Light Scattering from a Multiply Relaxing Fluid

Abstract

Formulas are derived for the roots of the dispersion equation for temporally damped hydrodynamic waves in a viscous, thermally conducting liquid having also a frequency-dependent viscosity with one or more relaxation times. Values of the roots are then computed for CCl4 at 25° for practically the entire range of wavenumbers, under the assumption that the extra viscosity has a relaxation time of 5.43 × 10−11 sec. Next, the values of the roots corresponding to k ≈ 2 × 105cm−1 (for 90° scattering of He–Ne laser light) are used to calculate both the unbroadened and the instrumentally broadened Rayleigh–Brillouin spectrum. A similar calculation under the assumption that CCl4 is doubly relaxing shows radically different velocity dispersion curves according to the relaxation time τ2 assigned to the longitudinal viscosity. For τ2 = 10−13sec, viscous overdamping reduces the sound velocity to zero for a narrow range of wavenumbers above about k = 1.2 × 107cm−1. For τ2 = 10−12sec, the velocity is an increasing function of frequency with points of inflection at about 3 and 100 GHz, as anticipated for a process having two widely separated relaxation frequencies.