Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 SHOCK TUBE AND ADIABATIC COMPRESSION 125the diaphragm with a sharp needle. This produces a shock wave which enters thelow-pressure region and moves rapidly towards the end of the tube. Just before theend it passes several observation points located along the side of the tube, and, byfollowing the changes in properties of the mixture as the shock wave passes, thereaction can be characterized kinetically.What form does this “shock wave” take and how is it produced? A useful modelfor visualizing the formation of a shock was first proposed by Becker3’ in 1922.At the moment the diaphragm breaks, the high-pressure region may be comparedwith a tight-fitting piston in a tube; it is instantaneously at rest but rapidly acceleratesas the boundary moves into the low-pressure area. The acceleration can bethought of as a stepwise process (cf. Fig. 4): each displacement generates a pressurepulse which travels into the gas ahead. Each pulse raises the gas tothepiston velocityand also raises its temperature adiabatically, but because the speed of sound ishigher at higher temperatures the second, third, and later pulses tend to catch upwith the first. Eventually, these pulses all coalesce and form a discontinuity whichmoves at a constant speed along the tube. This speed is considerably greater than thespeed of sound in the undisturbed, relatively cool, gas. The term “shock wave” isperhaps a little misleading since in the shock tube the pulse is actually a singlesharp transition which is characterized by two sets of essentially uniform conditions.What is of interest, then, is to see how the chemical system readjusts to thenew conditions behind the shock.It is not proposed to deal in any detail with the hydrodynamical theory of shockwaves, which has been considered thoroughly by Greene and ToenniesZ9. In an idealsystem (i.e., one in which the medium is continuous, is non-viscous and does notconduct heat) the shock wave should be abrupt in nature and it would then bepossible to treat it as a mathematical discontinuity. However, real systems are notcontinuous, and they are viscous and heat-conducting. Interestingly, it is found thatthe actual size of the transition zone between the high- and low-pressure areasis very small. It is very difficult to measure this thickness experimentally, but thereare indications that it is typically of the same order of magnitude as the wavelengthof visible light, about cm. For convenience the coordinates of the system arereferred to the moving shock front as the origin rather than the laboratory. On thissystem the gas enters the transition zone smoothly with the velocity of the shockwave. Within a few collision path-lengths it is heated very rapidly-ix., it gains aconsiderable amount of kinetic energy and entropy in a short time- and it leavesthe “transition zone” with new physical properties. On this model, three conservationrelationships are expressed mathematically in terms of the physical parametersof the system-the conservation of mass, of energy and of momentum. By combiningthese expressions with two equations of state of the gas, equations can bederived which relate any three of the energy, pressure, density and temperature ofthe gas on entering and leaving the transition zone (a total of six parameters). Inorder to define the state behind the shock front it is necessary to measure oneReferences pp. 176-1 79