation of combustion systems: 1. The selected oxidant must produce oxygen at sufficiently high pressure to sustain combustion at the temperature required for the particular application. 2. Since oxidant dissociation can be the ratelimiting process, the kinetic rate of dissociation must be compatible with the required rate of combustion. The pertinent thermodynamic and kinetic relations and measurements are considered next because they form the basis of the combustion model proposed in Section IV. A. Pressure and Temlmmttm~ Ranges of Solid Oxidant Decomlmsition Figure 2 gives the Gibbs free energy change AG as a function of temperature T for the chemical reactions stated in the caption. The full lines refer to the dissociation of higher oxides to lower oxides. The dashed lines refer to the process of formation of the lower oxides from the elements. From these data the equilibrium pressures Po of oxygen at a given temperature can be calculated from AG = - R T l n Po. Thus, the abscissa at AG = 0 is the isobar for Po = 1 atm. The figure then yields the equilibrium pressure of oxygen that each oxidant will produce at a given temperature (upper part) and the equilibrium pressure of oxygen necessary to prevent dissociation of the lower oxides (lower part). Thus, the upper part of the figure gives a measure of the extent to which each oxidant can sustain the combustion at a given temperature range, provided the kinetic rate of dissociation is sufficiently high. For example, the process CO30¢---~3CoO+½0 2 can be expected to produce oxygen at a pressure of 1 atm at approximately 1200°K, while a temperature of nearly 1800°K must be reached before Fe203 can serve as an oxidant to the same extent. On this basis, it is seen that ThO 2, CeO2, AI20 3, and other highly

D.M. SPEROS and J. R. DEBESIS stable oxides would be inactive for combustion temperatures not exceeding 4(KD-5000°K. The lower oxides constitute the final state of dissocation of the higher oxides if the combustion temperature does not exceed the temperature range at which P0 becomes appreciable. For example, the process C o O ~ 3 C o + ½ 0 2 can be expected to occur at temperatures approaching 2800~K, while at 120ffK CoO can be considered as the "final" product of the dissociation of Co304.

B. Kinetics of Solid Oxidant Decomposition Appropriate oxidant decomposition pressures constitute a necessary but not sufficient criterion for oxidant selection; to be useful, the rate of oxygen release must be adequate. Accordingly, the kinetics of thermal decomposition of the pertinent oxidants were independently studied by means of thermogravimetry (TGA) and differential scanning calorimetry (DSC). In the thermogravimetric experiments a Mettler Thermoanalyzer Instrument No. 91 was used, as previously described [5]. The differential scanning calorimetric investigation employed the methods and the instrument originally developed in this laboratory [6]. The kinetics of thermal decomposition of unconsolidated powders of the prototype oxidants Co304 and BaCrO4 are illustrated here. The thermal decomposition of both substances was found to obey the rate law

dN ~ - =k(No-N~)",

(l)

where N O is the number of moles of reactant (undissociated oxide) at time t = 0, N, is the number of moles of product (lower oxide or metal), and therefore N o - N t is the number of moles of reactant at time t. Equation (1) is derived from thermogravimetric and differential scanning calorimetry equations [5], [-6] as follows:

dW d t = kM a'-'(W o - %)"

239

SOLIDOXIDANT-FUELSYSTEMCOMBUSTION 160

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-140

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,

.-'~"

/

-160 III 0

-180

, , I , I , , I I I, 500 T* K 1000

II t I I I It 1500 R000

Fig. 2. Gibbs free energy versus temperature for the reactions 1. ThO 2 -, TbO + -~O~, 2. CeO s -* CoO + {rO2, 3.3 Fe208 ~ 2 Fe804 + -~r02, 4. ~BaCrO, ~ -~dCr2Oa + ~BaO + t~rO2, 5. Co804 ~ 3 CoO + ~ 0 2 , 6. {MnO 2 ~ {MnaO 4 * ~rOz, 7 . 0 2 at 300°K, 1 atm, 8. NaCIO 8 decomposes over narrow T range at approximately 450°K, 9. Co + {iO 2 --* CoO,

10 ~ e ÷~ - - ¼Fo~O,, II. ~Mn

+

~tO 2 --*¼MnaO 4,

12. ~Cr ÷ ~O~ ~ ~r~O~, 14. Th + ~tO 2 -~ ThO. Data from Refs. [ 1-3 ].

I

240

D.M. SPEROS and J. R. DEBESIS

and

by x-ray diffraction, and with increasing porosity, as determined by scanning electron microscopy and B.E,T. surface area measurements. These latter trends are consistent with previous work I-5] where it was shown that the "order" n increases with the ease of escape of gaseous product from (1) the crystallographic produce-reactant interface and (2) from the interior of the microscopic sample. Preliminary results indicate that the kinetics of the thermal decomposition of Fe203 are also dependent on particle size, porosity, and crystallinity. The decomposition occurs in two stages: for a typical 100-mg sample (Baker Analyzed Reagent) the first stage covers approximately the temperature range of 1300-1600°K and the second begins approximately at 1800°K and continues beyond the 1873°K limit of the instrument. X-ray diffraction indicates that the first stage results in a mixture of black magnetite (Fe30,) and or-hematite (Fe203), and the second in a mixture of Fe304 and FeO. As a result of this complex, two-stage dissociation, Fe203 in combustion systems produces the effect of two different oxidants releasing oxygen at two different temperature ranges, a lower one bridging the gap between Co304 and BaCrO4 and another at a higher range beyond that of BaCrO4 (see Figs. 3 and 4). The profound influence of these kinetic variables on the combustion of actual systems incorporating these oxidants was demonstrated by the necessity of routinely using Arrhenious plots such as that of Fig. 3 in factory acceptance tests for incoming Co304 used in flashlamps: batches of the oxide giving values of n, k below certain limits resulted in unacceptable combustion behavior and were returned to the supplier. Future shipments were screened on this basis.

dH dt = k A H rl -"(H° - Ht)"'

where M ~= Wo =

molecular weight of oxygen, total weight change during measurement, weight change up to time t.

the

Therefore N o = I4Io. M'

M'

and dN

1 dW

dt

M

dt "

Likewise change in heat content of the reaction at reference temperature T [7]. total heat effect of the decomposition being measured heat effect up to time t.

AHr=

H0=

H! Therefore X 0 ~

Ho _ AHr '

N =

_

H AHr '

-

and dN dt

1

dH

A H r dt "

Arrhenius plots are given in Figs. 3 and 4 for the dissociations in a nitrogen flow. Straight line behavior for over 909/0 of the dissociations (i.e., N ON! from 1 to 2% of N O to over 95%) is obtained for the values of the "order" n given in the figures. These values are precise to within +0.05 as demonstrated in Fig. 3, where plots for values of n departing from n =0.30 by +0.05 result in obvious departures from linearity. The dissociation of BaCrO, is irreversible and accordingly [5] the value of n for loosely packed powders was found to be unity, reverting to 2/3 for pressed compacts. The dissociation of Co304 is reversible and the value of n was found to increase with decreasing sample crystallinity, as determined

IV. C O M B U S T I O N M O D E L

If we assume that 1. oxidant decomposition limits the rate of combustion in solid oxidant-fuel systems, 2. the differential equation (1) describes the thermal decomposition of the oxidants also during a rapid (msec) combustion process,

SOLID OXIDANT-FUEL SYSTEM COMBUSTION

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242

D.M. SPEROS and J. R. DEBESIS

10-2 8

6 95%

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m

n=l.O0

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Fig. 4. Arrhenius plot for the thermal decomposition ~BaCrO4 --*~Cr203 + ~BaO + ½02; AE = 72.6 kcal/gram atom of oxygen.

SOLID OXIDANT-FUEL SYSTEM COMBUSTION

243

then we can develop a useful understanding of combustion in practical systems consisting of intimately mixed oxidant-fuel powders. Consider the simplest case of a single composite fuel/oxide particle (Fig. 5a) incorporating a single oxidant. The rate of heat production dQ/dt by such a particle can be written

where kc is the specific condfictance characterizing heat transfer through a contact area A' across an effective thickness l.To is the temperature of the heat sink. Electronic processes symbolized by

dQ = A re - e/Rr(No -- Nt)"(AHc- AHox), dt

(2)

w h e r e A r exp ( - E / R T ) = k , i.e., the Arrhenius equation pertaining to the oxidant; AHc is the heat of combustion of the fuel (such as Zr) per mole of gaseous oxygen consumed; and AHo~ is the heat of dissociation of the oxidant per mole of oxygen evolved. T is the single, volume-average temperature characterizing the composite solid at time t. The rate of heat loss is taken to be the sum of the following terms:

Radiation energy loss per unit of particle area A, approximately given by

5.67 x 10-12A. E'T 4 W/cm 2,

(3)

where E is the emittance. Conduction energy loss, given by A' k¢.~- (T-To),

(a)

(4)

0

%

I

/

i J

(c)

de~at,

(5)

where the term dE/dt is related to appropriate forms of the Boltzmann equation for electronic excitation and to the Saha equation for thermal ionization Such a model can now be extended by considering a system of two such composite particles (Fig. 5b) linked with an energy transfer bridge. Finally the many-particle network of Fig. 5c can be used to simulate a real, multiparticle system.-This model can be further extended to approach finite difference models of "continuous media" [8]. Before this model can be tested quantitatively, it must be noted that the minimum temperature of applicability of Eq. (2) is the temperature at which the particular oxidant considered begins decomposing at an appreciable rate. To attain that temperature the combustion process must be initiated by external heating or through combustion of a part of the fuel by ambient gaseous oxygen or oxygen released over a narrow temperature range by compounds such as chlorates, perchlorates, peroxides, etc. For example, a mixture of Zr and Co304 must be heated to approximately 1000°K (Figs. 2 and 3) for self-sustaining combustion according to Eq. (2). During the period At of heating from ambient to the oxidant decomposition temperature, the heat generation will obey some relation other than Eq. (2). It was found experimentally that the combustion of mixtures of Zr with Co304 and KC104 in air taking place in the cell of Fig. 1 is described by m

At = const. ~ in (T-To),

Fig. 5. Schematic representation of combustion model: (a) single particle; (b) two-particles system linked with energy transfer bridge; (c) many-particle network.

(6)

where for the above mixture, T=1000°K and To = 300°K. m is the average particle mass and A the average particle area of the Zr powder. At was determined by measuring the time interval between the application of the ignition spark and the first

244

D.M. SPEROS and J. R. DEBESIS

detection of visible light emission, which occurs at approximately 1000°K [Eq. (3)]. This coincides with the temperature of decomposition of Co30 4 and, therefore, the temperature at which Eq. (2) comes into effect. The value of the constant in Eq. (6) was determined by using in the mixture a Zr powder of narrow particle size distribution peaking at 3 #m (Ventron). This value was found to be 0.49 sec cm2/g. Using this value in Eq. (6), At was calculated for other particle sizes by introducing the appropriate values of m and A. The values of At

I0 -2

I

1

I

thus calculated are shown on the abscissa in Fig. 6. Close agreement was obtained between the At value calculated for 15-#m particle size and that measured using a polydispersed powder with particle size peaking at 15-/~m (60% 10-20 /~m, A products; Fig. 6). The applicability of relation (6) to other systems was not investigated; this relation may be general since it appears to be the integrated form of a conduction equation expressing the heat input into a particle of mass m through an area proportional

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m Fig. 6. T i m e d e p e n d e n c e of light o u t p u t for the particle sizes s h o w n .

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SOLID OXIDANT-FUEL SYSTEM COMBUSTION to the particle area A to raise its temperature from To= 300°K to T = 100(FK. The theoretical implication is that during At, a period during which combustion relies on ambient gaseous oxygen, heat transfer between particles (Fig. 5c) is predominantly by conduction,causing the overall heat release rate to be nearly linear in T. Above 1000°K, Eq. (2) is applicable, and the calculated behavior of the system using Eqs. (2)-(4) is shown by the full lines in Fig. 6. In these equations the kinetic quantities used were those measured and the thermodynamic quantities were calculated. The area A was taken as that of the composite single particle and an emissivity value E= 0.75 was adopted for the dark grey mixture of black Co30 4 with Zr and white KC10 4. Also the values for heat capacity and density adopted were suitably weighted average values for the mixture under consideration. Computer simulation for oxidants other than Co30 4 also gave results consistent with those in Fig. 6. These calculated results for all particle sizes were consistent with experimental results for At, as stated, and the photometric relative light intensity behavior. The role of electronic excitation [Eq. (5)] is demonstrated in Fig. 7, which shows the spectrum of visible light emitted from 0.5 mg of a combustion system such as the above but containing NaC10 3 as tracer. The spectrum was obtained using a Tractor-Northern Optical Multichannel Analyser, Model 1710. The merged Na lines of the resonance levels at 589 nm are prominent and among other features the Na lines at 514.8 and 515.3 are clearly seen above the thermal continuum. This demonstrates that an amount of energy is channeled to populate higher electronic levels; an application of the Saha equation shows that thermal ionization also can play a role in these combustion systems. Finally, if the combustion occurs in an electric field, thermionic and field-induced electron emission can also take place [9]. It is pointed out, however, that the presence of excited or ionized species does not demonstrate their energetic importance and that the term dE/dt should already be included in Eq. (2) in an equilibrium process. Nevertheless, as stated in Section II, the detection of these excited species is of interest because, for example, preliminary results

245

l

58{9 Na 515 Na

l 5~5.3Na 514.8 Na

589Na

515.3 Na 514.8 Na

Fig. 7. Spectrum of light emitted from combustion system with NaCIOa tracer.

246

D.M. SPEROS and J. R. DEBESIS

show that an effective temperature may be calculated by the ratio of these spectral lines. This can supplement "color temperatures" I-1] obtained by the "blue to red" ratio at two wavelengths of the continuum as resorted to at present. V. COMBUSTION RATE AMPLIFICATION

A. Combustion Model Predictions 1. Oxidant-Fuel Coupling In Eq. (2) valid in the range of solid oxidant decomposition, the rate of heat production dQ/dt is exponentially dependent on the temperature T through the kinetic rate constant k(T); i.e., d__QQoc e . . . . . ,/r.

(7)

dt This leads to what may be thought as a thermally autocatalytic effect due to coupling or synergy between the processes of oxidant dissociation and fuel combustion; i.e., the combustion process raises the temperature thus increasing the rate of oxidant dissociation which produces more oxygen to burn more fuel to increase further the temperature, and so on, until a temperature limiting process is reached [1, 10]. This thermochemical coupling expressed by Eq. (7) is contrasted to that expressed by Eq. (6) for combustion in gaseous oxygen where dQ/dt~:T. This contrast will be demonstrated in Fig. 9 by comparing curve A, showing the combustion behavior of Zr in gaseous oxygen, with the other curves showing combustion behavior of solid oxidant-Zr mixtures, and constitutes a basic difference between combustion systems relying on gaseous versus solid oxidants.

2. Sequential Oxidant Coupling Figure 8 shows Arrhenius plots for the thermal decompositions of C0304, BaCrO4, and FezO3; 1 1 For simplicity, the lower temperature (1300-1600°K) decomposition of Fe2Os, bridging the gap between Co~O4 and BaCrO4, is not shown; the upper temperatrue decomposition has been plotted in the correct temperature range, but the slope and range of k are tentative because of differences in these parameters encountered in samples of different origins.

these cover the range of specific reaction rate constant k of over six orders of magnitude and a temperature range of over 1000°k. The lower dashed curve shows the lower detection limit of decomposition and the upper dashed curve shows the maximum rate of decomposition attained by a 100-mg sample of each oxidant in the kinetic measurements (Section IIIB). Suppose these oxidants are part of a combustion system with Zr as a fuel and also containing NaC103. In a practical application this system is ignited by an electric spark in an atmosphere of oxygen. Consider the temperature rising in the system from room temperature, three times the length of the abscissa to the right, where the spark first initiates the combustion with gaseous oxygen according to Eq. (6). Next NaCIO a releases oxygen over a narrow temperature range. Then we enter the field of the figure with oxygen contribution from Co304, then from BaCrO4, and subsequently from higher-temperature species such as Fe203, the kinetic and thermodynamic constants in Eq. (2) changing sequentially with each successive oxidant. This sequence was already discernible along the P0 = 1-atm isobar of Fig. 2. However, Fig. 8 shows the kinetic juxtaposition: each specific rate takes over not far from where the last rate left off. The net effect is that of a "kinetic stepladder." If we were to take out of the combustion system one of the oxidants shown, one of the necessary steps of the ladder would be missing. Suppose that we attempted to compensate for the missing step, for example, BaCrO4, by doubling the amount of Co304 on the lower step. Then the same amount of oxygen would be produced but at a k and T that would not exceed the last point of the dotted line shown; while if BaCrO4 were left in the system, a k value at least 100 times higher would have been reached. Thus, this sequential oxidant coupling permits the combustion system to attain oxygen release rates, and consequently combustion rates, that would be impossible with a single oxidant. Inspection of Eq. (2) and Fig. 8 shows that in effect the kinetic ladder is described by the proportionality

dQ ~ e _ j ( r )/r dt

(8)

SOLID OXIDANT-FUEL SYSTEM COMBUSTION which is even more temperature dependent than proportionality (7) for combustion involving a single solid oxidant.

B. Experimental Confirmation The theoretical predictions were tested by igniting mixtures containing oxidants in various combinations. Table 1 gives examples of such formulations. The cell fo Fig. 1 was used for all experiments in these tables. It is emphasized that the relative positioning of igniter and sample, and sample shape, i.e., height-to-base-diameter ratio, can have large effects on combustion duration, etc., time variables. The variations shown in Table 1 and as error bars in Fig. 9 reflect a reasonable extent of consistency in igniter positioning and sample shape. For all experiments the igniter was positioned near (1-2 mm) the top of the samples except for the experiments in Table 1D, where it was in contact with the samples. Table 1A gives the characteristic time delay, time to peak intensity, and combustion duration for the formulations shown in the first three columns. These results are plotted in Fig. 9. Comparison of curve A in Fig. 9 with curve B offers experimental confirmation of combustion rate amplification due to solid oxidant-fuel coupling. Comparison of curve B with curve C and subsequently curve D offers experimental confirmation of combustion rate amplification due to sequential oxidant coupling. These sequences in Fig. 9 are as predicted by Eq. (2) and the kinetic ladder concept of Fig. 8.2 Table 1B illustrates the results obtained using kinetic ladders with missing steps. As predicted, the missing Co304 step in composition E results in lower combustion rates than those of compositions D or C, but in higher rates for combustion after ignition than composition B. Composition F resuits in rates intermediate between those of compositions C and D because the lower temperature decomposition stage of Fe 203 compensates for the missing Co304. 2 Combustion systems exemplified by curve D in Fig. 9 f'md practical applications in the "primer," i.e., the flash initiating or igniter device of commercial flashlamps of the "FlipFlash"® type.

247 It is well known [11] that oxidants such as Co304 and F e 2 0 3 have a catalytic effect on the decomposition of chlorates and perchlorates. In order to eliminate the possibility that the observed combustion rate amplification, as illustrated in Fig. 9, is due solely to this catalytic effect, KCIO4 was eliminated altogether in formulations exemplified in Table 1C. The results shown in the table and Fig. 10 (upper) indicate that combustion rate amplification is again obtained. Again, as expected, the combustions are slowed down because of the missing KC104 step. Efforts were made to determine whether these combustion amplification effects could be reversed. Reversal was obtained by using Fe203 and contact ignition. In Table 1D and Fig. 10 (lower) is shown that the peak time of three-step composition L is approximately 2 msec longer than the peak time of two-step composition K. However, all compositions containing Fe203 presented larger variations than this, reflecting the oxidant's complex thermal decomposition behavior described in Section III. Furthermore, contact ignition, i.e., combustion initiated by a single reaction front, was found to give results more susceptible to sample heterogeneities and shape variations than the generalized ignition method normally employed. Highspeed photography shows that the latter tends to average out sample irregularities by igniting simultaneously a large number of randomly distributed sites over the entire sample area. VL DISCUSSION AND CONCLUSIONS The thermodynamic and kinetic criteria given in Section III lead, through the proposed model, to the concept of combustion rate amplification bythe selection of sequential oxidants to form a kinetic ladder. This constitutes the third criterion. It is not surprising that sequential oxidant and fue! formulations have been used empirically for decades. For example, a metallothermic reaction such as the "Thermite" reaction involves an oxidant ladder consisting of the two-stage dissociation of Fe203 at 1300°K and at 1800~K, and possibly a fuel ladder of Mg and AI. As in the case of sequential oxidants, sequential fuels may contribute to combustion amplification by sequential reaction. This may involve a different kinetic concept, as for

248

D.M. SPEROS and J. R. DEBESIS

1500

2500 iO-I

10-2

*K 1200

I000

8OO

I

-

I

I

Fe203 I

10-3

I I I I I

-

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t 10-4

-

10-5

-

~

BaCrO 4

10-S

10-7 -

%

Co 304 ~ ,

10-e 0.2

I

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0.4

0.6

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0.8 I / T X 10-3

I%

I.O

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1.2

NoClO 3 " - - - 2 . 3 02 - " 3 . 3

Fig. 8. The "kinetic ladder" concept.

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1.4 X

10 -3

X I0 -3

SOLID OXIDANT-FUEL SYSTEM COMBUSTION

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8

12

16

20

24

28

32

36

m SEC

Fig. 9. Relative light intensity versus time for the combustion in air of the Zr-oxidant systems shown, demonstrating combustion rate amplification (see Table 1A).

example sequential rates of oxidation. Then coupling between the sequential dissociation of the oxidants and the sequential oxidation of the fuels may also be expected. Interpretation of combustion processes ideally embody all dominant reaction steps and energy flows in a single model. The model proposed here falls short of this ideal. The model does predict the oxidant-fuel coupling and ladder synergies, and these concepts are fully supported by the experimental results. However, at this stage, the model postulates an orderly sequence or transition in which oxidant-fuel coupling leads to sequential oxidant synergy. In the real phenomenon, the situation is far more chaotic: for example, highspeed photography reveals heterogeneities in

brightness (or temperature) in various regions of the sample and sometimes even between neighboring particles. It is possible that the model is successful because it gives some average of this random state. Preliminary computer simulations using the model of Fig. 5c, in which the energy transfer bridges are randomized, supports this possibility.

It is a pleasure to acknowledge helpful discussions with Professors D. E. Rosner, F. E. Williams, and K. D. Carlson; collaboration with Dr. H. R. Werner in the thermogravimetric studies, Dr. G. J. Kazek in the spectroscopic studies, and J. R. Cooper in the x-ray studies; and discussion with numerous colleagues in

250

D.M. SPEROS and J. R. DEBESIS

i~

......

Fig. 10. Relative light intensity versus time for the combustion in air of the Zr-oxidant systems. (Upper) From right to left, compositions: G, H, I (Table 1C). Abssissa: 10 msec/cm. Ordinate: 0.5 v/cm. (Lower) From right to left, compositions: J, L, K (Table 1D). Abssissa: 10 msec/cm. Ordinate: 0.2 v/cm.

the laboratories of the Lighting Group and at the Corporate Research and Development Center, and especially with Dr. R. M . Potter on all phases o f this work.

REFERENCES 1. (a) Gupta, S. K., and Maloney, K. M., £ AppL Phys. 44:3339 (1973). (b) Nelson, L. S., Levine, H. S., Rosner, D. E., and Kurzius, S.C., High Temp. Science 2:343 (1970). 2. Rossini, F. D., et al., "Selected Values of Chem. Thermod. Properties", N.B.S. Circular 500. 3. Kubaschewski, O., and Evans, E. LL., Metallurgical Thermochemistry, Pergamon Press, New York, 1958. 4. Glassner, A., US Atomic Energy Commission ANL5750. 5. Speros, D. M., Werner, H. R., in Analytical Calorime. try, Vol. 3, Plenum, New York, 1974, p. 511.

6. Speros, D. M., and Woodhouse, R. L,, Nature 197: 1261 (1963); d. Phys. Chem. 67:2164 (1963); US Patent No. 3,319,456, May 16 (1967); Z Phys. Chem. 72:2846 (1968). 7. Speros~ D. M., in ThermalAnalysis, Vol. 2, Academic Press, New York, 1969, p. 1191. 8. (a) Summerfield, M., Suthefland, G. S., Webb, M., Taback, H. J., and Hall, K. P., ARS Progress in Astronautics and Rocketry, Vol. i, Academic Press, New York, 1960, p. 141. (b) Price, E. W., Bradley, H. H., Jr., Dehority, G. L., and Ibkicu, M. M., AIAA J. 4:1153 (1966). 9. Speros, D. M., and BucciUi, P. R., J. Appl. Physics 41:1512 (1970). 10. (a) Wise, H., Inami, S. H., and McCulley, L., Combust. Flame 11:483 (1967). (b) Inami, S. H., Rosser, W. A., Jr., and Wise, H., Combust. Flame 12:41 (1968). 11. Wydeven, T., £ Catalysis 19:162 (1970).

Received 3 January 1980; revised 5 June 1981