Far-from-equilibrium gas kinetic theory : reactive systems and sound propagation

• Main Author: Napier, Duncan George
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/7436

There exist many physical situations that involve large departures from thermodynamic equilibrium. These systems may be spatially nonuniform and/or time dependent. Traditional kinetic theory involves a perturbation type of approach that implies small departures from equilibrium. The present thesis is devoted to the development of theoretical methods valid for systems far removed from equilibrium. The techniques are applied to a study of the departure from equilibrium in reactive systems, and for the propagation of acoustic waves in gases. The rates of gas phase reactions can be calculated from averages of the appropriate reactive cross sections over the distribution of velocities of the reacting species. Reactive processes, especially for reactions with activation energy, tend to remove translationally energetic species and the velocity distribution is perturbed from a Maxwellian. The extent of the departure from a Maxwellian can be estimated from solutions of the Boltzmann equation. If there is a good separation of elastic and reactive time scales, steady solutions of the Boltzmann equation can be obtained with a procedure analogous to the Chapman-Enskog (CE) method. Nonequilibrium effects for model reactive systems with and without reverse reactions and in the presence and absence of products are studied. The range of validity of the CE method is studied by comparing results from a CE method and an explicitly time-dependent solution method. The CE approach assumes a weak perturbation and is referred to as a Weak Non-Equilibrium (WNE) approach. A Strong Non-Equilibrium (SNE) approach that treats the distribution functions of each of the components as Maxwellians at different temperatures is applied to strongly perturbed systems in which the reaction causes the temperatures of each species to differ from the system temperature. A third approach is a modification of the SNE approach and is referred to as Modified Strong Non-Equilibrium (MSNE). All three methods are compared with the results of an explicitly time-dependent solution. The CE method was found to be valid only when the ratio of elastic to reactive collision frequencies is greater than 105. The propagation of acoustic waves through a gas perturbs the velocity distribution function of the gas. In a collision-dominated gas, the velocity distribution function can be approximated by a Maxwellian and the phase velocity and attenuation of the sound wave can be determined from a dispersion relation derived from the Navier-Stokes equations of fluid dynamics. In the rarefied region, hydrodynamics is no longer valid and kinetic theory methods must be used. The method of solution of the Boltzmann equation by Wang-Chang and Uhlenbeck (WCU) fails to describe the behaviour of sound waves as the frequency of oscillation approaches that of the interparticle collisions in the gas. A generalized Boltzmann equation (GBE) introduced by Alexeev is applied to the sound problem and the results are compared with those of the WCU method and experiment. The kinetic theory description for sound propagation in a simple gas introduced by Sirovich and Thurber (ST) is applied to binary mixtures of gases and the results compared with those of experiment. It is shown that the ST method provides better agreement with experiment than the WCU method. The results with the GBE do not converge.