Kinetic phenomena in the gas mixture flow through nanodimensional capillaries: The effect of surface forces

The flow of a gaseous mixture in ultrafine capillaries whose size is comparable to the range of surface forces is studied with allowance for the effect of surface forces on gas component transport in the capillaries. The effect of surface forces is shown to be twofold. On the one hand, it is necessary to take into account the Boltzmann distribution of the molecular density in the capillary: it turns out that the contribution of this effect to the transport coefficient values may amount to 20%. On the other hand, an additional kinetic contribution to these coefficients may arise if the temperature in the gas is nonuniform. In this case, the temperature gradient may change the gas component transport coefficients several times, giving rise to a new mechanism of gas component separation that is associated with different potentials of interaction between the gas components and capillary walls. Also, surface forces modify the structure of phenomenological equations for gas component transport that implies entropy production in an inhomogeneous gas. However, the Onsager symmetry between cross coefficients is retained.     

Generalized hydrodynamics of thermal transpiration,thermal force and friction force

Transport processes in a rarefied gas are treated phenomenologically by means of generalized hydrodynamics with appropriate boundary conditions. The integral mass and heat flows through a capillary of arbitrary width are calculated from the differential constitutive laws and boundary conditions. The coefficients connecting these flows with the driving forces - pressure and temperature differences - automatically fulfil the well-known integral second law requirements and Onsager symmetry which de facto had been incorporated in the basic generalized hydrodynamics and boundary conditions. The formula obtained for thermal transpiration can account for the experimental data over a wide pressure range. Furthermore, expressions for the frictional and thermal forces on a spherical particle suspended in a gas are derived. These expressions have the correct behavior all the way from the ordinary hydrodynamical to the Knudsen regime. In particular, thermal force data are well represented, with suitably chosen surface coefficients, for small and large ratios of the particle/gas heat conductives.     

On thermopower in hopping transport

Certain general aspects of hopping transport in the context of thermopower are reinvestigated. Onsager symmetry of the macroscopic kinetic coefficients is derived from detailed balance of the microscopic coefficients of the kinetic equation by an expansion of the kinetic equation around local equilibrium in an external potential and temperature gradient. The resulting expression for the thermopower differs from expressions proposed in the literature. The difference however, seems to be small.     

The effect of infrared laser radiation on the selectivity of gas-mixture flow through metal capillaries

The effect of infrared laser radiation on the flow of gas mixtures through metal capillaries is investigated. It is found that many characteristic features of the processes depend on the interaction of resonant molecules with the surface as well as on the input pressure at the capillary entrance. Special attention is paid to the establishment of conditions where there exists a selective effect of the laser radiation on the flow of the components of the gas mixture through the capillary.     

Pulsed alkali pump light sources for Nd:YAG lasers

Pulsed arc discharges in alkali metal vapours are investigated for use as pump light sources for Nd:YAG lasers. Alkali lamps have a very high radiation efficiency and emit strong lines near the laser pump bands. These absorption bands are fitted by the emission spectrum of sodium and potassium lamps by changing the vapour pressure and input power. The spectral radiation distributions of the lamps are measured by a spectrograph with a gated OMA system. Ray tracing calculations for a laser cavity are used to evaluate the efficiency of the alkali radiation emission for Nd:YAG pumping. The results show that the excitation efficiency of the alkali lamps is twice as high as that of usually used rare gas lamps. For sodium resonance lines the side-on spectral radiance is calculated by a radiation transport model to estimate the pressure and the temperature profile. The results indicate that the alkali vapour lamps could be used as pump light sources with high efficiencies and low heat loading of the laser cavity.     

Light-induced heat and mass transfer in a single-component gas in a capillary

A theoretical analysis is presented of light-induced heat and mass transfer in a single-component gas in a capillary tube at arbitrary Knudsen numbers. Surface and collisional mechanisms of transfer are analyzed, due to differences in accommodation coefficient and collision cross section between excited-and ground-state particles, respectively. Analytical expressions for kinetic coefficients characterizing the gas drift and heat transfer in a capillary tube are obtained in the limits of low and high Knudsen numbers. Numerical computations are performed for intermediate Knudsen numbers. Both drift and heat fluxes are determined as functions of the light beam frequency. In the case of an inhomogeneously broadened absorption line, the light-induced fluxes are found to depend not only on the sign, but also on the amount, of light beam detuning from the absorption line center frequency.     

On the collisional transfer of nonequilibrium in the velocity distribution of resonant particles in a laser radiation field

The collisional transfer of nonequilibrium in the velocity distribution of resonant particles in a laser radiation field is investigated theoretically. It is shown numerically that the transfer effect is weak. This makes it possible to use simpler approximate one-dimensional quantum kinetic equations instead of three-dimensional equations to solve spectroscopy and light-induced gas kinetics problems, where it is important to take account of the velocity dependence of the collision frequency. It is shown for anomalous light-induced drift, calculations of which are most sensitive to neglecting the transfer effect, that in a wide range of spectroscopy and light-induced gas kinetics problems the transfer of nonequilibrium can be neglected without risking the loss of important fine details of the phenomena being described.     

Dynamic gas anisotropy under optomechanical parametric resonance

An approximate kinetic equation describing a gas of two-or three-level atoms in an external laser field is found under conditions of optomechanical parametric resonance, which causes atomic oscillations along the field wave vector. The approximation is applicable to a gas of cylindrical particles whose axes retain their spatial orientation, making the gas anisotropic. The closed set of equations for macroparameters allows for a numerical solution. Expressions for direction-dependent transfer coefficients such as diffusion, viscosity, and thermal conductivity are derived phenomenologically. A two-temperature medium is shown to arise if a fluid consists of several gases with the optomechanical parametric resonance conditions satisfied for one of them.     

Kinetic theory of gas-surface interaction

The kinetics of particle and energy exchange between gas and surface is treated in analogy to the transport of particles and energy in solutions using Onsager's theory of nonequilibrium thermodynamics. In addition to the coefficients of sticking and thermal accommodation a third kinetic coefficient is introduced describing the coupling of particle and energy transport. This coupling turns out to be particularly important at low temperatures reducing the accommodation coefficient from 2 to 1.The Onsager coefficients are then expressed in terms of the scattering properties of the surface. A simple model is treated to illustrate the general results and to provide estimates for the kinetic coefficients.Extract from doctoral thesis of H.M. submitted to Fachbereich Physik, Techn. Universität München, 1978     

Kubo formulas for relativistic fluids in strong magnetic fields

Magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev’s non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of the equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green’s functions defined with respect to the equilibrium statistical operator.     

Heat conduction in relativistic neutral gases revisited

The kinetic theory of dilute gases to first order in the gradients yields linear relations between forces and fluxes. The heat flux for the relativistic gas has been shown to be related not only to the temperature gradient but also to the density gradient in the representation where number density, temperature and hydrodynamic velocity are the independent state variables. In this work we show the calculation of the corresponding transport coefficients from the full Boltzmann equation and compare the magnitude of the relativistic correction.     

Stochastic dynamics of atoms in a resonant light field in the quasi-classical approximation

The stochastic dynamics of atoms with degenerate energy levels in a resonant nonuniformly polarized laser field is considered within the framework of the quasi-classical approach. The regular force entering into the Langevin equation and the correlation function of a random force are represented in the form of expansions in spatial gradients of the total light field. Specific features of kinetic distributions that are caused by the multiplicative character of noise, by anisotropy of dissipative processes, and by the presence of a vortex component in the light-induced force are considered for the example of a model system and a two-dimensional field configuration.     

Note on phase space contraction and entropy production in thermostatted Hamiltonian systems

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state, are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas. (c) 1998 American Institute of Physics.     

Statistical mechanics of thermal diffusion

Expressions of the flows of atoms A and B of a binary system in a crystal are derived as the response to the imposed gradients of temperature and chemical potentials. The formulation is done using the pair approximation of the Path Probability Method of irreversible statistical mechanics and atomic migration is assumed to be via the vacancy mechanism. The energy carried by photons (and electrons) under the temperature gradient is assumed to be independent of the atomic flux. For the case near equilibrium, linear relations are derived among the atomic fluxes, the energy flux (associated with atomic flux) and the gradients. The Onsager reciprocal relations are proved to hold among the coefficients, including those related to energy flows. The heat of transport (energy carried by a diffusing atom) and the heat conduction due to atomic flux are thus unambigously derived.     

Diffusion simulation with a deterministic one-dimensional lattice-gas model

A one-dimensional lattice-gas model is proposed and used to simulate diffusion processes in one dimension. Explicit forms of transport coefficients are given as a function of density and kinetic energy within the Boltzmann approximation. Without definitions of temperature and pressure, a steady nontrivial solution is given analytically in the nonconvective case when the kinetic energy is kept constant.     

Heat and mass transfer in a gas in a capillary induced by light with nonuniform intensity distribution over the beam cross section

An analysis is presented of the heat and drift fluxes induced by velocity-selective light absorption in a single-component gas in a capillary tube. The light intensity distribution across the beam is assumed to have a Gaussian profile. Kinetic equations are solved numerically to calculate flux profiles and kinetic coefficients quantifying the contributions of surface and collisional mechanisms to light-induced transfer as functions of the Knudsen number, the ratio of the rate of radiative decay of the exited level and intermolecular collision frequency, accommodation coefficient, and the ratio of the tube radius to the light beam radius.     

Coherent population trapping (Electromagnetically induced transparency) resonance in cells of finite sizes

The formation of the coherent population trapping (CPT) resonance in cells of finite sizes without a buffer gas is studied. It is found that, depending on the laser spectrum width, different CPT resonance narrowing mechanisms take place; these are the Dicke effect and the light-induced narrowing effect. Under light-induced narrowing conditions, the CPT resonance parameters are found to weakly depend on the cell size and the type of wall coating.     

Nonclassical transport in a nonequilibrium laser plasma

The onset of a nonequilibrium distribution function in a plasma produced by laser radiation at fluxes I - 10¹⁴ W/cm² is considered. The model employed takes consistent account of the nonlocality of the electron distribution at large density and temperature gradients, the demaxwellizing effect of the external hf field of the laser, and the nondiffusion of the transport in the high-energy part of the electron-distribution spectrum. Numerical solution of the corresponding kinetic equations shows that establishment of a nonequilibrium electron distribution in the corona suppresses the heat transport substantially. Good agreement is obtained between the kinetic value of the heat flux and the phenomenological value needed to reconcile the hydrodynamicsimulation results with the experimental data.Quantum Radiophysics Division, Lebedev Physics Institute. Translated from Preprint No. 179 of the Ledebev Physics Institute, Academy of Sciences of the USSR, Moscow, 1989.