Light Scattering from a Chemically Reactive Fluid. I. Spectral Distribution

Abstract

The spectral distribution of light scattered by fluctuations about equilibrium in a chemically reactive fluid is calculated from the time dependence of the fluctuations predicted by the linearized hydrodynamic equations of irreversible thermodynamics. The theory treats a system with an arbitrary number, n, of independent chemical reactions which are coupled to the hydrodynamic processes involving viscosity and thermal conductivity. However, diffusion and any frequency dependence of the transport coefficients are neglected. The scattered light as a function of frequency has a central component and two side or Brillouin components. The central component is analyzed as a sum of $\text{n\hspace{0.17em}+\hspace{0.17em}1}$ Lorentzian lines, one associated with a thermal diffusion relaxation process and n lines associated with the relaxation of the chemical reactions. In the limit of zero angle of scattering the widths of all Lorentzian lines associated with transport properties (thermal conductivity, viscosity, etc.,) vanish, and the entire width of the central component is related to the chemical relaxation processes. In fact, in this limit each chemical process contributes a Lorentzian line whose half‐width is the reciprocal of the relaxation time for that process. The analysis of the widths for all the Lorentzian lines in the central component is given in detail for small but nonzero scattering angles and for the case of reactions having small enthalpy and volume changes for all scattering angles. The effect of chemical reaction rates on the position and width of a Brillouin or phonon component is also analyzed and parallels the treatment of ultrasonic dispersion and attenuation of sound waves.