Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

8 FLAMES 16Yheld up progress in flame kinetics. In addition the pressure (assumed to be constantthroughout the flame), the mass flow rate and the gas composition at the inlet canbe determined relatively easily. From a knowledge of these quantities, and by applyingcontinuity equations for each species (in which the rate of formation is balancedagainst the mass flux across the flame) and the energy conservation equation, valuesof the rate coefficients involved may be deduced. In general, for a reaction of unknownmechanism it is not possible to work out the complete kinetic pattern froma single Aame1O3. Thus, for example, the properties in two flames of different concentrationratios at positions of the same temperature would have to be compared.Temperature is defined statistically in terms of the way in which the energy of theparticles comprising the system is distributed, which means that the temperatureis defined effectively by the Maxwell-Boltmann distribution function. Because thespecies encountered in flames are generally polyatomic, they have internal degreesof freedom (rotational, vibrational or electronic), and it is possible to define separatetemperatures with respect to translation and, say, vibration, provided that theenergy in each degree of freedom has an equilibrium distribution of the form describedby the Maxwell-Boltzmann equation. These temperatures will be the sameonlyifthe energy is equilibrated throughout the system, but in flames we are dealingwith time scales which may be short compared with the relaxation times for thisenergy redistribution. Thus it may be that in the reaction a species is produced inwhich some particular energy level is populated to an unusual extent. In this caseit is quite conceivable that the temperatures defined for the various degrees of freedomare not equal, and so the term “temperature” may have no precise meaning’.To circumvent this difficulty,it is usually assumed that equilibrium exists on a localscale (which is usually true in the slower and cooler flames) and that the particleshave an essentially Maxwellian energy distribution and so may be assigned a singletemperature. The matter has been discussed in greater detail by Broida”’.A very schematic representation of a system for following kinetics in flames isshown in Fig. 22. The arrangement used in a given case will depend to a large extenton the nature of the reaction. The type of equipment available has been discussedvery thoroughly by Fristrom and We~tenberg”~; it will be considered herebriefly under four headings.(i) The burner. One of the most important requirements of a flame used in akinetic investigation is that it be “stabilized”.-This means that a stable equilibriumsituation must exist such that the combustion zone maintains its fixed position relativeto the observation points. Theoretically, it should be possible to stabilize aflame by balancing the propagation velocity against the gas velocity, but this cannotbe done in practice since the gas pressure, and so the gas velocity, cannot be keptsufficiently constant. It has already been noted that considerable simplification arisesIndeed, if the energy distribution in a particular degree of fradom is far from Maxwcllian, notemperature may be defined for that degree of freedom.Rc/crcnees pp. 176-1 79