Showing papers on "Knudsen number published in 1976"
TL;DR: In this article, the terminal velocity of cloud and precipitation size drops has been analyzed for three physically distinct flow regimes: 1) slip flow about a water drop treated as rigid sphere at negligible Reynolds numbers, 2) continuum flow past a non-circulating water drop of equilibrium shape with an unsteady wake at moderate to large Reynolds numbers.
Abstract: The terminal velocity of cloud and precipitation size drops has been analyzed for three physically distinct flow regimes: 1) slip flow about a water drop treated as rigid sphere at negligible Reynolds numbers, 2) continuum flow past a water drop treated as a rigid sphere with a steady wake at low and intermediate Reynolds numbers, and 3) continuum flow around a non-circulating water drop of equilibrium shape with an unsteady wake at moderate to large Reynolds numbers. In the lower regime the effect of slip was given by the first-order Knudsen number correction to Stokes drag. In the middle regime a semiempirical drag relation for a rigid sphere was used to obtain a formula for the Reynolds number in terms of the Davies number. In the upper regime a correlation of wind tunnel measurements on falling drops was used in conjunction with sea level terminal velocities for raindrops to obtain a formula for the Reynolds number in terms of the Bond number and physical property number. The result for the u...
617 citations
TL;DR: In this article, the authors present a complete, modernized theory of the transient hot-wire method for measuring the thermal conductivity of fluids which can be employed in the form of an absolute instrument and can be operated with a precision of 0.02% and an accuracy of 2.2%.
Abstract: The paper contains a complete, modernized theory of the transient hot-wire method for measuring the thermal conductivity of fluids which can be employed in the form of an absolute instrument and which can be operated with a precision of 0.02% and an accuracy of 0.2%. It is a companion paper for ref. 1.
The analysis demonstrates that the instrument can be designed to imitate very closely the behaviour of a finite portion of an infinite line source of constant heat flux, q, which transfers the heat radially into an infinite fluid.
Expressions for the corrections are obtained by a general perturbation method which allows us to examine them one or several at a time. The principal corrections discussed in the form of nine subproblems are: finite inner cylinder, composite cylinders, Knudsen effects, radiation, outer cell circumference, compressibility and natural convection, finite cell dimensions, variable fluid properties and heating over a finite length.
The last section summarizes the most important corrections for a reader who is interested in using them rather than in following the analysis itself. The main text supplies all data required by the designer of an instrument of this type.
390 citations
TL;DR: In this paper, an expression for the gas temperature dependence of the particle slip correction is derived from kinetic theory considerations and is related to experimental measurements of the gas viscosity The expression is simplified for air in the temperature range from 200 to 1000 K and is found to increase with gas temperature more rapidly than the absolute gas temperature.
60 citations
01 Mar 1976
TL;DR: In this paper, the evaporation kinetics of submicron aerosol droplets have been studied by measuring the size of single droplets as a function of time using laser light scattering from the droplet.
Abstract: The evaporation kinetics of submicron aerosol droplets has been studied by measuring the size of single droplets as a function of time using laser light scattering from the droplet. By suspending a charged droplet in an electric field in a light scattering cell, precise measurements of droplet size have been made over a range of total pressures corresponding to diffusion-controlled evaporation and Knudsen aerosol evaporation. The results are compared with available theoretical and semitheoretical predictions for Knudsen aerosol transport processes. For the systems studied, dioctyl phthalate in helium and in nitrogen, the results are consistent with an evaporation coefficient of unity. Furthermore, the technique can be used to determine diffusion coefficients and vapor pressures for relatively nonvolatile species.
53 citations
TL;DR: In this paper, the authors applied the direct simulation Monte Carlo method to typical skimmer flows associated with the production of molecular beams from a supersonic stream and found that the onset of skimmer interference is best correlated with a modified Knudsen number based on the collision cross section at the stagnation temperature, rather than the cross section for the undisturbed stream.
Abstract: The direct simulation Monte Carlo method is applied to typical skimmer flows associated with the production of molecular beams from a supersonic stream. Attention is concentrated on the skimmer interference arising from intermolecular collisions when the mean free path in the stream is of the same order as the diameter of the skimmer entrance. The effects of skimmer geometry, Knudsen number, molecular model, speed ratio, and surface temperature have been investigated. It is found that the onset of skimmer interference is best correlated by a modified Knudsen number based on the collision cross section at the stagnation temperature, rather than the cross section for the undisturbed stream. The interference becomes serious at modified Knudsen numbers of order unity. There are qualitative differences between the flows in slender and wide angle skimmers, the most striking effect being a very sudden breakdown of the flow in a slender skimmer.
42 citations
TL;DR: An expanded use of the mass-loss Knudsen effusion experiment is described in this paper, where the nonstoichiometry created by ionic substitutions in complex oxide systems that contain only one volatile oxide component, can be determined at temperature.
Abstract: An expanded use of the mass-loss Knudsen effusion experiment is described The nonstoichiometry created by ionic substitutions in complex oxide systems that contain only one volatile oxide component, can be determined at temperature A two-phase sample of known composition, prepared rich in the volatile component, is sealed within a Knudsen cell and heated isothermally in vacuum The continuous effusion of the volatile oxide introduces linear mass-loss, and gradually depletes the second phase, whereupon mass-loss becomes non-linear The amount of linear mass-loss establishes the concentration of the volatile oxide component within the single-phase sample and allows description of the sample's defect structure The method is illustrated at 1100°C by resolving the nonstoichiometry produced by the equilibrium substitution of 8 mole % La3+ into Pb(Zr065Ti035)O3, which vaporizes only PbO The experiment eliminates several defect models, and demonstrates that La3+ substitutes completely on the Pb2+su
34 citations
TL;DR: In this article, the distribution of pure vapor between two plane parallel surfaces under the influence of strong evaporation and recondensation is treated by the nonlinear BGK kinetic equation.
Abstract: The distribution of pure vapor between two plane parallel surfaces under the influence of strong evaporation and recondensation is treated by the nonlinear BGK kinetic equation. The boundary conditions allow for evaporation, condensation, and diffuse reflection. The corresponding system of integral equations is brought into a form that allows numerical treatment down to a Knudsen number of 0.1. For two special cases the flux rates as well as the density and temperature profiles are given. In the case of evaporation into an infinite half‐space at the maximum attainable flow rate about 15% of the particles leaving the surface are backscattered.
26 citations
TL;DR: In this paper, the concentration dependences of the binary diffusion coefficients of the systems He-Ar and He-O 2 were reported at 300 K and 1 atm pressure, respectively.
Abstract: The concentration dependences of the binary diffusion coefficients of the systems He-Ar and He-O 2 are reported at 300 K and 1 atm pressure. Two independent sets of data, obtained with a two-bulb cell and a shearing-cell of Loschmidt design, agree within the error of measurement. The data for the two-bulb cell were obtained at pressures where Knudsen effects are important. It was found necessary to improve the extrapolation procedure of van Heijningen et al . by using the results of the dusty-gas model as described by Mason et al.
18 citations
TL;DR: In this article, the transmission probability of molecular gas flow through orifices and especially through circular cylindrical tubes has been compared with the equations of Knudsen, Dushman, Clausing, De Marcus, Berman, and, very recently, Nawyn and Meyer.
Abstract: Starting with the fundamental theory of Knudsen about molecular gas flow through orifices and especially through circular cylindrical tubes, several investigators have derived formulas for the calculation of the transmission probability. Here the equations of Knudsen, Dushman, Clausing, De Marcus, Berman, and, very recently, Nawyn and Meyer are compared. For very accurate calculations the calculation method of Nawyn and Meyer must be used. If accuracies of 0.1% are adequate, the simple equations of Berman can be used.
17 citations
TL;DR: The essential validity of the theories for nonequilibrium effects and the effectiveness of the methods for circumventing background effects were verified by experimental studies with molded nitroglycerin tablets.
10 citations
TL;DR: In this paper, the activities of zinc in solid Al-Zn alloys in the temperature range 625-696 K were determined by means of a multiple rotating Knudsen source coupled with a mass spectrometer.
TL;DR: In this article, the conductive heat transfer in simple monatomic gases and in binary mixtures thereof has been investigated both experimentally and theoretically for temperature differences up to 300 K and for a Knudsen number range of 10 −4 Kn 1.
TL;DR: In this paper, Brownian coagulation of aerosols has been extended into the transition regime, i.e., 0.8-1.6, using the same range of particle size as earlier, but at a reduced pressure.
Abstract: Earlier experimental studies of Brownian coagulation of aerosols have been extended into the transition regime, i.e. Knudsen number values 0.8–1.6. This was done by working with the same range of particle size as earlier, but at a reduced pressure. A number of modifications were made in the experimental technique, including the use of diethylhexylsebacate instead of dibutylphthalate in order to avoid the possibility of loss to the walls by evaporation.
The rate of coagulation at Kn = 0.2 agreed closely with that predicted, using Smoluchowski's coagulation constant for the continuum regime as modified by the Cunningham correction. The rate at higher Knudsen numbers (Kn = 0.8–1.6) was somewhat lower (about 20%) than that predicted by Fuchs' formula for interpolation between the continuum and free molecule regimes.
TL;DR: The mass-loss Knudsen effusion experiment as discussed by the authors is a primary and efficient means for characterizing, at temperature and under equilibrium conditions, the accurate location of all non-isothermal high temperature phase boundaries in any multicomponent material system that incongruently, and preferentially, vaporizes a single subcomponent.
Abstract: The mass-loss Knudsen effusion experiment is described as a primary and efficient means for characterizing, at temperature and under equilibrium conditions, the accurate location of all non-isothermal high temperature phase boundaries in any multicomponent material system that incongruently, and preferentially, vaporizes a single subcomponent.The isothermal equilibrium effusion of the volatile subcomponent is monitored continuously by recording the mass-loss of a Knudsen cell containing a condensed sample of pre-determined composition. The rate of mass-loss is a function of the continuously changing composition of the condensed sample. Consequently, a single experiment can provide several points along either a solidus or liquidus, as well as describing the isothermal nature and extent of single-phase nonstoichiometry.The method is applicable, for example, to a wide range of complex lead, molybdenum, bismuth, lithium, sodium, and tin oxide systems. The ferroelectric PbO-TiO2 binary is selected for illustra...
TL;DR: In this article, the dusty gas model is used to establish the effects of temperature and pressure gradients on catalyst pellet effectiveness factors for reaction systems in which species molecular weights and transport coefficients are indistinguishable and Σνi = 0.
TL;DR: In this article, a semi-empirical formula expressing the volume flow rate of the thermal creep flow and one expressing the thermal transpiration effect were derived, which were in fairly good agreement with the experimental data over the whole range of inverse Knudsen number.
Abstract: Thermal creep flow of a rarefied gas in a circular tube, the flow resulting from a thermal gradient, was analyzed on the basis of the kinetic theory of gases. The thermo-molecular pressure ratio due to the thermal transpiration effect was measured by use of the relative method, and the conductance of the creep flow was obtained from thermo-molecular pressure ratio data. As a result, a semi-empirical formula expressing the volume flow rate of the thermal creep flow and one expressing the thermal transpiration effect were derived. They are in fairly good agreement with the experimental data over the whole range of inverse Knudsen number. A short discussion of the influence of thermal creep flow upon rarefied gas tube flow is also given.
TL;DR: In this paper, a mathematical model is presented to predict the collision cross section for aerosol particles on much larger cooler liquid droplets, under the restriction of small Reynolds number, including consideration of inertial, viscous and thermal forces.
Abstract: A mathematical model is presented to predict the collision cross section for aerosol particles on much larger cooler liquid droplets, under the restriction of small Reynolds number. The model includes consideration of inertial, viscous, and thermal forces and is valid for particles of arbitrary Knudsen number. The results are presented in terms of a collection efficiency, defined as the ratio of the collision cross section to the cross section of the droplet.
TL;DR: In this paper, a general expression involving the transverse radiometer effect for the response of a Knudsen gauge, valid for any vane and heater shape, is derived, and the formula is also valid for all distances and dimensions.
01 Dec 1976
TL;DR: In this article, a set of fluid equations for ternary flow with disparate mass were derived from the kinetic equation assuming a 95 percent, 5 percent mixture of light molecules to heavy molecules.
Abstract: The analysis presented is based on two methods of numerically determining flow parameters: finite-difference solution of the governing fluid dynamic equations, and Monte Carlo simulation. A set of fluid equations for ternary flow with disparate mass were derived from the kinetic equation assuming a 95 percent, 5 percent mixture of light molecules to heavy molecules. The finite-difference solution of these equations initially was obtained for a simple two-dimensional channel separator. A direct simulation method also was applied to the channel. Results of the two methods are presented. The extension of the direct simulation method to separation devices of practical size required the tracing of sample particle trajectories. The flow predicted by the sample particle method is compared with direct simulation results. Results obtained for systems of practical size and Knudsen number are presented for parametric variations of geometry and flow conditions.
TL;DR: In this article, the system of BGK (Bhatnagar, Gross, Krook) equations describing the isothermal flow of a binary gas mixture in a capillary with arbitrary accommodation of the tangential momentum is solved by the Bubnov-Galerkin method.
Abstract: The system of BGK (Bhatnagar, Gross, Krook) equations describing the isothermal flow of a binary gas mixture in a capillary with arbitrary accommodation of the tangential momentum is solved by the Bubnov-Galerkin method. General expressions are given for the kinetic thermodynamic coefficients which are valid in the whole range of Knudsen numbers and have the correct free-molecule and viscous limits. The diffusion-slip coefficients, calculated by using test values of the fraction of diffuse reflection, are compared with the experimental results.
TL;DR: In this article, the problem of recondensation in a binary mixture is treated by the method of moments for "Maxwellian∝ molecules, and analytical expressions are obtained for the rates of mass transfer and the heat fluxes.
Abstract: A rigorous solution of the problem of recondensation between two surfaces with arbitrary Knudsen numbers is possible only on the basis of a consecutive kinetic consideration. For the single-component case, this problem was solved in [1] using the BGK model of the collision integral in the kinetic equation. In [2], for the same purpose, the method of moments for “Maxwellian∝ molecules was used. The case of a binary mixture, in which one of the components is a noncondensing gas was discussed in [3, 4]. Under these circumstances, in [3], a single-relaxation lumped model was used for each component; the model did not reflect many of the properties of the exact collision integral. A more rigorous model (the collision integral in the Hamel form) was applied in [4]. Here there was written a system of integral equations for the hydrodynamic quantities, and its numerical solution is examined in several specific partial cases. In the present article, the problem of recondensation in a binary mixture is treated by the method of moments for “Maxwellian∝ molecules. For the case of small relative difference in the temperature of the surfaces, analytical expressions are obtained for the rates of mass transfer and the heat fluxes, making it possible to shed light on the principal special characteristics of the process of recondensation in a binary mixture.
TL;DR: In this article, an electromagnetic self-adjusting compensation of the radiometric force effected by a definite but non-uniform distribution of temperature in a rarefied gas is given.
TL;DR: In this paper, the problem of acoustic dispersion in rarefied gases is solved on the basis of the hydrodynamical equations of Predvoditelev, and the theoretical equation is compared with the experiments of Greenspan for five monatomic gases.
Abstract: The problem of acoustic dispersion in rarefied gases is solved on the basis of the hydrodynamical equations of Predvoditelev. The theoretical equation is compared with the experiments of Greenspan for five monatomic gases. Theory and experiment are compared up to a Knudsen. number of order unity.
TL;DR: In this paper, a measurement of density and temperature on the stagnation line of a cylinder in cross flow at Mach number M∞ = 5, Knudsen number Kn∞=0.06−0.33, and with temperature factor varying from 1 to 0.11.
Abstract: Results are presented of a measurement of density and temperature on the stagnation line of a cylinder in cross flow at Mach number M∞=5, Knudsen number Kn∞=0.06−0.33, and with temperature factor varying from 1 to 0.11. The effect of degree of rarefaction and the temperature factor on the structure of the perturbed region ahead of the cylinder has been investigated.