amount vaporized, there is a complex coupling between the flame and the fuel source. Solid fuels are the most difficult to understand. The heat from the overhead flame (flame above the surface) is critical to generating the gases needed for flaming combustion. In some cases, the solid fuel can melt, forming a liquid that can be vaporized. In others, complex surface chemistry occurs, leading to the release of gaseous fuels that can feed the flame as well as to changes on the surface such as charring, which can block the emission of radiation. As is obvious from this brief discussion, there are complex flows that must be treated together with the chemistry if one is to really understand flames and fires. In the simpler case, the flow is smooth or laminar, and the adjacent layers of the fluid do not mix by mechanical means. If, however, there is random mixing of the fluids, a turbulent flow has been generated. In general vortices will be generated over a wide range of spatial scales, leading to complex mixing behavior that is not well understood.
In order to better understand how to design new fire suppression agents, it is necessary to understand some basic concepts about combustion. Given a fuel, we can write down its reaction with oxygen and calculate how much energy is released (the heat of combustion), providing we know the heats of formation of the reactants and products. For a hydrocarbon, the reaction is usually written as
Given the heat of combustion and the composition of the reaction mixture, it is possible to calculate the maximum or adiabatic flame temperature. The assumption that goes into this calculation is that all of the heat goes into heating the product gases and any other gases that are present. This calculation requires knowing the heat capacities of all of the gases. The heats of formation of all of the species are needed as well as the heat capacities in order to calculate the temperature dependence of the heat of reaction. From the expression ΔG = -RTlnK where K is the desired equilibrium constant and ΔG is the free energy, one needs to know the free energy of the process. From ΔG = ΔH - T ΔS, it is clear that one needs not only the enthalpy of the process (ΔH) but also the entropy (ΔS) of the process. Again, the entropies are needed for all important species. The overall equilibrium composition can then be calculated by an iterative procedure. Tables of thermodynamic properties exist, and methods have been developed for computing missing information.11,12,13,14
The reaction thermodynamics described above describe what happens at equilibrium but do not predict how fast the system will reach equilibrium. In order to determine the speed of the process, kinetic information is required. From the global reaction mechanism, we need to write down a reaction mechanism based on individual reaction steps, each of which is a fundamental chemical process, a unimolecular, bimolecular, or termolecular reaction. Then we have to determine the kinetics of each fundamental reaction step and use the rate constants to solve for a global kinetic rate. This is a complex process because much of the required data is not known. However, if the data are not available, methods exist for estimation.15
The types of reactions important in the combustion process are based on radicals.16 If the chain reactions have long chain lengths, then the flame can continue to exist. It is important to note that combustion temperatures tend to be high, >800 K, so that generation of radicals is more important than loss due to recombination. The first reactions in the chain are the initiation reactions that lead to the initial formation of radicals. Most initiation reactions involve breaking a chemical bond and thus have high activation energies. They tend to be slow even at flame temperatures. The chain propagation reactions consume fuel or oxidizer but do not change the number of radicals; hence the chain continues. The chain may branch, leading to an increased number of radicals and hence a higher global reaction rate. These reactions generally consume the oxidizer, in most cases O2. As most of the fuels are molecules containing carbon and hydrogen, H is an important radical in the chain. The most important branching reaction is