One-component Gas Research Articles

Photophoresis of coarse aerosol particles with nonuniform thermal conductivity

The photophoresis of a coarse solid spherical aerosol particle in a one-component gas of nonuniform temperature is examined with consideration of the inertial effects in the hydrodynamic equations and the temperature jump in the Knudsen layer. The problem is solved in the spherical coordinates r, Θ, and ϕ. The photophoresis of a homogeneous particle is considered first. Then the results are generalized to an inhomogeneous particle. A particle whose thermal conductivity χ i varies as a function of r is chosen as a model which describes a broad class of natural and artificially produced aerosol particles. It is shown that the error can be significant if the variable internal thermal conductivity χ i =χ i (r) of the particle is ignored and only the value of the thermal conductivity on its surface χ i (a) is considered, on the assumption that the particle is homogeneous. It is also shown that a particle with a variable internal thermal conductivity χ i =χ i (r) and a density of heat sources within it q i (r,Θ) can be regarded as a homogeneous particle with a thermal conductivity γχ i (a) and a heat-source density m(r)q i (r,Θ). Recurrence formulas for gand m(r) in the general case are presented. Analytical expressions for γ and m(r) are found for a model particle with pronounced inhomogeneity.

Analysis of Adsorption Isotherms: Lattice Theory Predictions, Classification of Isotherms for Gas–Solid Equilibria, and Similarities in Gas and Liquid Adsorption Behavior

Adsorption at fluid–solid interfaces is considered in the framework of a lattice with boundaries. Using ideas proposed by S. Ono and S. Kondo (in“Molecular Theory of Surface Tension in Liquids” (S. Flügge, Ed.), Encyclopedia of Physics, Vol. 10, p. 134. Springer-Verlag, Berlin, 1960), a lattice model is derived, both rigorously and phenomenologically, and applied to macro-, meso-, and microporous adsorbents by imposing different boundary conditions. It is shown that this lattice theory can predict the entire spectrum of behavior observed when gases, liquids, or supercritical fluids adsorb on solid surfaces. In particular, it is able to predict steps in the isotherms, scaling behavior near saturation conditions, supercritical behavior, and adsorption hysteresis. It is shown that there is a profound analogy in the adsorption behavior of a one-component gas to that of a binary liquid mixture. This analysis leads to a new classification of physisorption isotherms for fluid/solid equilibria.

Phase transitions in the multicomponent Widom-Rowlinson model and in hard cubes on the bcc lattice

We use Monte Carlo techniques and analytical methods to study the phase diagram of the M-component Widom-Rowlinson model on the bcc lattice: there are M species all with same fugacity z and a nearest-neighbor hard core exclusion between unlike particles. Simulations show that for M ⩾ 3 there is a “crystal phase” for z lying between z c ( M) and z d ( M) while for z > z d ( M) there are M demixed phases each consisting mostly of one species. For M = 2 there is a direct second-order transition from the gas phase to the demixed phase while for M ⩾ 3 the transition at z d ( M) appears to be first order putting it in the Potts model universality class. For M large, Pirogov-Sinai theory gives z d ( M) ∼ M − 2 + 2/(3 M 2) + …. In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e. spatial symmetry but not particle symmetry is broken. For M → ∞ this transition approaches that of the one-component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition at y c ≅ 0.71 which is consistent with the simulation z c ( M) for large M. This transition appears to be always of the Ising type.

Supersymmetric Liouville theory: A statistical mechanical approach

The statistical mechanical system associated with the two-dimensional supersymmetric Liouville theory is obtained through an infrared-finite perturbation expansion. Considering the system confined in a finite volume and in the presence of a uniform neutralizing background, we show that the grand-partition function of this system describes a one-component gas, in which the Boltzmann factor is weighted by an integration over the Grassmann variables. This weight function introduces the dimensional reduction phenomenon. After performing the thermodynamic limit, the resulting supersymmetric quantum theory is translationally invariant. \textcopyright{} 1996 The American Physical Society.

Light-induced drift of a one-component gas in a flat channel

Light-induced drift of a one-component gas in a flat channel

Separation of phases at low temperatures in a one-dimensional continuous gas

We show the existence of a phase separation at low temperatures in a one-dimensional one-component classical gas in the canonical ensemble with interactionhard core −1/r α , 1<α≦2. This implies that for sufficiently low temperatures there are values of the chemical potential at which the pressure is not differentiable as a function of the chemical potential.

Light-induced viscous flow originating from velocity-selective heating or cooling.

An alternative mechanism is demonstrated to bring about light-induced kinetic effects in gases without the necessity of a state-dependent collision cross section. This is achieved by velocity-selective optical excitation followed by collisional deexcitation in the subsequent collision. This process may be termed velocity-selective heating and gives rise to an enhanced transport coefficient for a selected velocity class. A mean-free-path description of this phenomenon is given for the case of momentum transport in a one-component gas. For nonuniform illumination, a shear stress is found to result, which gives rise to light-induced viscous flow. Experimentally this effect is demonstrated for ${\mathrm{CH}}_{3}$F, ${\mathrm{CD}}_{3}$F, ${\mathrm{CO}}_{2}$, and ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$, rovibrationally excited by a ${\mathrm{CO}}_{2}$ laser. It is shown that the magnitude of the effect is determined by the rotational energy transfer. It can be of either sign (velocity-selective heating or cooling), depending on R- or P-branch excitation, and it can easily overwhelm the contribution to light-induced viscous flow arising from a state-dependent collision cross section.

Explicit relations in Bowen fluorescence - Applications to nebulae, the sun, Scorpius X-1, and laboratory plasmas

A general analysis of the fluorescent process is described which emphasizes the differing roles of escape probabilities in one-component and two-component gases, and the existence of discrete fluorescent saturation regimes. Explicit formulas are obtained and discussed for astrophysical Bowen fluorescence, as a concrete example, with applications to planetary nebulae, the solar atmosphere and the X-ray binary Sco X-1. An expression is also provided and evaluated for the profile overlap integral involved in the pumping process. A preliminary conclusion is deduced that densities in the fluorescent line-emitting regions of nebular sources may be higher than those derived from forbidden line ratios. The analysis is extended to a proposed laboratory investigation which would exploit the possibility of controlling the determining factors in the fluorescent process, i.e., O III/He II abundance ratio, optical depth, and photoexciting radiation field.

Stochastic forces and fluctuation-dissipation theorems in a relativistic one-component gas

The relativistic generalization of fluctuation-dissipation-theorems for a dilute relativistic gas are derived both on the level of the relativistic Boltzmann-Langevin equation and of the relativistic hydrodynamics. The second moments of the fluctuating heat flow and stress-tensor are calculated by two different approaches analogous to the methods of Fox and Uhlenbeck and Landau and Lifshitz. The results are the naturally covariant generalization of the nonrelativistic results of these authors.

Correlation energy of a one-component layered electron gas.

A calculation of the kinetic, exchange, and correlation energies of a quasi-two-dimensional electron gas is presented. In this model, the electrons could occupy two subbands. Since one of our aims is to examine the qualitative changes in the ground-state energy as electrons start to occupy the second subband, calculations of the correlation energy are carried out in the Bohn-Pines random-phase approximation (RPA). Numerical results are also presented for the ground-state energy of a superlattice of quantum wells which are represented by two-dimensional electron-gas layers.

Vicious random walkers in the limit of a large number of walkers

The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP () ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP () in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limitt≫p.

Light-induced viscous flow of a one-component gas.

A new phenomenon, light-induced viscous flow in a one-component gas, is observed in ${\mathrm{CH}}_{3}$F upon velocity-selective vibrational excitation. The effect originates from a state-dependent kinetic collision rate in combination with nonuniform illumination. The theory for this effect is derived using a Chapman-Enskog approach. Good agreement between theory and experiments in the near-hydrodynamic regime is found.

Anomalous transport in strongly inhomogeneous systems. I. A kinetic theory of nonlocal hydro- and plasma dynamics

Starting from the Fokker–Planck or Boltzmann type of linearized kinetic equation, and using a projection operator technique, a general evolution equation is derived for the hydrodynamical component of the distribution function with a renormalized collision operator providing extra dissipation mechanisms. Generalized Fourier and Newtonian laws are derived leading to nonlocal transport in time and space. Explicit evaluation of the transport coefficients is performed after a discussion of various truncation procedures. The results are applied to the study of dispersion and damping of sound in a rarefied one-component gas. A comparison with experimental results shows that a 14-moment approximation is very satisfactory.

Fluctuation properties of thermal solitons.

The thermodynamic properties of soliton-bearing systems can be obtained from the statistics of their soliton components, which reflect restrictions on phase space due to interactions. Going beyond the established agreement of the free energy with transfer-integral results, we have successfully tested first derivatives (energy, number density) and second derivatives (specific heat, compressibility) for a one-component soliton gas (corresponding to the case of the low-temperature sine-Gordon chain). A complete description of the equilibrium statistical properties of the soliton gas is given in terms of the averages of occupation numbers and their fluctuations. The latter are characterized by the absence of off-diagonal correlations.

Observation of surface light-induced drift.

In a one-component low-pressure gas, velocity-selective excitation can produce a drift due to state-dependent molecule-surface interaction. The first observation of this effect is reported for rovibrationally excited ${\mathrm{CH}}_{3}$F colliding with quartz. Experiments involving different rotational sublevels within the ${\ensuremath{\nu}}_{3}$ vibrational band indicate a strong dependence of the effect upon rotational quantum number.

Intracrystalline diffusion in zeolites. Communication 4. Influence of heat effects and diffusion in transport pores on the kinetics of adsorption of n-butane by caa zeolite

1. In the adsorption of n-butane by CaA zeolite from a one-component gas phase, the relative role of diffusion in transport pores decreases with an increase in the degree of filling, and the role of the thermal component increases. 2. The contribution of the thermal component increases with a decrease in the size of the adsorbent granule, and when the thickness of the plate is 2L < 0.01 cm, the adsorption kinetics are basically determined by the rate of dissipation of the heat of adsorption with all degrees of filling studied.

Mode coupling theory for purely diffusive system

A mode-coupling formalism is developed for multicomponent systems of particles performing diffusive motion in a uniform host medium. The mode-coupling equations are derived from a set of nonlinear fluctuating diffusion equations by expanding the concentration-dependent diffusion constants about their equilibrium values. From the mode-coupling equations the dominant long time behavior of current-current and super-Burnett correlation functions is derived. As specific applications I consider the long time behaviors of these correlation functions for collective and tracer diffusion in a one-component lattice gas with particle-conserving stochastic dynamics. The results agree with those from exactly solvable models and computer simulations.

Dynamic correlations in a charged lattice gas.

The many-particle hopping problem in a one-component lattice gas of charged particles is investigated. A method is pointed out which allows the simultaneous treatment of correlations induced by the lattice and by the Coulomb interaction. Results are obtained for the concentration and temperature dependence of the tracer correlation factor and the quasielastic width of the incoherent scattering function. In addition, we discuss the long-wavelength charge fluctuation spectrum and possible anisotropy effects in layered systems.

Quantum corrections to the low-frequency-component microfield distributions

We evaluate the low-frequency-component microfield distribution for a one-component classical gas of ions interacting through an effective potential. The screening of the ions is a way to account approximately for the effect of the electrons. In this paper the ion-ion effective interaction is calculated by a quantum-mechanical treatment of the electrons. We compare our results for the low-frequency microfield distributions with theories using a classical Debye-H\"uckel treatment of the electron screening of the ions.

Nonisothermic flow of gas mixture in a channel at intermediate Knudsen numbers

Solution of the problem of gas mixture flow in a plane channel at intermediate Knudsen numbers is considered on the basis of the 20-moment approximation as a function of distribution. The applied method consists of averaging moment equations valid throughout the flow region (including the Knudsen layers) with the determination of boundary values of macroscopic parameters on the wall using the approximate Loyalka method /1,2/. Expressions are obtained for a binary mixture for the mean molar velocity averaged over the channel cross section, difference of component velocities, and the relative heat flux in the presence of longitudinal gradients of partial pressures, and for the temperature gradients. Respective kinetic coefficients of the Onsager matrix are calculated. Dependence of these coefficients on the Knudsen number, and the properties of molecule scatter on the channel wall are analyzed in detail in the case of one-component gas and of a binary mixture with small relative difference of mass and diameters of molecule scatter.