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 CCI. at 25°C for practically the entire range of wavenumbers, under the assumption that the extra viscosity has a relaxation time of 5.43 X 10-11 sec. Next, the values of the roots corresponding to k",,2X1()6 cm-I (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 CCI. is doubly relaxing shows radically different velocity dispersion curves according to the relaxation time T2 assigned to the longitudinal viscosity. For T2= 10-18 sec, viscous overdamping reduces the sound velocity to zero for a narrow range of wavenumbers above about k = 1.2X 10 7 em-I. For n= 10-12 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. whose molecules have internal degrees of freedom weakly coupled to their translational degrees by a process having a single relaxation time. 2 ,3 His explicit (and approximate) expression for the intensity spectrum of the scattered light predicts Brillouin peaks which are symmetric Loren tzians, apart from overlap with the central components.This symmetry has been verified frequently by 2 R. D. Mountain, J. Chern. Phys. 44, 832 (1966).

Brillouin-Streuung an dichten Fluiden/ On Brillouin Scattering in Dense Fluids

“…Weiters gilt: k -2,527 • 10 5 cm -1 , a* = 1,1763 • 10-3 cm 2 /s [13], b 0 = 0,01524 cm 2 /s, r R = 138 ps und D= 1,41 • 10~5cm 2 /s [17].…”

“…In diesem Abschnitt werden die einzelnen spektralen Komponenten eines Brillouin Analytische Beziehungen für die Wurzeln der Dispersionsgleichung G (r) sind nur näherungsweise berechnet worden [7], Exakte Resultate, wie sie für die korrekte Beschreibung theoretischer Spektren von CC1 4 notwendig sind, können zweckmäßiger-weise nur mit dem Computer erhalten werden [13].…”

“…Numerische Ergebnisse, insbesondere die Frequenzabhängigkeit der Intensitäten der einzelnen spektralen Komponenten, konnten für die verschiedenen Theorien in der Literatur mit Ausnahme der Wurzeln der Dispersionsgleichungen G(z) der MOUETA-Theorie [13] nicht gefunden werden. Dies ist mit ein Grund für die umfangreiche Darstellung der Komponenten der Brillouin-Spektren von CCI4 in dieser Arbeit.…”

Hyperschalleigenschaften von Wasser-Äthanolmischungen

“…Dies geschieht, indem man bei der Lösung der Dispersionsgleichung 8 Die auf die oben beschriebene Weise erhaltenen Relaxationsfrequenzen /p;h sind in Abb. 2 dargestellt.…”

Sound propagation in sodium di-2-ethyl-hexylsulfosuccinate micelles and microemulsions

“…For simple liquids, the spectrum consists of three Lorentzian lines. However, for molecular Auids, an additional, prominent continuous background is found between the Rayleigh and the Brillouin doublet [1,29,30]. This additional scattering results from the internal degree of freedom of the molecules, which couples to the compressional motion, and thus contributes scattered light intensity [1].…”