Showing papers on "Knudsen number published in 1982"

Transport Phenomena with Single Aerosol Particles

Abstract: This is a review of theory and experiments related to single aerosol particle transport processes. The theories of mass, heat, momentum, and charge transfer are outlined, with emphasis on mass transport in the continuum and noncontinuum regimes. Included in the discussion of mass transfer are single and multicomponent droplet evaporation, a comparison of the results of solutions of the Boltzman equations for Knudsen aerosol evaporation and growth and experimental methods for the study of single droplet evaporation or growth. Of particular concern here are the experimental apparati and techniques developed for single particle measurements. These range from the Millikan oil drop experiment through the electrostatic balance (the Millikan condenser with automatic stabilization of the particle) to the electrodynamic balance. The principles and applications of these instruments are reviewed.

Viscous Resistance of Straight-Chain Aggregates of Uniform Spheres

Abstract: The viscous resistance of a straight-chain aggregate of uniform spheres is of particular interest because it approximates the resistance of a particle shape frequently observed in aerosol systems, namely, a straight-chain aggregate of roughly uniform, roughly spherical particles. Moreover, this nonspherical particle shape is readily generated in the laboratory and used to calibrate aerosol instruments and processes. A method for calculating the viscous resistance is described for such a particle shape, and example results are presented for a broad range of chain lengths and Knudsen numbers. The method employs an interpolation between the continuum resistance and that for free-molecule flow. The results are discussed in connection with the few experimental data available.

An efficient computation of near-continuum rarefied gas flows

Abstract: A numerical scheme for solving integral equations of rarefied gas dynamics is modified to provide more accurate results in the near continuum flows. The modified scheme is applied to the Poiseuille flow of a rarefied gas between parallel plates and in a cylindrical tube. Flow rate results obtained for both geometries are good over the complete range of Knudsen numbers. In particular, the results are found in excellent agreement with the analytic asymptotic formulas in the near continuum regime even when fairly low order of quadrature formulas are used.

Viscous dissipation at the Venus ionopause

Abstract: A study of the effects of the transfer of momentum of the shocked solar wind to the Venus ionosphere near the terminator region is presented. It is shown that the deficiency of momentum flux within the velocity boundary layer in the ionosheath is comparable to the momentum flux present in the upper ionosphere near the terminator. Using the observed concentration of planetary O+ ions in the wake it is also shown that mass loading processes are not sufficient to account for the loss of momentum flux above the ionopause and that, instead, an efficient coupling must exist between the plasma above and below that boundary. With reasonable values of the thickness and length of the velocity boundary layer it is possible to estimate an effective viscosity coefficient of the flow and the energy released through viscous dissipation. The results indicate that a column integrated energy deposition of the order of 10−2 ergs cm−2 sec−1 can be predicted near the terminator. This number is comparable to that required to heat up the nightside ionosphere as assumed in the modeling studies of Knudsen et al (1979), Cravens et al (1980), Hoegy et al (1980), and Merritt and Thompson (1980).

Thermal transpiration and mechanocaloric effect. IV. Flow of a polyatomic gas in a cylindrical tube

Abstract: The phenomenological coefficients for mass and energy flows due to axial pressure and to temperature gradients on long capillary tubes containing a polyatomic gas at all degrees of rarefaction are reported. The Hansen and Morse polyatomic gas model of the linearized Wang Chang and Uhlenbeck equation was used together with Maxwell’s diffuse scattering boundary conditions. The results are consistent with previous results obtained for flow between parallel plates. Experimental isothermal flow data are nearly quantitatively represented by the theory in the transition flow regime (Knudsen number ∼ 1). Experimental thermal transpiration effect ratios (Δp/p0)/(ΔT/T0) are also quantitatively represented for simple gases, argon, air, and carbon dioxide. Thermal transpiration measurements on sulfur dioxide correlate as the other gases but the transpiration effect ratio is not quantitatively given by the theory due to inadequacy of the Hansen–Morse model and the continuum theory for strongly polar gases.

A Model for Gap Conductance in Nuclear Fuel Rods

Abstract: Computation of nuclear reactor fuel behavior under normal and off-normal conditions is influenced by gap conductance models. These models should provide accurate results for heat transfer for arbitrary gap widths and gas mixtures and should be based on considerations of the kinetic theory of gases. There has been considerable progress in the study of heat transfer in a simple gas for arbitrary Knudsen numbers (Kn = l/similar to d, where l is a meanfree-path and similar d is the gap width) in recent years. Using these recent results, a simple expression for heat transfer in a gas mixture (enclosed between parallel plates) for an arbitrary Knudsen number has been constructed, and a new model for gap conductance has been proposed. The latter reproduces the free molecular (small gap, Kn >> 1) and the jump limits (large gaps, Kn << 1) correctly, and it provides fairly accurate results for arbitrary gap widths. The new model is suitable for use in large fuel behavior computer programs.

Film thickness distribution at oblique evaporation

Abstract: The film thickness distribution and lateral distribution of the arrival rate of atoms or molecules at a substrate using evaporation sources with nonperpendicular and nonrotating substrates were determined for gold films and compared with two theoretical models—a cosine distribution and a Knudsen effusion model. (AIP)

A mean free path theory of void diffusion in a porous medium with surface diffusion. II. Numerical evaluation of the effective diffusivity for arbitrary Knudsen number

Abstract: A mean free path kinetic theory of gaseous void transport with simultaneous surface diffusion on the pore walls has been developed for diffusion through a porous medium. A variational upper bound expression for the effective diffusivity is applied to a model porous medium, a bed of randomly placed, freely overlapping solid spheres all of the same radius. The effects of tortuosity are rigorously considered by explicitly including the flux of diffusing material around obstructions in its path in the trial functions. Numerical calculations of the variational integrals are performed for porosities from 0.01 to 0.90 and the full range of Knudsen numbers and surface diffusivities. From asymptotic values at large Knudsen numbers, a table of effective diffusivities versus the surface diffusion coefficient is presented for pure Knudsen diffusion in the voids.

Flutter interpretation of thermal conduction with application to Alcator

Abstract: A previously presented magnetic fluctuation interpretation of anomalous thermal conduction in Tokamaks is extended to the high field, high density regime of Alcator. Density fluctuations are fully taken into account but found not to significantly alter the predictions. If the electron parallel thermal conductivity is corrected for high Knudsen number effects, the authors find that the mean squared relative magnetic fluctuation level must scale as (density)-2, to fit Alcator scaling.

Numerical investigation of processes in strongly nonequilibrium Knudsen layers

Abstract: Numerical solutions of model kinetic equations in Knudsen layers on surfaces with strong evaporation “into the corresponding gas” and excitation of internal degrees of freedom of the molecules are considered. It is shown that excitation of the molecules has a strong influence on the structure of the Knudsen layers and the parameters of the evaporating gas.

Heat conduction in a nearly collisionless molecular gas

Abstract: Transport phenomena in molecular gases and the respective field effects have so far been analyzed in the hydrodynamic and Knudsen regimes. In between there is a rather large gap covered by the transition regime. For the case of heat conduction through a diatomic diamagnetic gas between parallel plates an attempt is made to partially bridge the gap by the beginning of a density expansion derived through iteration of an integral form of the Boltzmann equation. Second-order perturbation in non-sphericity of both intermolecular and gas-wall interactions is applied to determine the effect of a magnetic field. Explicit expressions are derived for a simple model.

Evaporation of spherical drops in a binary gas mixture at arbitrary Knudsen numbers

Abstract: The quasisteady evaporation of drops in a binary gas mixture is investigated at arbitrary Knudsen numbers. The analysis is based on the solution of kinetic equations with collision integrals in the Boltzmann form by Lees's method [9]. The obtained solution makes it possible to consider an arbitrary model of intermolecular interactions. Formulas for the evaporation time of the drops are analyzed, the model of rigid elastic spheres being used for the interaction of the molecules.

Permeability of gases through an asymmetric polyvinyl trimethyl silane membrane

Abstract: It was shown that gas flow through an asymmetric polyvinyl trimethyl silane membrane may be presented as flow consisting of three components—activated diffusion, Poiseuille viscosity flow and Knudsen capillary flow. By experimental measurement of the dependence of flow on pressure for nitrogen and argon the effect of each component on overall flow was calculated. Using the equations derived hydrogen and helium flow values were calculated from results for nitrogen and argon; deviation of calculated flow values from experimental results was less than ∼ 2%.

Thermodynamics of incongruently vaporizing tungsten diselenide

Abstract: The incongruent vaporization of WSe/sub 2/ was investigated by a simultaneous weight-loss-mass-spectrometric Knudsen effusion technique in the temperature range 1290-1720 K. For the reaction (1/2)WSe/sub 2/(s) ..-->.. (1/2)W(s) + Se(g), ..delta..H/sub 298//sup 0/ = 311 +/- 3 kJ/mol.

Sharp flat plate heat transfer in helium at Mach numbers of 22.8 to 86.8

Abstract: Surface heat transfer rates were measured on a sharp flat plate at zero angle of attack with helium over a Mach number range of 228 to 868 in a hypersonic shock tunnel The density and leading edge Knudsen numbers were varied to span the continuum to near free molecule regimes The strong interaction parameter varied from 11 to 16,000 with leading edge Knudsen numbers from 056 to 171, respectively For high unit Reynolds number the rate of change of the heat transfer coefficient with the strong interaction parameter agreed well with the strong interaction theory of Li and Nagamatsu (1953, 1955)

The bulk stress in a suspension of spherical particles of condensed phase in its slightly rarefied vapour gas

Abstract: The rheological behaviour of a dilute suspension of spherical particles of condensed phase dispersed in its own slightly rarefied vapour gas is investigated on the basis of suspension theory (Batchelor 1970) and generalized slip-flow theory for a two-phase system of a gas and its condensed phase derived from the Boltzmann equation. The rarefaction of the gas and the phase-change process at the interfaces of the particles have the effect of reducing the Einstein coefficient of ϕ, volume fraction, in the expression for the effective viscosity in the suspension. In the case in which the pure rarefaction effect alone enters the problem, the coefficient is $\frac{5}{2}(1-2.702\,K)$ , where K is the Knudsen number, a rarefaction parameter defined by K = l / L , l and L being respectively the mean free path of gas molecules and the radius of a spherical particle. When both the rarefaction and the phase-change process are taken into account, this becomes $\frac{5}{2} (1-3.533\,K)$ . These modifications are not small, even at ordinary pressures, when the size of the particles is of the order of microns.

Nonuniform pressure diffusion of a ternary gas mixture in a circular tube in the transition region

Abstract: A new, explicit equation for nononiforni pressure diffusion of a ternary gas mixture in a circular tube is obtained The theory employed is based on the authors'' existing kinetic model of foursided local velocity distributions The diffusion equation shows that transport of the individual components is expressed by a simple summation of two separated terms of diffusional and hydrodynamic flows Validity of the equation is shown by comparison of the fluxes with those measured for a He-Ne-Ar mixture through a diffusion bridge The diffusion equation gives a physical explanation for striking phenomena at low pressures, such as Hoogschagen''s nonequimolar counter-diffusion at a uniform pressure, diffusio-molecular pressure effect, velocity slip at the channel wall, and Knudsen''s minimum in volume flow The concept of "diffusional momentum slip" is newly proposed Use of this concept is effective in deriving the solutions to transport of gases at low pressures directly from the continuum theory