The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.
Mixtures of relativistic gases are analyzed within the framework of Boltzmann equation by using Grad's moment method. A relativistic mixture of r constituent is characterized by the moments of the distribution function: particle four-flows, energy-momentum tensors and third-order moment tensors. By using Eckart's decomposition and introducing 13r + 1 scalar fields -related with the four-velocity, temperature of the mixture, particle number densities, diffusion fluxes, non-equilibrium pressures, heat fluxes and pressure deviator tensors -Grad's distribution functions are obtained. Grad's distribution functions are used to determine the third-order tensors and their production terms for mixtures whose constituent's rest masses are not too disparate, so that it follows a system of 13r + 1 scalar field equations. By restricting to a binary mixture characterized by the six fields of partial particle number densities, four-velocity and temperature, the remainder 21 scalar equations are used to determine the constitutive equations for the non-equilibrium pressures, diffusion fluxes, pressure deviator tensors and heat fluxes. Hence the Navier-Stokes and generalized Fourier and Fick laws are obtained and the transport coefficients of bulk and shear viscosities, thermal conductivity, diffusion, thermal-diffusion and diffusion-thermal are determined. Analytic expressions for the transport coefficients in the non-relativistic and ultra-relativistic limiting case are given. Furthermore, solutions of the relativistic field equations for the binary mixture are obtained in form of forced and free waves. In the low frequency limiting case the phase velocity and the attenuation coefficient are determined for forced waves. In the small wavenumber limiting case it is shown that there exist four longitudinal eigenmodes, two of them corresponding to propagating sound modes and two associated with non-propagating diffusive modes.
Rayleigh-Brillouin spectral profiles are measured with a laser-based scatterometry setup for a 90 degrees scattering angle at a high signal-to-noise ratio (r.m.s. noise below 0.15 % w.r.t. peak intensity) in sulphur-hexafluoride gas for pressures in the range 0.2 -5 bar and for a wavelength of λ = 403.0 nm. The high quality data are compared to a number of light scattering models in order to address the effects of rotational and vibrational relaxation. While the vibrational relaxation rate is so slow that vibration degrees of freedom remain frozen, rotations relax on time scales comparable to those of the density fluctuations. Therefore, the heat capacity, the thermal conductivity and the bulk viscosity are all frequency-dependent transport coefficients. This is relevant for the Tenti model that depends on the values chosen for these transport coefficients. This is not the case for the other two models considered: a kinetic model based on rough-sphere interactions, and a model based on fluctuating hydrodynamics. The deviations with the experiment are similar between the three different models, except for the hydrodynamic model at pressures p 2 bar. As all models are in line with the ideal gas law, we hypothesize the presence of real gas effects in the measured spectra.
The sound propagation through a gas in the free-molecular regime is studied on the basis of the linearized collisionless Boltzmann equation. The two principal quantities that characterize the sound propagation, namely the phase and amplitude of the perturbation, are determined by taking into account the influence of the receptor. It is shown that at a small distance between the source and the receptor the presence of the last changes qualitatively the sound characteristics. Two phase velocities are introduced: a differential and an integral, which are different in the free molecular regime.
High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N2O) gas at an incident wavelength of 403.00 nm, at 90 • scattering, at room temperature and at gas pressures in the range 0.5 − 4 bar. The resulting Rayleigh-Brillouin light scattering spectra are compared to a number of models describing in an approximate manner the collisional dynamics and energy transfer in this gaseous medium of this polyatomic molecular species. The Tenti-S6 model, based on macroscopic gas transport coefficients, reproduces the scattering profiles in the entire pressure range at less than 2% deviation at a similar level as does the alternative kinetic Grad's 6-moment model, which is based on the internal collisional relaxation as a decisive parameter. A hydrodynamic model fails to reproduce experimental spectra for the low pressures of 0.5-1 bar, but yields very good agreement (< 1%) in the pressure range 2 − 4 bar. While these three models have a different physical basis the internal molecular relaxation derived can for all three be described in terms of a bulk viscosity of η b ∼ (6 ± 2) × 10 −5 Pa·s. A 'rough-sphere' model, previously shown to be effective to describe light scattering in SF6 gas, is not found to be suitable, likely in view of the non-sphericity and asymmetry of the N-N-O structured linear polyatomic molecule.
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