Quantum kinetic theory of polyatomic gases

A review is given of the kinetic theory of polyatomic gases as based on the quantum mechanical Waldmann-Snider kinetic equation. The transport properties in the Navier-Stokes and Burnett regimes and their dependence on external electric and magnetic fields (Senftleben and Senftleben-Beenakker effects) as well as flow and heat-flow birefringence are discussed for gases consisting of linear, spherical top and symmetric top molecules. The relaxation phenomena associated with sound propagation, Rayleigh-Brillouin, depolarized Rayleigh and Raman light scattering are considered in some detail as well as nuclear magnetic and electron spin relaxation and pressure broadening of microwave spectral lines. Finally an overview is given of the quantum mechanical methods for the quantitative calculation of all these phenomena from the nonspherical intermolecular potential.     

On unsteady-state heat-and-mass transfer in polyatomic gases

The problem of a nonstationary source of heat or particles in a polyatomic gas is solved analytically. The temperature and concentration distributions vs. distance to the source are constructed. It is shown that a nonstationary heat source may generate acoustic vibration. The solution obtained can be helpful in studying acoustic wave propagation, temperature and concentration fields produced by heat or particle sources of various configuration (in particular, by a laser beam in an absorbing media), etc.     

Kinetic model analysis of time-dependent problems in polyatomic gases

In this work we analyze time-dependent problems like sound propagation and light scattering in dilute polyatomic gases by using a kinetic model of the Boltzmann equation that replaces the collision operator by a single relaxation-time term which is compatible with Grad's 6-moment approximation. Comparison of the theoretical results with available experimental data in nitrogen, oxygen, carbon dioxide and methane shows that the model equation can be used to describe the acoustic properties and the light scattering spectrum of polyatomic gases in both hydrodynamic and kinetic regimes as long as the external oscillation frequency is smaller than the frequency required for the translational and the internal degrees of freedom to come to thermal equilibrium.     

The thermal conductivity of three polyatomic gases and air at 27.5°C and pressures up to 36 MPa

The paper reports accurate measurements of the thermal conductivity of ethane, ethylene, nitrous oxide, air and argon-free air as a function of density at a temperature of 27.5°C. In the case of ethane the experimental data extend over the pressure range 0.6–3.4 MPa, for ethylene over the range 0.6–5 MPa and for nitrous oxide over the range 0.6–4.5 MPa. The measurements on the two samples of air cover the range 0.8–36 MPa. All the measurements have been carried out in a transient hot-wire instrument and have an estimated uncertainty of ±0.2%.For air the few experimental data that exist deviate by up to 5% from the present results which are to be preferred owing to their higher accuracy. In the case of the pure gases the experimental data are combined with accurate viscosities and employed to estimate collision numbers for rotational relaxation in the gases.     

Electron clusters in inert gases

This Letter addresses the counterintuitive behavior of electrons injected into dense cryogenic media with negative scattering length L. Instead of strongly reduced mobility at all but the lowest densities due to the polaronic effect involving the formation of density enhancement clusters (expected in the theory with a simple gas-electron interaction successfully applied earlier to electrons in helium where L>0) which should substantially decrease the electron mobility, an opposite picture is observed: with increasing |L| (the trend taking place for inert gases with the growth of atomic number) and the gas density, the electrons remain practically free. An explanation of this behavior is provided based on consistent accounting for the nonlinearity of the electron interaction with the gaseous medium in the gas atom number density.     

Statistical mechanics of convex bodies

The difficulties inherent in the construction of two-dimensional pressure ensembles are discussed, and are tackled by defining an energy cost depending on the convex hull of the set of particles. An energy proportional to the area of the convex hull is not able to prevent evaporation of the system, whereas an energy proportional to the area of the circumcircle of the convex hull ensures a thermodynamic behavior. In the latter model, which turns out to be exactly solvable, various characterizations are given of the geometry of a typical state.     

Adsorption of interacting monomers on spanning clusters of polyatomic species

The adsorption-desorption process occurring on heterogeneous surfaces is studied by considering a special case where a fractal is used as adsorbent. The fractal surface is the spanning cluster corresponding to the random deposition of objects that occupy more than one site (k-mers) on a square lattice. Such a surface is characterized according to the deposited k-mer. Then, the adsorption of repulsively interacting particles adsorbed on the fractal surface is studied by using Monte Carlo simulations. Different thermodynamic quantities (adsorption isotherms, coverage susceptibility, etc.) are calculated and explained in terms of the characteristics of the substrate. A scheme to characterize the structure of the substrate by just considering the adsorption isotherm is presented and discussed.     

On the solution to the Boltzmann kinetic equation in calculating the heat flux in polyatomic gases

The solution of the linearized Wang Chang-Uhlenbeck equation using the Hanson-Morse model for calculating the heat flux in a plane molecular gas layer has been considered. General expressions (independent of the form and method for solving the kinetic equation) of the dependence of heat flux on the energy accommodation coefficients have been derived. The values of the temperature jump coefficient for specific gases have been obtained.     

Theory of field effects on transport properties of polyatomic gases in the transition regime

A simple method is presented for describing the effects of external magnetic or electric fields on the transport properties of polyatomic gases over the entire range from the continuum to the Knudsen regime. Instead of treating bulk and boundary-layer effects separately, both molecular and surface scattering are included from the beginning in the collisional part of the Boltzmann equation, and the surface is treated as one component of a multicomponent mixture. A simple first-order solution of this problem is sufficient to account for the dependence of the transport coefficients on the Knudsen number in the presence of a field. Detailed results for the longitudinal and transverse viscomagnetic effects in a single gas are presented, and shown to be in good agreement with experimental data for CO and N₂.     

Core potential of intermolecular forces applied to third virial coefficients and transport coefficients of polyatomic gases

The three-molecular cluster integrals for oxygen, nitrogen, and carbon tetrafluoride and the coefficients of viscosity and self-diffusion for nitrogen and carbon dioxide are discussed on the basis of the Kihara convex-core potential of intermolecular forces. For the equilibrium property, the relative size of the core is essential; for the transport properties, the nonspherical character of the molecule plays an important role.     

Three-atomic clusters of rare gases within Faddeev approach

The properties of the rare gas clusters of helium and neon are studied. The calculations of the bound state energies of helium and neon trimers are performed within Faddeev differential equation in total angular momentum representation.     

Collective properties of polyatomic gases in a magnetic field: Effects on light scattering spectrum

The effect of magnetic fields on collective properties of polyatomic gases has been extended outside the hydrodynamic regime. The calculations are based on a linearized Waldmann-Snider equation. The Waldmann-Snider collision operator is truncated yielding a finite matrix equation. The resulting matrix equation is solved on a computer to yield the polarized and depolarized light scattering spectra. These spectra are calculated in the absence and presence of a magnetic field. For long wavelengths it is found that the magnetic effects are of the same order of magnitude as in the Senftleben-Beenakker effects. For shorter wavelengths the effects disappear due to Doppler effects.This work was supported by NSF GP22881.Alfred P. Sloan Foundation Fellow.NIH Predoctoral Fellow.     

Multi-velocity and multi-temperature model of the mixture of polyatomic gases issuing from kinetic theory

In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservation laws due to mutual interaction between species. In particular, source terms that describe the rate of change of momentum and energy of the constituents appear. These source terms are computed with the help of kinetic theory for mixtures of polyatomic gases. Moreover, if we restrict the attention to processes which occur in the neighborhood of the average velocity and temperature of the mixture, the phenomenological coefficients of extended thermodynamics can be determined from the computed source terms.     

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent.     

Scaling properties of eden clusters in three and four dimensions

We study the scaling properties of noise reduced Eden clusters in three and four dimensions for variant B in the strip geometry. We find that the width W for large times behaves as a(s)g(L/s^d−1), where L is the width of the strip, s the noise reduction parameter, d the dimension of space, and a(s) a decreasing function of s, g is a scaling function with the property g(u)→1/2 as u→0 and g(u)u^x as u→∞, where χ is the roughness exponent. This scaling result leads to a new way of determining χ. In 3 dimensions, our numerical values for χ support a recent conjecture by Kim and Kosterlitz: χ = 2/(d + 2), and contradict all the former analytical conjectures. In 4 dimensions, we cannot distinguish between the conjectures of Kim and Kosterlitz and the conjecture of Wolf and Kertész, because large crossovers and finite size effects make the measurement of the exponents difficult.     

Entropy driven demixing in binary mixtures of hard convex bodies: influence of molecular geometry

The recently introduced approach (Bosetti, H., and Perera, A., 2001, Phys. Rev. E, 63, 021206) for studying entropy driven demixing in binary mixtures of hard convex bodies is applied here to analyse the influence of molecular geometrical factors such as shape and size ratio on isotropic fluid-fluid phase separation. The theory is shown to be self-consistent, in the sense that it allows the calculation of both the binodal and the spinodal of the demixing, and both curves merge at the same lower consolute point. In the case of 3-dimensional fluids, demixing is usually allowed for sufficiently thick solutes, provided no orientational ordering destabilizes the mixture. Fluid—fluid demixing is explicitly forbidden in cases of equal breadth of the solute and the solvent molecules, regardless of the aspect ratio of both particles. In particular, mixtures of prolate and oblate particles will demix more easily. The influence of shape is more importantly seen at moderate elongations. Finally, within the present approximation, demixing is forbidden for binary mixtures of 2-dimensional fluids, irrespective of the shape of the bidimensional molecules.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.