Nonequilibrium relaxation methods. Acoustic effects in transient chemical reactions

The hydrodynamic equations of motion describing the interaction of sound with transient chemical reactions are written for adiabatic conditions to take account of changes in enthalpy and stoichiometry, and the possibility of temperature and pressure dependent rate coefficients. The equations are linearized in small inhomogeneous perturbations away from the time‐dependent homogeneous state of the reacting system and solved by asymptotic expansion methods in the limit of high acoustic frequencies. Depending on the properties of the reaction, amplification, attenuation, and frequency changes of the sound may occur. Details are given for the ideal gas reactions $\mathrm{A}\to \mathrm{B}+\mathrm{C}\mathrm{,\hspace{0.17em}}\mathrm{A}\to \mathrm{B}$ . Numerical solutions of the hydrodynamic equations of motion confirm the predictions of the theory quantitatively. The asymptotic expansion method is compared to WKB‐type solutions and, in lowest order, the results of the two methods agree for the acoustic but not the reactive modes. Measurements of the rate of change of amplitude and frequency of the sound wave due to reaction provide information on rate coefficients and their temperature and pressure dependence. The theory is developed for standing acoustic waves and propagating wave packets. The analysis provides an extension of relaxation methods to transient reactions far from chemical equilibrium.