Showing papers on "Knudsen number published in 1986"
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TL;DR: In this paper, a light-scattering technique for measuring the diameter of transparent droplets is described, based on the theory of ray optics, which is done on-line by a microcomputer.
227 citations
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TL;DR: In this paper, the most recent studies of rarefied gas flow can be traced back to the early work of Knudsen, who described desorption, evaporation and scattering of molecules from surfaces using the cosine law of scattering.
Abstract: Following a brief historical introduction an overview is given relating the most recent studies of rarefied gas flow to the early work of Knudsen. The first paper submitted in October 1908 (published in 1909) initiated a period of intense activity by Knudsen, Smoluchowski (1910) and, a little later, by Gaede (1913) and Langmuir (1912). This also covered the transition to the already well established hydrodynamic flow expressed in terms of the ratio of mean free path to critical apparatus dimension: which is now referred to as the Knudsen number. The desorption, evaporation and scattering of molecules from surfaces was described in terms of the Knudsen cosine law of scattering. The Knudsen effusion method for determining vapour pressure, also introduced in 1909, has become the main tool for studies of the related problem of the dissociation, chemical bonding and the vaporisation process itself. Clausing (1926) developed, as an alternative to conductances, the concept of transmission probability, still referred to as the Clausing factor, and provided a procedure for their more accurate evaluation in long and short tubes. A number of misconceptions of these early efforts have found their way into the literature and current books on vacuum science and technology. However, detailed studies have clarified the problem of gas-surface interactions; the gas flow in tubes has been tackled with Clausing-type integral equations and by statistical computation techniques based on Monte Carlo analysis procedures adaptable to more complex systems. Results have been confirmed experimentally using molecular-impact pressure probe measuring techniques.
125 citations
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TL;DR: In this article, a theoretical and experimental study is performed for the bulk separation of a ternary mixture by pressure swing adsorption, and three concentrated products can be obtained by cycling the pressure in the adsorber.
Abstract: A theoretical and experimental study is performed for the bulk separation of a ternary mixture by pressure swing adsorption. Three concentrated products can be obtained by cycling the pressure in the adsorber. Three models are formulated for the cyclic process: equilibrium, Knudsen diffusion, and Knudsen plus surface diffusion. The latter model provides the best results when compared with the experimental data, due to the important contribution of surface flux to the total flux in the sorbent pores.
110 citations
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TL;DR: The analytical principles and applications of the theory of Knudsen diffusion are reviewed, with emphasis on gas transport in the soils of planetary bodies as discussed by the authors, where the mean free path of diffusing gas molecules surpasses the size of the pores through which diffusion proceeds.
Abstract: The analytical principles and applications of the theory of Knudsen diffusion are reviewed, with emphasis on gas transport in the soils of planetary bodies. Knudsen diffusion occurs when the mean free path of diffusing gas molecules surpasses the size of the pores through which diffusion proceeds. The process is then dominated by collisions with the pore walls. Computational techniques for deriving the Knudsen coefficient for soils with a nonreentrant cross-section shape are reviewed, along with methods of deriving a coefficient for soils which permit both Knudsen and bulk diffusion. Sample calculations for three pore-size distributions are provided to illustrate the decrease in transport efficiency with increasingly smaller soil pore sizes.
60 citations
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TL;DR: In this paper, the dynamics of a test particle in an infinite tube is investigated and it is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero.
Abstract: The dynamics of a test particle in an infinite tube is investigated. It is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero. This justifies the hypotheses underlying an experiment of Clausing (1930).
33 citations
01 Jan 1986
TL;DR: In this article, the dynamics of a test particle in an infinite tube is investigated and it is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero.
Abstract: The dynamics of a test particle in an infinite tube is investigated. It is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero. This justifies the hypotheses underlying an experiment of Clausing (1930).
33 citations
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TL;DR: In this paper, the behavior of a binary mixture of a vapour and an inert gas around the spherical condensed-phase droplet is studied analytically using kinetic theory, and the results obtained are capable of describing the transition from the diffusion-control to the kinetic-control mechanism in the mass transfer process.
Abstract: The behaviour of a binary mixture of a vapour and an inert gas around the spherical condensed-phase droplet is studied analytically using kinetic theory. By the singular-perturbation method, the linearized Boltzmann equation of B–G–K type is first solved for problems with spherical symmetry under the diffusive boundary condition when the Knudsen number of the problem is small. The macroscopic equations and the appropriate boundary conditions in the form of the temperature and partial-pressure jumps on the interface between the droplet and the gas phase, which enable us to treat the problems at the level of ordinary fluid dynamics, are derived together with the Knudsen-layer structure formed near the interface. Then the velocity, temperature and pressure fields around the droplet are explicitly obtained, as well as the mass, heat and energy flows from it. The results obtained are capable of describing the transition from the diffusion-control to the kinetic-control mechanism in the mass-transfer process. The negative-temperature-gradient phenomenon, a common phenomenon for pure-vapour cases (absence of inert gas), is also possible, manifesting itself more easily as the kinetic-control mechanism becomes prevalent and the critical condition for its existence is given. The present analysis could be applied to other problems with spherical symmetry as well.
28 citations
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TL;DR: In this article, the electron energy distribution is determined to be anisotropic in a low-temperature plasma, when it is far from equilibrium, and the experimental criterion of threshold is true over a wide range of the Knudsen parameter.
Abstract: The electron energy distribution is determined to be anisotropic in a low-temperature plasma, when it is far from equilibrium. This leads to a kinetic instability of the highly concentrated beam in rarefied and dense plasmas over a wide range of the Knudsen parameter. The experimental criterion of threshold is true over a wide range of the Knudsen parameter. The beam isotropisation in plasma oscillations is shown to be realised simultaneously with the energy relaxation.
20 citations
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TL;DR: In this paper, the authors developed a new model for calculating the rate of heat transfer from a particle to a surrounding gas, which assumes no relative motion between the particle and gas, and is applicable at all Knudsen numbers.
19 citations
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TL;DR: In this article, an experimental test of the angular distribution function of particles originating from long capillaries has been performed and the results can be described very well by the elementary Clausing theory.
15 citations
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TL;DR: In this paper, the change in the flow due to molecular precession around an external magnetic field was investigated by studying the change of the flow in a flowing Knudsen gas, and the results suggest a strong correlation between type of polarization produced and molecular structure.
Abstract: In a flowing Knudsen gas, molecular angular momentum polarization can be produced by tangential forces resulting from nonspherical molecule–surface interaction. This is investigated by studying the change in the flow due to molecular precession around an external magnetic field. Various types of polarization are observed in CH4, N2, and HD flowing through a Au‐plated channel. The results suggest a strong correlation between type of polarization produced and molecular structure. These data call for model calculations which include surface corrugation.
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TL;DR: In this article, molecular trajectories inside pore walls are computed in the Knudsen region to obtain both collision density and collision numbers, and it was found that these parameters were strongly dependent on the pore structure.
Abstract: In previous papers, Monte Carlo simulations of the Knudsen diffusion of gases in porous solids having convex or concave pore walls have been performed. In the present paper, molecular trajectories inside pores are computed in the Knudsen region to obtain both collision density and collision numbers. It was found that these parameters were strongly dependent on the pore structure. The results obtained here will have applications to reactive flow and heterogenous catalysis.
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TL;DR: In this paper, a linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half-range Hermite polynomials.
Abstract: A linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half‐range Hermite polynomials. The solution retains correct results up to O(Kn2) and suggests that, if the thermal conductivity of the spherical particle is infinite and the impinging molecules suffer complete energy accomodation at the surface, the thermal force of O(Kn2) disappears (or thermal force is very small) in the near continuum regime. The present results also indicate that the thermal force is sensitive to the variation in the energy accomodation coefficient for the accommodation coefficient of tangential momentum nearly equal to unity. With the effect of such accommodation coefficients, the present results are used to explain the existing experimental results from the viewpoint of kinetic theory as long as the Knudsen number is small.
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TL;DR: In this article, a nonlinear model of compressible flow through an orifice, in the region of transition from free molecular to isentropic expansion flow, has been developed and tested for accuracy.
Abstract: A model of compressible flow through an orifice, in the region of transition from free molecular to isentropic expansion flow, has been developed and tested for accuracy. The transitional or slip regime is defined as the conditions where molecular interactions are too many for free molecular flow modeling, yet not great enough for isentropic expansion flow modeling. Due to a lack of literature establishing a well‐accepted model for predicting transitional flow, it was felt such work would be beneficial. The model is nonlinear and cannot be satisfactorily linearized for a linear regression analysis. Consequently, a computer routine was developed which minimized the sum of the squares of the residual flow for the nonlinear model. The results indicate an average accuracy within 15% of the measured flow throughout the range of test conditions. Furthermore, the results of the regression analysis indicate that the transitional regime lies between Knudsen numbers of approximately 2 and 45.
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TL;DR: The simulation of organic haze production ion Titan is selected as an example experiment for detailed study to simulate the photolysis of methane and the subsequent formation of the organic haze particles in the upper atmosphere of Titan.
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TL;DR: In this paper, a kinetic theory is presented for the drag force on objects in rarefied gas flows as a function of the inverse Knudsen number, and it is shown how the coefficients of this expansion are related to various sequences of collisions among the gas molecules and the object.
Abstract: A kinetic theory is presented for the drag force on objects in rarefied gas flows as a function of the inverse Knudsen number. It is demonstrated that an expansion of the drag force around the free molecular limit contains terms that depend logarithmically on the inverse Knudsen number. It is shown how the coefficients of this expansion are related to various sequences of collisions among the gas molecules and the object. The analogy between the inverse Knudsen number expansion for the drag force on objects in rarefied gases and the density expansion of the transport properties of moderately dense gases is elucidated.
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TL;DR: In this article, a predictive model was developed by incorporating the Z-potential approach into the jump theory and the predictions of the model were explored through a case study, which indicated that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions.
Abstract: The Knudsen effect on mass transfer between a plasma gas and a small particle is investigated. A predictive model is developed by incorporating the Z-potential approach into the jump theory. The predictions of the model are explored through a case study. The results indicate that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions. The plasma and the particle surface temperatures are also found to be determining factors. Under certain conditions, it is observed that the Knudsen effect can enhance the plasma-particle mass transfer, contrary to the predictions of the previous near-isothermal models.
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31 Jul 1986
TL;DR: In this article, the authors proposed a method to generate gas with low noise and at low cost by installing a partitioning wall having a number of minute penetration holes permitting Knudsen diffusion between the high-temperature side and the low-tem temperature side and installing a temperature-difference generating mechanism onto the high or low temperature side.
Abstract: PURPOSE:To generate gas with low noise and at low cost by installing a partitioning wall having a number of minute penetration holes permitting Knudsen diffusion between the high-temperature side and the low-temperature side and installing a temperature-difference generating mechanism onto the high-temperature side and/or low-temperature side. CONSTITUTION:In a gas transferring device, a partitioning wall 2 made of Knudsen substance is installed at a proper place in a gas passage 1, and said partitioning wall 2 has a number of penetration holes which satisfy the following equation: k=lambda/a>1, in which the average free path of a gas particle is A, and the diameter of penetration hole is a. A heater 3 is installed onto the high- temperature side of the partitioning wall 2 and a water cooling pipe 4 is installed onto the low-temperature side, and when a temperature difference over 20 deg.C is provided between the high-temperature side and the low-temperature side of the partitioning wall 2, a large amount of gas is transferred from the high-temperature side to the low-temperature side through minute gas holes (penetration holes) permitting Knudsen diffusion. The partitioning wall 2 is constituted from resin film, composite-material film, or ceramic film.
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TL;DR: In this article, the magnetic field effect on a particle flux is investigated by means of the non-spherical molecule surface interaction, which indicates that the gas-surface scattering is dominated by adsorbates.
Abstract: Polarization of molecular angular momentum in a Knudsen flow, which is caused by non-spherical molecule-surface interaction, is investigated by means of the magnetic field effect on a particle flux. Experiments are reported on a number of gases flowing through channels coated with Au, Pt or mica. The results show that the characteristic features of the effect do not vary significantly with the surface, which indicates that the gas-surface scattering is dominated by adsorbates. The differences in magnitude of the effects in the three channels can be explained with a gas-independent scaling factor reflecting differences in macroscopic surface roughness.
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TL;DR: In this article, the steady behavior of a non-condensable gas contained in a vapor by a negligibly small amount is discussed in general terms based on kinetic theory when the Knudsen number of the system is small but the Reynolds number is finite.
Abstract: The steady behavior of a noncondensable gas contained in a vapor by a negligibly small amount is discussed in general terms based on kinetic theory when the Knudsen number of the system is small but the Reynolds number is finite. The macroscopic equations and the appropriate boundary conditions are derived for the description of the behavior of the noncondensable gas at the level of fluid dynamics together with the Knudsen layer corrections near the interfaces between the vapor and its condensed phases. The result shows that, in the present case, the behavior of the noncondensable gas is subject to the motion of the vapor and does not affect it at all. As expected, it indicates clearly the large variation of the number density and pressure of the noncondensable gas during the evaporation and condensation processes of the vapor. The half-space problem of evaporation and condensation is treated briefly as an example of this general analysis to show explicitly some of the qualitative nature of the noncondens...
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TL;DR: In this article, the effect of a magnetic field upon the flow of a rarefied gas between paralel plates is evaluated by a variational method based upon the linearized Boltzmann equation.
Abstract: The effect of a magnetic field upon the flow of a rarefied gas between paralel plates is evaluated by a variational method based upon the linearized Boltzmann equation. With a small set of trial functions, the results are obtained in terms of known matrix elements of the Boltzmann collision operator, so that there are no adjustable parameters. The results, which cover the nearhydrodynamic regime and part of the transition regime, compare well with existing experimental data. Simple formulae, including a sum rule, are given for the Knudsen corrections for the field effect upon viscosity, and interpreted in terms of a parallel decay mechanism. A change of sign, observed in the longitudinal field effect, is also explained.
01 Apr 1986
TL;DR: The analytical principles and applications of the theory of Knudsen diffusion are reviewed, with emphasis on gas transport in the soils of planetary bodies as mentioned in this paper, where the mean free path of diffusing gas molecules surpasses the size of the pores through which diffusion proceeds.
Abstract: The analytical principles and applications of the theory of Knudsen diffusion are reviewed, with emphasis on gas transport in the soils of planetary bodies. Knudsen diffusion occurs when the mean free path of diffusing gas molecules surpasses the size of the pores through which diffusion proceeds. The process is then dominated by collisions with the pore walls. Computational techniques for deriving the Knudsen coefficient for soils with a nonreentrant cross-section shape are reviewed, along with methods of deriving a coefficient for soils which permit both Knudsen and bulk diffusion. Sample calculations for three pore-size distributions are provided to illustrate the decrease in transport efficiency with increasingly smaller soil pore sizes.
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TL;DR: In this article, a singular perturbation method is used to find the normal solutions of the Boltzmann equation with small Knudsen number, and it is proved that the secular terms may be removed by improving the Hilbert expansion and the Enskog expansion.
Abstract: A singular perturbation method is used to find the normal solutions of the Boltzmann equation with small Knudsen number. It is proved that the secular terms may be removed by improving the Hilbert expansion and the Enskog expansion.
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TL;DR: In this paper, the pressure difference induced by a magnetic field in a heat conducting Knudsen gas is investigated and the effect results from molecular angular momentum polarization produced in molecule-surface collisions.
01 Jan 1986
TL;DR: The Direct Simulation Monte Carlo method is used to study the positional history of individual molecules in a gas that is homogeneous at the macroscopic level and is in Maxwellian equilibrium at the microscopic level as discussed by the authors.
Abstract: The Direct Simulation Monte Carlo method is used to study the positional history of the individual molecules in a gas that is homogeneous at the macroscopic level and is in Maxwellian equilibrium at the microscopic level The behavior at small times is characterized by 'persistence of velocity' effects, and a 'random walk' type of dispersal occurs over a longer timescale It is shown that the rate of dispersal can be directly related to the self-diffusion coefficient In addition, the diffusion coefficients are obtained directly from one-dimensional calculations, and the local Knudsen number at which the Chapman-Enskog theory breaks down is determined Results are presented for both simple gases and gas mixtures
01 May 1986
TL;DR: In this article, the authors considered the process of heat and mass transfer of a multiatomic gas in a cylindrical capillary due to the longitudinal pressure and temperature gradients with arbitrary Knudsen numbers.
Abstract: Processes of heat and mass transfer of a multiatomic gas in a cylindrical capillary due to the longitudinal pressure and temperature gradients are considered, with arbitrary Knudsen numbers. The problem is solved on the basis of a linearized kinetic equation with a model collisional term taking account of the excitation of rotational and vibrational degrees of freedom of the molecules. The contributions of internal degrees of freedom of the molecules to the thermal fluxes are analyzed. The dependence of these fluxes on the character of the interaction between the molecules and the channel surface is considered.
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TL;DR: In this article, a study is made of the weak isothermal and nonisothermal evaporation of a particle, taking account of thermodiffusion, for arbitrary Kn numbers and conditions, including the potential of intermolecular interaction.
Abstract: In this paper, a study is made of the weak isothermal and nonisothermal evaporation of a particle, taking account of thermodiffusion, for arbitrary Kn numbers, evaporation-condensation coefficient α, vapor concentration c, and arbitrary potential of intermolecular interaction.
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TL;DR: In this paper, the authors extend their method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer.
Abstract: We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.
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TL;DR: In this article, the smoothed distribution function (SDF) is proposed to obtain a solution to the system of Maxvell-Boltzmann moment equations, which makes possible a considerable simplification in the procedure for calculating moments of the collision integral.
Abstract: A new method is proposed, called the method of “the smoothed distribution function,” which makes possible a considerable simplification in the procedure for calculating moments of the collision integral, and enables us to obtain a solution to the system of Maxvell-Boltzmann moment equations. The approximating distribution function used in the collision integral in the Boltzmann form ensures a limiting process towards continuous expressions for the flux of molecular characteristics. For the example of the solution to the classical problem of heat transfer between two parallel plates with arbitrary Knudsen numbers, a comparison was made of the theoretical results with the results of other analyses, and also with experiment.