Branching chains Explosions

Their reactions are explosive without appreciable self-heating (branched chain explosion without steady temperature rise). Explosion usually occurs when passing from region 1 to region 2 in Fig. 3.9. Explosions may occur in other regions as well, but the reactions are so fast that we cannot tell whether they are self-heating or not. 

Belles prediction of the limits of detonability takes the following course. He deals with the hydrogen-oxygen case. Initially, the chemical kinetic conditions for branched-chain explosion in this system are defined in terms of the temperature, pressure, and mixture composition. The standard shock wave equations are used to express, for a given mixture, the temperature and pressure of the shocked gas before reaction is established (condition 1 ). The shock Mach number (M) is determined from the detonation velocity. These results are then combined with the explosion condition in terms of M and the mixture composition in order to specify the critical shock strengths for explosion. The mixtures are then examined to determine whether they can support the shock strength necessary for explosion. Some cannot, and these define the limit. 

H +C>2 - OH+ O, so called because the disappearance of one chain carrier leads to the appearance of two. If chain carriers are produced at a rate faster than they are removed (by chain-breaking or chain-terminating reactions), a branching-chain explosion can occur without any preliminary temperature rise at all (hence "isothermal )... 

Formaldehyde, in sufficient quantities, can suppress cool-flame formation. Jost (27) presents evidence indicating that cool flames are a form of branched-chain explosions. It has been suggested that the cool-flame reaction is quenched by its own reaction product, formaldehyde, and arrested short of complete release of chemical enthalpy. This seems unlikely, however, because in systems exhibiting multiple cool flames the concentration of formaldehyde after the first cool flame does not drop in some cases it increases, and yet does not suppress subsequent cool flames. Bardwell (5), and Bard well and Hinshelwood (4) explain cool flame phenomena by a modified theory of Salnikov. This thermal theory is further supported by the results of Knox and Norrish (30) in the ethane-oxygen system. The key intermediate is presumed to be a peroxide by Bardwell and Hinshelwood (4). Formaldehyde is considered an inert, stable product with little effect on the reaction. 

I he occurrence of a spontaneous explosion in a chemically reacting system is a complicated process. However, the events that lead to explosion can be characterized as being either of a branching chain or of a thermal nature. Branching-chain explosions occur in systems that react by a chain mechanism, the details of which allow the chain carrier concentration, and hence, the over-all reaction rate to increase without limit, even under isothermal conditions. Such a condition is possible only if one or more of the steps in the reaction chain results in a multiplication of chain carriers—i.c., X + A — Y + Z + , where X, F, and Z arc chain carriers. 

Induction Periods in Branching Chain Explosions. Induction periods in the case of chain-branching explosions are often observed (22, 23, Ifl, 41) and may be interpreted in any one of the following ways ... 

One of the remarkable features of these branched chain explosions is the astounding speed at which the system moves from a zero rate, through the steady state, through the build-up and thence to explosion. This induction period is short and can have a duration ranging down from seconds to milliseconds, or even less. 

The Branching Chain Explosion Upper and Lower Limits... 

Systems showing the characteristic of a branching chain explosion (e.g., oxidation of P4, PH3, NH3, H2, etc.) exhibit critical explosion limits of the... 

Few reactions have been studied as extensively as the classical reaction of hydrogen and oxygen. Because of its relative chemical simplicity, it has served as a prototype and proving ground for theories of branching chain explosions. 

Above 400°C the rate of production of water becomes measurably fast (above 100 mm Hg total pressure), and between about 400 and 600°C the reaction shows all the characteristics of a branching chain explosion replete with three explosion limits. Figure XIV.4, taken from work of Lewis and Von Elbe, illustrates this behavior for a stoichiometric mixture (2112 02) in a 7.4-cm-diameter pyrex vessel coated with KCl (volume = 220 cc). 

The model scheme described by equations (44) and (45) represents a simplification of mechanisms that apply to real branched-chain explosions. Initiation steps are seldom ever unimolecular R X 2C X or 2R carriers would be more realistic, and the latter would introduce further nonlinearity. The stable species produced in the termination step are not all products but instead include substantial amounts of other molecules, such as reactants. Finally, there are generally more than one reactant,... 

Examples of catalysts in combustion reaction include the effect of H2O on the carbon monoxide oxidation reaction CO H- 2 C02- Nitric oxide also catalyzes CO oxidation through the mechanism 2 NO 4-O2 2NO2 (overall) and NO2 -f CO NO H- CO2. In both of these examples, an intermediate compound (for example, NO2) is formed and then destroyed. The addition of a small amount of NO2 to an H2 — O2 mixture leads to a branched-chain explosion by introducing the relatively rapid initiation step NO2 H- X NO H- O H- X, with the O atoms so produced generating the usual H2 — O2 chain. The NO2 also participates in the efficient termination step NO2 H- O NO H- O2, which is sufficiently important at large concentrations of NO2 to cause a slow reaction to be... 

Critical explosion limits for a typical branching chain explosion showing explosion pe-ABCD represents explosion limits. The region ABC is called the explosion peninsula. 

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