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Showing papers on "Knudsen number published in 1983"


Journal ArticleDOI
TL;DR: In this paper, the experimental investigation discussed here gives experimental confirmation of the slip-flow theory for modeling hydrodynamic gas bearings with clearances below 0.25 microns, and the effects of molecular rarefaction are studied by operating the slider bearing in different gas media of different mean free paths.
Abstract: : The experimental investigation discussed here gives experimental confirmation of the slip-flow theory for modeling hydrodynamic gas bearings with clearances below 025 microns An interferometric technique employing two CW lasers is used to measure the small clearances with an accuracy of 0025 microns The effects of molecular rarefaction are studied by operating the slider bearing in different gas media of different mean free paths Bearings operating at extremely high local Knudsen numbers are studied without approaching excessively high bearing numbers Experimentally measured trailing edge clearances and pitch angles are compared with theoretical predictions using the modified Reynolds equation with velocity slip boundary conditions Excellent agreement between experiment and theory is found for clearances as high as 160 microns to as low as 0075 microns with corresponding ambient Knudsen numbers of 004 and 251, respectively

274 citations


Journal ArticleDOI
TL;DR: In this paper, a correction factor which depends on the Knudsen number was introduced into the expressions for heat fluxes obtained previously based on the continuum approach, and the correction factor was shown to be stronger for smaller particles and it is also more pronounced for an Ar-H2 plasma.
Abstract: The Knudsen effect on heat transfer to a particle exposed to a thermal plasma is important for many practical situations experienced in plasma chemistry and plasma processing. This paper provides theoretical results of this effect based on the “heat conduction potential jump” approach. It is shown that a correction factor which depends on the Knudsen number must be introduced into the expressions for heat fluxes obtained previously based on the continuum approach. The Knudsen effect is stronger for smaller particles and it is also more pronounced for an Ar-H2 plasma (compared to Ar and nitrogen plasmas at the same temperature). Since the Knudsen effect depends on the surface temperature of a particle, calculation of particle heating becomes more complicated.

164 citations


Journal ArticleDOI
Abstract: In this paper computational results are presented which reveal the effects of the Knudsen number on heat transfer and drag of small particles in a flowing thermal argon plasma. The Knudsen number is restricted to moderate values so that “temperature jump” and “velocity slip” conditions may be employed, and for the governing equations the continuum approach remains valid. It is shown that the ratio of the heat fluxes with and without the Knudsen effect is almost identical to the ratio obtained by the authors for the case of pure heat conduction. This fact is very important for modeling of the behavior of particles injected into an actual plasma reactor when the Knudsen effect has to be taken into account.

96 citations


Journal ArticleDOI
TL;DR: In this paper, a diffusion equation for gas permeation through microporous media in the Knudsen regime was obtained theoretically, considering the potential energy between a gas molecule and the solid surface of pores.
Abstract: A diffusion equation for gas permeation through microporous media in the Knudsen regime was obtained theoretically, considering the potential energy between a gas molecule and the solid surface of pores. The equation as a function of temperature contains four parameters, all of which have physical meanings. The most significant of these parameters is the effective potential energy e*, by which the gas diffusion equation as a function of temperature is characterized. Permeabilities of He, H2, CO, N2, O2, Ar, and CO2 through a microporous Vycor glass membrane were measured in the temperature range from 300 K to 950 K. The validity of the diffusion equation obtained was verified experimentally and was shown to express well the previous data. For helium in particular, diffusion is almost gas-phase flow, with no adsorbed flow except at very low temperature. However, the diffusion is affected by the interaction energy between the gas molecules and the solid surface in the pores.

94 citations


Journal ArticleDOI
TL;DR: In this paper, the porosity, mean pore size, and standard deviation of the pore sizes were measured for both the Knudsen and ordinary diffusion regimes to predict diffusion rates.
Abstract: Porous solids have been simulated in the computer as assemblages of spheres. When such assemblages contain spheres distributed in size and randomly arranged in space, the structure of the resulting solid resembles that of a real porous solid. Monte Carlo calculations of gas molecule trajectories through the assemblages were carried out for both the Knudsen and ordinary diffusion regimes. Tortuosities calculated from the simulated diffusion “data” fell in the range obtained experimentally by other investigators. Correlations were obtained that enable the prediction of diffusion rates from measurement of the porosity, mean pore size, and standard deviation of the pore size.

75 citations


Journal ArticleDOI
TL;DR: Calculations for the photophoretic force on a spherical aerosol particle with size much larger than the mean free path of the surrounding gas molecules show that both components of the complex refractive index can be inferred from radiometric measurements.
Abstract: Calculations are presented for the photophoretic force on a spherical aerosol particle with size much larger than the mean free path of the surrounding gas molecules. Very good agreement is shown with recent experimental data. The results show that both components of the complex refractive index can be inferred from radiometric measurements.

39 citations


Journal ArticleDOI
TL;DR: In this article, the location of the top of the atmosphere boundary of a cylindrical rotor of a high-speed countercurrent gas centrifuge with UF/sub 6/ for the enrichment of uranium was investigated.
Abstract: A vacuum exists in the central region of the cylindrical rotor of a high-speed countercurrent gas centrifuge when operated with UF/sub 6/ for the enrichment of uranium. Since solutions of the Navier-Stokes equation are used to determine the isotopic distribution in the rotor, the location of the vacuum core boundary has a direct effect on the predicted separative work of the gas centrifuge. Because criteria for terminating the continuum region based on the Knudsen number are somewhat arbitrary, an approximate model developed by Onsager, which yields an analytical solution, has been used to evaluate the location of the boundary of the vacuum core more correctly. The results show that the location of this ''top of the atmosphere,'' in density scale heights, changes with the peripheral speed of the centrifuge. Using this location in the calculation of separation performance parameters of the gas centrifuge reduces, at the higher peripheral speeds, the contribution of axial diffusion to the effective stage length of a theoretical stage in the centrifuge. The correction due to imposing the top of the atmosphere limitation on axial diffusion becomes significant at high speeds and low countercurrent circulation rates.

35 citations


Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo simulation of the Knudsen diffusion of a gas in a porous solid was carried out using simulated solids whose pore walls are concave.
Abstract: In a previous paper, a Monte Carlo simulation of the Knudsen diffusion of a gas in a porous solid was carried out The simulated porous solid had pore walls that were convex In the present paper, the simulation is repeated using simulated solids whose pore walls are concave It was found that the results of both studies could be correlated by a single equation This equation enables the prediction of the Knudsen diffusiveness from the porosity and mean pore size without resort to a tortuosity factor

29 citations


Journal ArticleDOI
TL;DR: In this article, an exact analytical solution of the Fokker-Planck equation was obtained for the boundary conditions of the given problem and it was shown that Grad's moment method, if carried out to infinite order, does not yield the complete solution.

26 citations


Journal ArticleDOI
TL;DR: In this article, the diffusion coefficients for soot particles were measured in a flame with use of a dynamic light-scattering technique, and the results were in good agreement with the results of kinetictheory calculations.
Abstract: Diffusion coefficients for soot particles were measured in a flame with use of a dynamic-light-scattering technique. Experimental measurements for particle Knudsen numbers in the range from 10 to 75 are in good agreement with the results of kinetictheory calculations.

19 citations


01 Nov 1983
TL;DR: In this paper, the breakdown of the classical CBES field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined.
Abstract: The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Journal ArticleDOI
Kenichi Nanbu1
TL;DR: In this paper, the exact numerical solution of the Couette-flow problem is obtained over the whole range of the Knudsen number by use of the new direct-simulation method.
Abstract: By use of the new direct-simulation method, the exact numerical solution of the Couette-flow problem is obtained over the whole range of the Knudsen number. (The wall Mach number is 3.0) By comparing the obtained solution with the approximate six-moment solution, the accuracy of the latter is examined in detail: as to the flow velocity and shearing stress, the six-moment solution shows reasonable agreement with the simulation solution; as to the temperature, density, and heat flux, the error of the six-moment solution is fairly large in all flow regimes except the near-continuum one; as to the pressure, it is not uniform in the transition-flow regime, differently from the prediction of the six-moment solution.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the diffusion constants of aerosols whose size compares to the mean free path of the gas in three different aerosols, and their experimental diffusion constants do not agree with the kinetic-theory calculations in this intermediate Knudsen regime.
Abstract: The authors have measured the diffusion constants of aerosols whose size compares to the mean free path of the gas in three different aerosols. Their experimental diffusion constants do not agree with the kinetic-theory calculations in this intermediate Knudsen regime.

Journal ArticleDOI
TL;DR: Asymmetric heat generation is detected by Seebeck-voltage measurements in currentcarrying microcontacts, produced by adjoining two wedges of $n$-type silicon in ultrahigh vacuum.
Abstract: Asymmetric heat generation is detected by Seebeck-voltage measurements in currentcarrying microcontacts, produced by adjoining two wedges of $n$-type silicon in ultrahigh vacuum. Decreasing the contact dimensions increases this asymmetry, which arises in the Knudsen regime of ballistic electron transport when the geometric dimensions of the contacts are sufficiently reduced to become comparable to the electron mean free path.


Journal ArticleDOI
TL;DR: In this article, the authors examined pulsed molecular beams of room temperature argon from an electromagnetic valve, and their intensities, conditions for the optimum nozzle-skimmer distances and source pressures, with a flat beam intensity, and the speed ratios were measured.
Abstract: Pulsed molecular beams of about 5 msec duration of room temperature argon from an electromagnetic valve are examined, and their intensities, conditions for the optimum nozzle-skimmer distances and source pressures, with a flat beam intensity, and their speed ratios were measured. The optimum conditions were obtained for the Knudsen number based on the skimmer orifice Kns=2–6. The dependence of the beam intensity for the optimum conditions on the source pressure agrees very well with a modified expression given here based on the sudden freezing model. The attainable speed ratios agree with the semi-empirical relation of Anderson and Fenn.

Journal ArticleDOI
TL;DR: In this paper, the thermomagnetic effect in a Knudsen gas (i.e., the effect of the magnetic field on the heat flow between two surfaces) was investigated for nonspherical scattering of polyatomic molecules.
Abstract: The paper deals with the use of thermomagnetic effect in a Knudsen gas (i.e., the effect of the magnetic field on the heat flow between two surfaces) in studying nonspherical scattering of polyatomic molecules from a solid surface. The dependence of the effect on the field orientation has been experimentally investigated for the first time. As a result, it has become possible to establish the ranks of the tensors that determine the dependence of the scattering probability on the orientation of the angular momentum of a molecule. A new approach for constructing a theory of the effect has been proposed. This approach takes account of the arbitrary law of spherically symmetric scattering and examines the case of appreciable values of the nonsphericity parameters. From a comparison between the theoretical and experimental dependences of the heat flow on the field magnitude and orientation the expressions for the probability of inelastic nonspherical scattering of N 2 and CO molecules by gold and platinum surfaces have been obtained.

Journal ArticleDOI
TL;DR: In this article, conditions for the onset of particle breakup in normal shock waves have been investigated and a normalized particle drag behind the shock has been determined in terms of gas stagnation conditions and particle diameter for a range of gas Mach numbers.
Abstract: Conditions for the onset of particle breakup in normal shock waves have been investigated A normalized particle drag behind the shock has been determined in terms of gas stagnation conditions and particle diameter for a range of gas Mach numbers 1 ⩽ M1 ⩽ 5 by introducing appropriately defined particle Knudsen and Reynolds numbers into analytical expressions for the drag coefficient Numerical computations of the particle drag, normalized with gas stagnation pressure and particle area, indicate a peak at a gas Mach number M1 ≳ 22, The magnitude of the peak was found to decrease with increasing particle diameter and reservoir gas density Criteria for the onset of agglomerate breakup were defined in terms of a modified Weber number for the adhesion mechanisms due to Van der Waals forces, electrostatic attraction and adsorbed surface films These results indicate that larger more closely packed agglomerates made up of smaller constituent particles have a greater tendency to resist breakup for a gi

Journal ArticleDOI
TL;DR: In this paper, the tagged particle BBGKY hierarchy is systematically expanded in inverse powers of the square root of the particle mass in the Brownian limit of the repeated ring equation which itself reduces to the Fokker-Planck equation.
Abstract: The tagged particle BBGKY hierarchy is systematically expanded in inverse powers of the square root of the particle mass. In the Brownian limit, for fixed Knudsen number, the hierarchy reduces to the Brownian limit of the repeated ring equation which itself reduces to the Fokker-Planck equation. The friction coefficient of the Fokker-Planck equation is found to be a functional of the solution of Dorfman, van Beijeren, and McClure's extended Boltzmann equation for a fixed object in a flowing gas. As a consequence, the tagged particle diffusion coefficient calculated in the Brownian limit of the repeated ring equation is valid for all particle sizes.

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of evaporation and condensation for a two-phase system of a vapor gas and its cylindrical condensed phase on the basis of the Boltzmann-Krook-Welander equation when the Knudsen number of the system is small.
Abstract: A problem of evaporation and condensation for a two‐phase system of a vapor gas and its cylindrical condensed phase is considered on the basis of the Boltzmann–Krook–Welander equation when the Knudsen number of the system is small. The analysis was carried out based on the nonlinear equation so that the results can be applied to the case where the Reynolds number of the flow field produced by the evaporation and condensation is finite. The distributions of pressure, temperature, and velocity of the gas are obtained together with the mass and energy flows for both evaporation and condensation cases. Even for very weak condensation, the linearized theory is invalid, and the present nonlinear analysis is required.


Journal ArticleDOI
TL;DR: In this paper, the influence of a magnetic field on a Knudsen flow of N 2 between parallel gold surfaces was measured and changes in drag of order 10 −5 were observed.



Journal ArticleDOI
TL;DR: In this article, the properties of the solutions of the system of Boltzmann equations as the Knudsen number K→0 are considered for a binary mixture of monatomic gases with arbitrary ratios of the component molecular masses, and arbitrary concentrations and collision cross-sections.
Abstract: The properties of the solutions of the system of Boltzmann equations as the Knudsen number K→0 are considered for a binary mixture of monatomic gases with arbitrary ratios of the component molecular masses, and arbitrary concentrations and collision cross-sections. The conditions are found for the hydrodynamic description of the flows of such mixtures in general, and of the multitemperature description in particular, to be applicable. The desirability of introducing multivelocity gas dynamics is discussed. The equations are given in the Navier-Stokes approximation, valid in the case of strongly differing component molecular masses for any ratio between their concentrations, and any ratio between their interaction cross-sections.

Journal ArticleDOI
TL;DR: In this paper, a technique employing momentum equations averaged over channel section is used to obtain the kinetic coefficients describing nonisothermal flow of a gas mixture in a capillary at intermediate Knudsen number (Kn ≤ 0.25).
Abstract: A technique employing momentum equations averaged over channel section is used to obtain the kinetic coefficients describing nonisothermal flow of a gas mixture in a capillary at intermediate Knudsen number (Kn ≤ 0.25).

Journal ArticleDOI
TL;DR: In this article, the authors obtained expressions for Poiseuille flow and thermal creep flow in a capillary at intermediate Knudsen numbers (Kn⩽0.25).
Abstract: Using a method which averages the system of moment equations over the channel section, the authors have obtained expressions for Poiseuille flow and thermal creep flow in a capillary at intermediate Knudsen numbers (Kn⩽0.25).

Journal ArticleDOI
TL;DR: In this article, the authors considered the stationary flow of a binary gas mixture in a cylindrical capillary of radius R under the influence of gradients in pressure, concentration, and temperature, directed along the z axis.
Abstract: method and are valid only at low values of the Knudsen number RKn). Thus the treatment of the results in fact reduces to analysis of hydrodynamic or diffusion slip type equations. Moreover, the convergence of the moment method itself must be verified anew for each concrete problem. Individual attempts to describe isothermal motion of gas mixtures in channels at arbitrary Kn values have been based on solution of the model BirdHtrschfedder-Cur tis (BHC) equation with collision integral in Hamel form. However, it is known that this equation gives a false description of macroscopic characteristics upon transition to the diffusion approximation (Kn<< 1). In fact, the Hamel model contains only three independent free parameters. But even in the simplest case of isothermal expansion of a binary gas mixture accurate (by Chapman-Enskog theory) values of five transfer coefficients are required: viscosity coefficients for each component and the mixture as a whole, and mutual diffusion and barodtffusion coefficients. In the case of [nhomogeneous gas temperature the Hamel model is inapplicable in principle, since it does not describe the phenomenon of thermodiffusion. Thus, the results obtained are at best qualitative. The goal of the present study is a description of motion of a binary gas mixture in a cylindrical capillary under the influence of gradients in total pressure, concentration, and temperature at arbitrary values of Kn. The calculation is based on a third-order approximate kinetic equation [2], ensuring exact description of the system in the diffusion approximation and permitting use of an arbitrary intermolecular interaction potential. Formulation of the Problem. We will consider the stationary flow of a binary gas mixture in a cylindrical capillary of radius R under the influence of gradients in pressure, concentration, and temperature, directed along the z axis. Let the tgmperatures of the components be equal to each other at any point, but variable along the channel length. We assume that the capillary is sufficiently long, and that end effects may be neglected. Then the distribution functions for molecules of each type with weak inhomogeneity intotal pressure p, temperature T, and molar concentration Yi can be written in the form

Journal ArticleDOI
TL;DR: In this paper, the authors investigated gas transfer in cylindrical channels in the presence of heterogeneous physicochemical conversions (filler evaporation in a channel, evaporization on the internal surface of a channel and catalytic reaction of the first order).
Abstract: The paper presents the investigation of gas transfer in cylindrical channels in the presence of heterogeneous physicochemical conversions (filler evaporation in a channel, evaporation on the internal surface of a channel, catalytic reaction of the first order). With the use of the model kinetic equations for the gas molecule velocity distribution function, the solutions of the above problems have been obtained, suitable for the arbitrary ratios of free molecule path length to capillary radius, i.e. the Knudsen number. The comparison between the theoretical and experimental results on filler surface recession in a capillary during evaporation in the presence of a foreign gas is carried out. The applicability limits for the well-known phenomenological relations, used in the theory of drying, are established.