Inelastic light scattering from density fluctuations in dilute gases. The kinetic-hydrodynamic transition in a monatomic gas

Abstract

The number-density fluctuation spectrum, ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$, of xenon has been studied in the dilute-gas limit. Spectra of He-Ne laser light scattered through an angle of 10.58\ifmmode^\circ\else\textdegree\fi{} at room temperature were measured for pressures ranging from 0.02 to 0.6 atm. Over this range ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$ evolves from the Gaussian kinetic form to three peaked hydrodynamic form. Measured spectra were used to evaluate various kinetic and hydrodynamic calculations of ${S}_{n}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}, \ensuremath{\omega})$ through this transition. Spectra obtained from the Boltzmann equation using the Gross-Jackson kinetic modeling procedure, for both Maxwell and hard-sphere intermolecular potentials, are in excellent agreement with the measurements. Among the hydrodynamic theories tested only the generalized hydrodynamics of Selwyn and Oppenheim satisfactorily provides the initial nonhydrodynamic corrections to the Navier-Stokes equations.