Light Scattering from Chemically Reactive Fluids. IV. Intensity Calculations for the Eulerian Fluid with One Reaction

Abstract

The hydrodynamic equations for the reactive Eulerian fluid (zero transport coefficients, one chemical reaction) have been used in the thermodynamic approach to calculate in detail the spectrum of scattered light. The mathematical technique employed was the matrix eigenvalue formulation previously introduced [L. Blum and Z. W. Salsburg, J. Chem. Phys. 48, 2292 (1968)]. The method focuses on a particular matrix which is easily derived from the linearized hydrodynamic equations. The fluctuations of the set of independent variables are resolved into normal modes of relaxation. Each mode contributes one peak to the spectrum; the position and half-width of the peak are furnished directly by the eigenvalue, while the intensity is calculated from the corresponding normal mode projection matrix. Some general relationships between positions and half-widths are derived. The Rayleigh peak due primarily to chemical reaction relaxation is considered in detail. Various intensity ratios involving this peak are calculated, and simple criteria are set forth for determining whether it will be intense enough to be experimentally observed. If it is observable, the reaction rate constant can be obtained from measurements of its half-width. Two other chemical relaxation effects, dispersion of the sound speed and skewing of the Brillouin peaks, are also examined. For small scattering angles and very fast reactions, the rate constant may be extracted from measurements of the sound speed dispersion. The range of relaxation times for which experiments seem feasible is 10−4–10−11 sec.