Hydroacoustic analysis of multiple relaxation kinetics

This investigation presents a hydroacoustic theory which accounts for sound absorption and dispersion in a multicomponent mixture of reacting fluids (assuming a set of first‐order acoustic equations without diffusion) such that several coupled reactions can occur simultaneously. General results are obtained in the form of a biquadratic characteristic equation (called the Kirchhoff‐ Langevin equation) for the complex propagation variable χ = (α + ωi/c) in which α is the attenuation coefficient, c is the phase speed of the progressive wave, and ω is the angular frequency. Computer simulations of sound absorption spectra have been made for three different chemical systems each comprised of two‐step chemical reactions using physico‐chemical parameter data available in the literature. The chemical systems studied include (1) water‐dioxane, (2) glycine‐water, and (3) cobalt polyphosphate water mixtures. Explicit comparisons are made between the biquadratic characteristic solution and the approximate equation (sometimes referred to as a Debye equation) previously applied to interpret the experimental data for the total chemical absorption versus frequency. The relative chemical reaction and classical viscothermal contributions to the sound absorption are also presented. Several discrepancies that can arise when estimating thermodynamic data (i.e., chemical reaction heats or volume changes) for multistep chemical reaction systems when making dilute solution or constant density assumptions are discussed.