Light Scattering from a Multiply Relaxing Fluid

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 ${\text{k\hspace{0.17em}≈\hspace{0.17em}2\hspace{0.17em}×\hspace{0.17em}10}}^5{\mathrm{cm}}^{\text{−1}}$ (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 ${\tau }_2$ assigned to the longitudinal viscosity. For ${\tau }_2{\text{\hspace{0.17em}=\hspace{0.17em}10}}^{\text{−13}}\sec$ , viscous overdamping reduces the sound velocity to zero for a narrow range of wavenumbers above about ${\text{k\hspace{0.17em}=\hspace{0.17em}1.2\hspace{0.17em}×\hspace{0.17em}10}}^7{\mathrm{cm}}^{\text{−1}}$ . For ${\tau }_2{\text{\hspace{0.17em}=\hspace{0.17em}10}}^{\text{−12}}\sec$ , 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.