Showing papers on "Knudsen number published in 1988"
TL;DR: In this article, a microporous composite membrane consisting of an alumina support with a mean pore diameter of 160 nm and a top layer with 2-4 nm is discussed.
184 citations
TL;DR: In this paper, a theoretical study of thermophoresis of a solid sphere in a rarefied gas in which a uniform temperature gradient and a uniform velocity at infinity exist is made.
Abstract: A theoretical study is made of thermophoresis of a solid sphere in a rarefied gas in which a uniform temperature gradient and a uniform velocity at infinity exist. The analysis is carried out on the basis of the linearized Bhatnager–Gross–Krook (BGK) equation, from which simultaneous integral equations for the density, flow velocity, and temperature are derived. These equations are solved numerically over a wide range of Knudsen numbers covering the area from the slip flow to the nearly free molecular flow. A formula for the variation of the thermophoretic force acting on the sphere versus the Knudsen number is obtained for any value of thermal conductivity of the sphere when there is no imposed flow at infinity. The thermophoretic velocity of a suspended sphere in a gas is also calculated. The flow patterns as well as the distributions of temperature are shown.
77 citations
TL;DR: The correct form of the diffusion equation in the case of an inhomogeneous medium, whose temperature may also vary in space, has been the subject of some debate in this paper.
75 citations
TL;DR: In this article, the effect of particle orientation on the slip correction factor of nonspherical particles was investigated in a millikan apparatus as a function of the Knudsen number.
Abstract: The drag force on aggregate particles of uniform spheres was measured in a Millikan apparatus as a function of Knudsen number. Our experiment was designed to study the effect of particle orientation on the slip correction factor of nonspherical particles. The velocities of charged particles in a gravitational field with and without an applied electrical field were measured. An electrical field strength of 2000 V/cm was used to align doublet and triplet particles. Results showed that an aggregate particle moved in random orientation while in the gravitational field. The same particle moved with its polar axis parallel to the electric field (doublets) or with its plane of centers parallel to the electrical field (triangular triplets). Using a nonlinear regression method, both the dynamic shape factor and slip correction factor could be determined separately from the data. The dynamic shape factors at different orientations were in good agreement with those obtained previously in a sedimentation tank. The sl...
57 citations
TL;DR: In this article, a series of U-Zr alloys were studied by using a tantalum Knudsen cell coupled with a mass spectrometer in the temperature range 1700-2060 K.
38 citations
36 citations
34 citations
TL;DR: Calculations of flow profiles for cylindrical Couette flow of a Lennard-Jones fluid are reported on using the modified moment method for the Boltzmann equation.
Abstract: In this paper we report on calculations of flow profiles for cylindrical Couette flow of a Lennard-Jones fluid. The flow is subjected to a temperature gradient and thermoviscous effects are taken into consideration. We apply the generalized fluid dynamic equations which are provided by the modified moment method for the Boltzmann equation reported previously. The results of calculations are in good agreement with the Monte Carlo direct simulation method by K. Nanbu (Phys. Fluids 27, 2632 (1984)) for most of Knudsen numbers for which the simulation data are available.
29 citations
TL;DR: A comparison between measurements made in numerical experiments and approximate solutions to the Boltzmann equation for a dilute gas in a finite geometry and subjected to a temperature gradient is presented.
Abstract: We present here a comparison between measurements made in numerical experiments and approximate solutions to the Boltzmann equation for a dilute gas in a finite geometry and subjected to a temperature gradient. We first briefly recall a moment method that has been developed to solve the stationary state for the Boltzmann equation with boundary conditions independently of any small gradient expansions and we then apply it to the case of a temperature gradient within the so-called four- and six-moment approximations. These solutions are then compared to the results obtained by nonequilibrium molecular dynamics simulations of a dilute gas enclosed between parallel plates held at different temperatures: Local measurements of the moments of the one-particle distribution function, related to the densities, the temperature, and the fluxes, are reported for various Knudsen numbers and for various temperature gradients.
26 citations
TL;DR: In this article, a combination of Monte Carlo simulation techniques is used to study diffusion of gases in porous media whose structure can be represented by randomly overlapping cylindrical capillaries.
25 citations
TL;DR: In this article, it was shown that every steady discrete velocity model of the Boltzmann equation on the real line has solutions on the half-line (0, ∞) which take prescribed non-negativefi(O) ifξi>0 and approach a certain manifold of Maxwellians asx→∞.
Abstract: We show that every steady discrete velocity model of the Boltzmann equation on the real line,ξi·(d/dx)fi=Ci(f), which satisfies anH-theorem and for which allξi≠0, has solutions on the half-line (0, ∞) which take prescribed non-negativefi(O) ifξi>0 and approach a certain manifold of Maxwellians asx→∞. Such solutions give the density distribution in a Knudsen boundary layer in the discrete velocity case.
TL;DR: In this article, the authors derived an equation for the flow of a Knudsen gas through a pipe in the limit of a small diameter, by explicit calculation, in the form of a diffusion equation with nonconstant coefficients.
Abstract: As a model for diffusion in a nonhomogeneous medium, Landauer [Phys. Lett. A 68, 15 (1978)] proposed a pipe filled with a Knudsen gas. The wall temperature varies along the pipe, and the gas molecules, on colliding with the wall, assume its temperature. Here, by explicit calculation, in the limit of small diameter, an equation is derived for the flow of the gas through the pipe. The derivation is possible because the transverse motion of the gas particles rapidly establishes thermal equilibrium. It can therefore be eliminated using the method of eliminating fast variables. The surviving equation for the slow longitudinal flow has the form of a diffusion equation with nonconstant coefficients.
TL;DR: In this article, a model for slowly evaporating drops is set up and approximated numerically by a variation calculation based on a theorem of Cercignani, for an extended range of Knudsen number and indicated that the popular Fuchs-Sutugin formula is almost a universally valid approximation for a wide range of pressures, condensation coefficients, mass ratios and intermolecular potentials.
01 May 1988
TL;DR: In this article, the second-order slip model gives a better approximation to the FK equation than the first-order model for close spacings or high Knudsen numbers.
Abstract: Recently published air bearing calculations for close spacings or high Knudsen numbers have been contradictory. A. Burgdorfer (1959) introduced a first-order correction to the continuum nonslip boundary condition used in the Reynolds equation. A second-order correction was then suggested by Y. Hsia et al. (1983). Gans (1985) presented developments based on the linearized Boltzmann equation. S. Fukui and R. Kaneko (1986) re-examined Boltzmann's linearized equation and derived a different lubrication equation, the FK model. The present authors have carried out numerical simulations for actual taper-flat slider-bearing designs, using the continuum model, the first- and second-order slip corrections, and the FK model. The calculations show that for Knudsen numbers relevant to this application, the second-order slip model gives a better approximation to the FK equation than the first-order model. >
TL;DR: In this article, the volatilities of some organo-indium compounds have been measured by Knudsen mass loss effusion in the range 10-6 to 10-2 Torr ∗.
TL;DR: In this article, the Hanson-Morse model of the linearized Wang Chang-Uhlenbeck equation is used to calculate the heat transfer from a spherical particle situated in an infinite expanse of a polyatomic gas.
TL;DR: In this paper, the authors investigated the thermophoretic forces acting on a Small Knudsen particle in the neighborhood of a boundary in the case of constant collision cross-section.
Abstract: The thermophoretic forces acting on a Small Knudsen particle in the neighborhood of a boundary have been investigated. The applied temperature gradient is constant, but it is not normal to the wall, thereby leading to thermophoretic forces both normal to and parallel with the wall. Using the velocity distribution of the gas atoms for this problem it has been possible to obtain the variation of the thermophoretic force as a function of distance from the boundary. It is noted, that for equal temperature gradients, the force is greater in the direction normal to the wall than along it. In addition, it is observed that the velocity dependence of the mean free path has a significant effect on the force in the neighborhood of the wall. In contrast to the normal force, which is in the direction of decreasing temperature, the mass flow induced by thermal creep along the wall leads to a parallel wall force that moves the particle in the direction of increasing temperature. When these two forces are compounded they indicate that particles can move in curved paths en route to the wall surface. As a by‐product of the calculation, an exact expression for the thermal creep velocity as a function of distance from the wall for the case of constant collision cross‐section is presented.
TL;DR: In this paper, the authors derived a simple expression for the condensation rate where the jump coefficient is expressed in terms of the Chapman-Enskog solution for diffusion, assuming rigid sphere interactions between the vapor and gas molecules.
01 Mar 1988
TL;DR: In this article, an upper bound of 0.7489 was derived for fiber beds with axes oriented at random in three dimensions, which is slightly smaller than the corresponding factor 0.7630 for fiber axes mutually parallel.
Abstract: Variational upper bound calculations of the permeability to Knudsen flow are performed for several beds of overlapping, long fibers. When the fiber axes are oriented at random, perpendicular to the direction of the net flow, the permeability factor 0.7489 is slightly smaller than the corresponding factor 0.7630 for fiber axes mutually parallel. For fibers with axes oriented at random in three dimensions, the well‐known result 12/13 of Derjaguin is obtained for fiber beds.
TL;DR: In this article, the rate of condensation of a trace vapor on an aerosol particle with the use of the Grad method to solve the Boltzmann equation is extended to a nonisothermal case.
TL;DR: In this paper, a simplified asymptotic Knudsen equation was proposed for porous plugs on the basis of the classical flow equation for long mean free paths of gas flow at room temperature.
TL;DR: The influence of quantum effects during the elastic scattering of atoms on the velocity slip in the jets of some binary mixtures of inert gases is investigated in this article, with the shape of the potential function playing an essential part.
TL;DR: In this paper, the possibility of a laser control of the resonant gases transit through capillaries in the Knudsen and intermediate regimes was investigated and experimental results pointed to the possibility that a laser can be used to control the transit of resonant gas.
Abstract: New experimental results are reported pointing to the possibility of a laser control of the resonant gases transit through capillaries in the Knudsen and intermediate regimes.
TL;DR: In this paper, the drag force on a body (sphere and cylinder) moving in He II is discussed under the conditions that the size of the body is of the order of the mean free paths of thermal excitations.