Disparate-mass Gas Mixtures Research Articles

High-frequency sound wave propagation in binary gas mixtures flowing through microchannels

The propagation of high-frequency sound waves in binary gas mixtures flowing through microchannels is investigated by using the linearized Boltzmann equation based on a Bhatnagar-Gross-Krook (BGK)-type approach and diffuse reflection boundary conditions. The results presented refer to mixtures whose constituents have comparable molecular mass (like Ne-Ar) as well as to disparate-mass gas mixtures (composed of very heavy plus very light molecules, like He-Xe). The sound wave propagation model considered in the present paper allows to analyze the precise nature of the forced-sound modes excited in different gas mixtures.

Observation of fast sound in disparate-mass gas mixtures by light scattering.

Observation of fast sound in disparate-mass gas mixtures by light scattering.

Light-scattering studies of dynamical processes in disparate mass gas mixtures.

Results of light-scattering experiments on helium and xenon gas mixtures are presented for a large range of wave vectors, densities, and compositions. In the experiments these variables are varied independently from each other. In this manner we are able to show that the hydrodynamic eigenfrequencies, reduced with respect to the product of the wave vector k and the adiabatic sound velocity ${c}_{s}$, are a function of the product of the wave vector and the mean free path ${l}_{\mathrm{He}}$ only. By comparing the experimentally obtained dispersion curves and the predictions of the hydrodynamic theory, we find that the value of ${\mathrm{kl}}_{\mathrm{He}}$ at which the theory ceases to be valid is independent of the composition. We show that the longitudinal current-current correlation function ${\ensuremath{\omega}}^{2}$I(k,\ensuremath{\omega}) is a useful function in the study of light-scattering spectra that are featureless. For large reduced wave vectors we find a sound mode that is solely supported by the fluctuations in the xenon density. This is the slow sound mode.

Two-temperature hydrodynamics and multiple sound modes in disparate-mass gas mixtures

Gas mixtures of heavy plus light molecules can apparently support several different sorts of sound waves (the most recent such prediction is that of Campa and Cohen). The origin of the first such predictions is reviewed, along with the development of the two-temperature hydrodynamic equations which govern these mixtures at moderate wavenumbers and frequencies. Light scattering in the two-temperature regime is also discussed. Experiments in both sound propagation and light scattering are shown to confirm the existence of a two-temperature regime, and two simultaneous sound modes, in these disparate-mass gas mixtures.

On the existence of sound propagation gaps in disparate mass gas mixtures

Several scattering experiments indicate that the hydrodynamic theory is valid beyond the wavevector region in which the Brillouin-shift is linear with the wavevector. In this article extended hydrodynamic calculations are presented concerning the disparate mass mixture He+Xe, using Navier-Stokes equations. The calculations of the eigenvalues of the hydrodynamic matrix reveal the existence of sound propagation gaps for a low density gas mixture with x Xe < 0·16 at kσ ⋍ 0·006, similar to those which are obtained in a one component fluid at a triple point density for kσ = 2π. Results concerning the wavevector dependence of the amplitudes of the Rayleigh-Brillouin triplet are also given, as well as a discussion concerning ultrasound experiments. The predictions presented here can be tested by light scattering experiments.

Interspecies transfer of momentum and energy in disparate-mass gas mixtures

The collision integrals describing the rate of exchange of momentum and tensorial energy between the components in a binary mixture of neutral gases with very different atomic masses are determined for arbitrary values of their two temperatures and velocities, for realistic intermolecular potentials, and allowing for large departures of the heavy gas from equilibrium conditions. In the range of interest where the system is perturbed within times of the order of the slow relaxation time characterizing the transfer of energy between unlike molecules, the light gas distribution function is Maxwellian to lowest order, with corrections given asymptotically in powers of the small parameter m/mp formed with the ratio of the species molecular masses. Also, provided that the ratio Tp/T between the temperatures of the two gases remains much smaller than mp/m, the desired collision integrals may be evaluated asymptotically in powers of m/mp in all generality. The computation is carried out in detail for the case when the interaction between atoms is described by a Lennard–Jones potential. A combination of numerical computations with optimal matching of analytical expressions valid for large and small slip velocities leads to a set of compact formulas which hold for the limits of high and low temperatures and to a general approximate expression for all temperatures.

Anomalous dispersion in disparate-mass gas mixtures.

Dispersion of forced sound in Xe-He mixtures is found here to show mode coupling: interference between the sound mode and another excitation mode of the gas. Qualitatively different dispersion is found, depending upon whether the He mole fraction is greater or less than a critical value, if the frequency is higher than a critical frequency. Results also show that two-temperature hydrodynamics must be used to describe a disparate-mass gas in this frequency range.

Light-scattering predictions in the two-temperature regime for disparate-mass gas mixtures

Light-scattering predictions in the two-temperature regime for disparate-mass gas mixtures

Possibility of Double Sound Propagation in Disparate-Mass Gas Mixtures.

Possibility of Double Sound Propagation in Disparate-Mass Gas Mixtures.

Possibility of Double Sound Propagation in Disparate-Mass Gas Mixtures

Possibility of Double Sound Propagation in Disparate-Mass Gas Mixtures

Effect of cross-sectional mass dependence in the theory of disparate-mass gas mixtures

Equations previously derived for disparate-mass gas mixtures in the two-temperature regime are generalized to allow for an observed mass dependence of intermolecular forces.

Light scattering from gas mixtures

The special features of the light scattering spectrum of disparate-mass gas mixtures are analyzed via the dispersion equation for the hydrodynamic modes.