Reaction Rate in Detonation

This may be formed with a large entropy increase, and hence increase the probability of completion of the reaction 

As noted by Eyring, the rate of chemical reaction does not affect the detonation velocity nor any of the properties of the products (Ref 5, p 215). These properties at any point within the chemical reaction zone are determined only by the extent of completion (n), of the chemical reaction at that point, and not by the nature of the chemical reaction itself. This relation- 

The smallness of the temperature coefficient in initiation and detonation has led to one objection to the thermal theory. 

It is suggested that the objection can be overcome if initiation temperature is inde-. pendent of the size and duration of the hot spot and if these latter quantities are important only as they influence the hot spot temperature. In these spots, at least, the temperature in the shock front may be high enough to initiate chemical reaction in the ordinary sense. This brings both initiation and the subsequent chemical reaction into the domain of ordinary chemical kinetics (Ref 5,p 216) 

Cook et al (Ref 2, p 374) note that of all the possible reactions going on in the detonation zone, only one will be ratecontrolling. It may then be assumed that all other reactions are effectively in equilibrium, and (n) will then also have the significance of measuring (approximately at least) how far the critically slow reaction has proceeded toward equilibrium. 

---

Chapter 6 in the book of Cook is devoted to "Reaction Rates in Detonation ... 

Reaction rates in detonation) (14 refs) 7) Dunkle s Syllabus (1960-1961),... 

Heat pulse) 91-122 (Deton wave shape and density properties) 123-4 (Reaction rates in deton) 123 (Nozzle theory) 124 (Curved-front theory) 125-28 (Geometrical model) ... 

M,A.Cook et al, JChemPhys 24, 191-201 (1956) (Rate of reaction of TNT in detonation by direct pressure measurements) 22)Dunkle s Syllabus (1957-1958) (See Vol 4 of Encycl, p XLIX) p 126 (Reaction front in detonation) 135-42 (Thermal decomposition of solids) 23)M.A.Cook, "The Science of High Explosives , Reinhold NY(1958), pp 123-42 (Reaction rate in detonation) 174-87 (Thermal decomposition of soli ds) 386-89 (Thermochemistry of detonation and expltr) 24)F.A.Baum, K.P.Sranyukovich B.I.Shekhter "Fizika Vzryva , Moscow (1959), pp 81-108 (Thermochemistry of explosives) 25)K.K.An-dreev A. F. Belyaev, " Teoria Vzryvcha-rykh Veshchestv Moscow(1960), p 49-56 (Thermal expln in gases) p 56—61 (Thermal explosion in solids) 26) Encycl of Expls PATR 2700, Vol 1 (I960), p A501 (Atomic expins, chain reactions in) 27)F.M.Turner,... 

M. S. Shaw and J. D. Johnson, A Slow Reaction Rate in Detonations due to Carbon Clustering , Shock Waves in Condensed Matter 1987, Elsevier Science Publishers, pages 503-506 (1988). 

See Detonation Waves Steady-state, One-Dimensional Reaction Waves with Finite Reaction Rate in Vo 4, D7Q3-R to D704-R. Ref S. Brinkley, Jr J.M. Richardson, 4th SympCombstn, Williams Wilkins, Baltimore (1952), 450-57 CA 49, 6608 (1955)... 

Accdg to Roth (Ref 4) the geometrical theory is essentially the theory developed by him and described in his thesis (Ref 1). Roth also pointed out that this theory is mentioned in a paper by Wohler Roth (Ref 2) who also made use of the surface-erosion concept in describing reaction rates in the deton of expls. Roth lacked the necessary proof at that time to justify exploitation of his theory... 

Taylor (1952), 139-55 (Deton vel-charge diam relationship) 7) M.A. Cook et al, "Velocity-Diameter and Wave Shape Measurements and the Determinations of Reaction Rates in Metal Nitrate-TNT Mixtures , Univ of Utah Inst for Study of Rate Processes,... 

The last column of Table 1 lists some experimental detonation temperatures (T j) obtained by optical methods. Although there is considerable disagreement between measurements made by different investigators, these TCJ values are probably the best that are now available. Detonation temperature is a very important parameter in detonation theory, inasmuch as it provides 1) the best test for the validity of an equation of state of the detonation products (See Vol 4, pp D268—298) and 2) insight into the chemical reaction rates in the detonation process... 

The detonation process, at least in insensitive LE, can bae visualized as follows (Ref 17a) Microinhomogeneities in the LE (eg, fluctuation in density or composition) result in non-uniform reaction rates in the shocked LE. Because reaction rates are so strongly dependent on temp, these perturbations do not attenuate and eventually reach the shock front of the detonation wave and bend it, thus creating oblique shocks at its leading edge. 

Detailed measurements and calculations are made of the energy transferred to chemically inert "fillers by physical processes such as heat conduction and compression during the detonation of TNT- Further evidence was obtained that the temp coeff of the processes controlling reaction rates in the detn is small... 

The absolute quantity of the losses and the loss-dependent decrease in the detonation velocity are inversely proportional to the reaction rate. In a narrow tube, where the intensity of heat transfer is greater, the decrease in the detonation velocity is greater, etc. 

A. N. Dremin discovered and studied the phenomenon of detonation spin in condensed explosives as well. In liquid explosives the detonation front is also sometimes non-ideally smooth, as was proved in work by Ya.B. and his colleagues in which the smoothness was judged by reflecting light off of the wave front. One of the fundamental questions in the theory of detonation is this why is a plane detonation wave unstable K. I. Shchelkin proposed a theoretical explanation of the instability based on the strong temperature dependence of the reaction rate in a gas which leads to intensification of the pressure perturbation caused by the bending of the leading shock wave. 

Leiper, G.A., Kirby, I.J., and Hackett, A. Determination of Reaction Rates in Intermolecular Explosives Using the Electromagnetic Particle Velocity Gauge, Proc. 8th Symposium (International) on Detonation, NSWC MP 86-194, Albuquerque, NM, 1985, pp. 187-195. 

As in consideration of deflagration phenomena, other parameters are of import in detonation research. These parameters—detonation limits, initiation energy, critical tube diameter, quenching diameter, and thickness of the supporting reaction zone—require a knowledge of the wave structure and hence of chemical reaction rates. Lee [6] refers to these parameters as dynamic to distinguish them from the equilibrium static detonation states, which permit the calculation of the detonation velocity by C-J theory. 

When the detonation velocity was calculated in the previous section, the conservation equations were used and no knowledge of the chemical reaction rate or structure was necessary. The wave was assumed to be a discontinuity. This assumption is satisfactory because these equations placed no restriction on the distance between a shock and the seat of the generating force. 

The general features of the model in which a shock, or at least a steep pressure and temperature rise, creates conditions for reaction and in which the subsequent energy release causes a drop in pressure and density have been verified by measurements in a detonation tube [18], Most of these experiments were measurements of density variation by x-ray absorption. The possible effect of reaction rates on this structure is depicted in Fig. 5.14 as well [19],... 

---