Chain explosion development

In this section, consideration is given to an analytical development of this chain explosion induction period that has its roots in the early work on chain reactions carried out by Semenov [3] and Hinshelwood [4] and reviewed by Zeldovich et al. [5],... 

The limit may appear to be extraordinarily sharp. The stable velocity on one side of the critical limit may be quite small at the limit a stationary condition ceases to be possible and the reaction must accelerate thus, however small the velocity at a point just on one side of the limit, explosion takes place on the other side. The acceleration to the explosive point takes place in a time of the order of that required for chains to develop in the gas which may be an immeasurably small fraction of a second. Thus we have the remarkable phenomenon of a critical concentration limit, on passing which a very slow reaction suddenly changes into explosion. 

The limit at C is almost independent of the surface of the vessel thus in accordance with the considerations of the earlier section on critical limits, it represents the point at which some deactivation process in the gas phase becomes marked enough to prevent branching chains from developing explosively. It is suggested that the deactivation process in question is the mutual destruction of H202 molecules, which between B and C are the centres from which explosive chains develop, e. g. 

The lower limit at B would be the point at which the deactivating influence of the walls of the vessel is just great enough to keep the chains from developing explosively. 

A simple nuclear weapon derives its energy from nuclear fission. A mass of fissionable material is rapidly assembled into a critical mass, in which a chain reaction develops and releases tremendous amounts of energy. This is known as an atomic bomb. Nuclear fusion can be used to make a more powerful weapon. In such a weapon, the X-ray thermal radiation from a nuclear fission explosion is used to heat and compress a small amount of tritium, deuterium, or hthium, causing nuclear fusion, releasing even more energy. Such a weapon is called a hydrogen bomb and can be hundreds of times more powerful than an atomic bomb. 

When the Plutonium Project was established early in 1942, for the purpose of producing plutonium via the nuclear chain reaction in uranium in sufficient quantities for its use as a nuclear explosive, we were given the challenge of developing a chemical method for separating and isolating it from the uranium and fission products. We had already conceived the principle of the oxidation-reduction cycle, which became the basis for such a separations process. This principle applied to any process involving the use of a substance which carried plutonium in one of its oxidation states but not in another. By use of this... 

During the development of these criteria the Semenov analysis was extended to systems with heat-exchanger reservoir temperatures different from feed temperatures (Tr < Tq) and with delayed runaway (larger value of e), which resulted In significant concentration drift prior to runaway. Since values of e for chain-addition polymerizations are not nearly as small as those for the gaseous explosions Investigated by Semenov, R-A Is not as sensitive nor Is It as early In terms of extent of reaction. 

Risk analysis. The risk of accidents can be assessed in terms of two factors severity and probability of the accident. Severity is high if consequences of the accident to employees, the public, the environment, and the plant are significant. Severity is related to the amount and properties of hazardous (toxic, flammable, explosive) substances that can escape to the surroundings during the accident, and to the energy that is released during the accident. Probability is associated with the likelihood of the occurrence of unwanted chains of events and the time of development of undesired events starting from the disturbance. If the time... 

Many of the early contributions to the understanding of hydrogen-oxygen oxidation mechanisms developed from the study of explosion limits. Many extensive treatises were written on the subject of the hydrogen-oxygen reaction and, in particular, much attention was given to the effect of walls on radical destruction (a chain termination step) [2], Such effects are not important in the combustion processes of most interest here however, Appendix C details a complex modem mechanism based on earlier thorough reviews [3,4],... 

The essential feature of the initiation step is to provide a radical for the chain system and, as discussed in the previous section, the actual initiation step is not important in determining the explosive condition, nor is it important in determining the products formed. Either reaction (3.14) or (3.16) provides an H radical that develops a radical pool of OH, O, and H by the chain reactions... 

In Chapter 3, the conditions for a chain branching explosion were developed on the basis of a steady-state analysis. It was shown that when the chain branching factor a at a given temperature and pressure was greater than some critical value acrit, the reacting system exploded. Obviously, in that development no induction period or critical chain ignition time rc evolved. 

Humans are exposed to radiation from the testing and explosion of nuclear weapons and the wastes of nuclear reactors and power plants. Strontium-90 is a fission product from nuclear reactors. It is of particular concern because it has a long half-life of 38 years and becomes concentrated in the food chain, particularly plants-to-milk. The ban on atmospheric testing of nuclear weapons has reduced this hazard. Strontium-90 does have some industrial uses. Most people in developed countries receive minor exposure to radiation through medical procedures such as X-ray and various treatments for some diseases. 

The most vibrant development in the field of PAEs is the explosion of their structural features. There are conceptually different ways of how to vary PAE structures. The first approach deals only with PPEs, and the structural modification is introduced by the variation of the side chains. This concept is powerful for introducing macromolecular, amphiphilic, water-soluble, selfassembling, or protective side chains. In most cases, however, the electronic structure of the PPE is untouched. There are exceptions. If the substituent under consideration is conjugated, it will change the electronics of the backbone. Examples of this kind have been prepared by the Bunz and the Swager groups [24,25]. 

Such reactions have been used to explain the three limits found in some oxidation reactions, such as those of hydrogen or of carbon monoxide with oxygen, with an "explosion peninsula between the lower and the second limit. However, the phenomenon of the explosion limit itself is not a criterion for a choice between the critical reaction rate of the thermal theory and the critical chain-branching coefficient of the isothermal-chain-reaction theory (See Ref). For exothermic reactions, the temperature rise of the reacting system due to the heat evolved accelerates the reaction rate. In view of the subsequent modification of the Arrhenius factor during the development of the reaction, the evolution of the system is quite similar to that of the branched-chain reactions, even if the system obeys a simple kinetic law. It is necessary in each individual case to determine the reaction mechanism from the whole... 

Time Factor Prior to Occurrence of a Thermal Explosion (Induction Periods). In the study of spontaneous explosions occurring in closed vessels, a well defined induction period frequently elapses prior to the development of an actual explosion. The length of this time interval has been observed to be anywhere from a few seconds to several minutes, depending upon the experimental conditions employed. Such observations are not surprising, in view of the fact that in order for an explosion to occur a build-up either of the internal energy or of chain carriers is first required. The rate of such a nonstationary process would then be expected to determine the duration of these pre-explosion times. For the case of a purely thermal explosion, the over-all rate of heat release, dq/di, prior to explosion is given by... 

Provided (f - g) > 0, the chain carrier concentration, and hence, the reaction velocity will increase exponentially with time. However, (/ - g) may be small enough so that t, corresponding to the induction period, r, may be very long. If (f — g) < 0, a true explosion never develops. A slow change from — to + values of (/ - g) has been observed for hydrocarbon-oxygen systems. These phenomena are sometimes referred to as degenerate chain-branching explosions or cool flames (44, ) ... 

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