Showing papers on "Knudsen number published in 1995"

Gas flow in micro-channels

Abstract: An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 μm wide, 104 μm long, and ranged in depth from 0.5 to 20 μm. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.

Predicting failure of the continuum fluid equations in transitional hypersonic flows

Abstract: The manner in which the Navier–Stokes equations of fluid mechanics break down under conditions of low‐density, hypersonic flow is investigated numerically. This is performed through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. Both normal shock waves and bow shocks formed by flow over a sphere are considered for argon and nitrogen. It is found that a Knudsen number based on local flow conditions and gradients is a convenient and accurate criterion for indicating breakdown of the continuum flow equations. Failure of the Navier–Stokes equations in hypersonic transitional flows occurs both in the shock front and in the region immediately adjacent to the body surface.

Hydrodynamic electron flow in high-mobility wires.

Abstract: Hydrodynamic electron flow is experimentally observed in the differential resistance of electrostatically defined wires in the two-dimensional electron gas in (Al,Ga)As heterostructures. In these experiments current heating is used to induce a controlled increase in the number of electron-electron collisions in the wire. The interplay between the partly diffusive wire-boundary scattering and the electron-electron scattering leads first to an increase and then to a decrease of the resistance of the wire with increasing current. These effects are the electronic analog of Knudsen and Poiseuille flow in gas transport, respectively. The electron flow is studied theoretically through a Boltzmann transport equation, which includes impurity, electron-electron, and boundary scattering. A solution is obtained for arbitrary scattering parameters. By calculation of flow profiles inside the wire it is demonstrated how normal flow evolves into Poiseuille flow. The boundary-scattering parameters for the gate-defined wires can be deduced from the magnitude of the Knudsen effect. Good agreement between experiment and theory is obtained.

Slip Correction Measurements for Solid Spherical Particles by Modulated Dynamic Light Scattering

Abstract: The theoretical expression for the drag force on a spherical particle moving with low Reynolds number in a gas is customarily written by multiplying the Stokes' law expression by a slip correction factor of the form C x = 1 +Kn[γ1 + γ2 exp(-γ3/Kn)], where Kn is the particle Knudsen number and γ1, γ2, and γ3 are empirical constants. We have measured the drag forces on spherical polystyrene latex particles suspended in dry air using the modulated dynamic light scattering technique which is fundamentally different from the Millikan cell approach. Data are time autocorrelation functions of the intensity of light scattered by single test particles from the intersection volume of two coherent laser beams. The data provide detailed information about test particle Brownian motion including the value of the particle diffusion coefficient. Each test particle was held in air suspension by an electrostatic trap to permit measurements to be made on the same particle at air pressures ranging from 760 to 0.2 torr. Data ...

Thermophoresis of a spherical particle in a rarefied gas: Numerical analysis based on the model kinetic equations

Abstract: A kinetic theory for the thermophoretic force and velocity of a spherical particle in a rarefied gas is presented. The analysis is carried out on the basis of the linearized Bhatnagar–Gross–Krook (BGK) and S model [Fluid Dyn. 3, 95 (1968)] kinetic equations. The integral‐moment method of solution for arbitrary values of Knudsen number is employed. The set of integral moment equations was solved by the Bubnov–Galerkin method. The possibility of arbitrary energy and tangential momentum accommodation of gas molecules on the particle surface is taken into account in the boundary condition. The particle–gas heat conductivity ratio Λ is assumed to be arbitrary. The results obtained are compared to the available theoretical and experimental data.

The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation

Abstract: We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures There is a constant external force parallel to the boundaries which may themselves also be moving The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder

Particle behavior in a two-fluid turbulent plasma jet

Abstract: This paper is concerned with the application of a two-fluid turbulence model for plasma spray processes at atmospheric pressure, for improving our physical insight into the plasma/particle interactions. In this two-fluid turbulence model, the turbulent stream is treated as a two-phase mixture. The fluid parcels are assumed to be arranged in fragments, and they can exchange mass, momentum, and other properties. A stochastic approach is then used to study particle behavior under the influence of the two-fluid parcels. The Stokes number is introduced as an indicator of particle dispersion behavior. A series of simulations is performed to include the influence of different injection locations, particle sizes, and injection velocities. The results indicate the importance of the existence of large-scale eddies and variable property, Knudsen, and mass-transfer cooling effects on the particle motion and heating history.

Damping and gas viscosity measurements using a microstructure

Abstract: The equations for squeeze-film damping of a microstructure comprising two plates oscillating normal to each other are used to derive the damping, and hence the viscosity, of six different gases under flow conditions ranging from molecular to almost viscous flow. For all the gases, the effective viscosity, normalized to the free gas viscosity, for flow in the gap between the plates is the same function of pressure when this is expressed as the inverse Knudsen number. The function is identifical in form to Knudsen's pipe-flow correction, but requires a scale change that effectively defines an equivalent diameter for parallel plates. Relative viscosity measurements are made with an accuracy of 1% by the phase technique used, and with a time resolution of 1 s. The possibility of a gas sensor based on the method is discussed.

Spatiotemporal electron dynamics in radio-frequency glow discharges: fluid versus dynamic Monte Carlo simulations

Abstract: A particle-in cell/dynamic Monte Carlo simulation technique was developed to study the spatiotemporal electron dynamics in radio-frequency glow discharges. The electric field profile in a parallel plate one-dimensional geometry was obtained from a self-consistent fluid simulation. Using this profile, the particle-in-cell/dynamic Monte Carlo simulation yielded the spatiotemporal electron velocity distribution function between the electrodes. A strongly electronegative chlorine discharge and an electropositive argon discharge were considered. At a pressure of 100 mTorr, the distribution function was non-Maxwellian except at the midgap of the chlorine discharge. The tail of the distribution was strongly modulated inside the sheath. Electron 'pile-ups' near the walls, charge double layers and negative plasma potential during part of the cycle were observed in the electronegative discharge at 13.56 MHz. Time-average results from the particle-in-cell/dynamic Monte Carlo simulation matched the fluid simulation favourably, even at a local Knudsen number Kn approximately=1, with differences confined mainly to the volume around the plasma/sheath interface.

Modelling binary, Knudsen and transition regime diffusion inside complex porous media

Abstract: The problem of gaseous diffusion inside complex porous media arises in the modeling of many chemical processes (e.g. Chemical Vapor Infiltration (CVI), heterogeneous catalysis in porous catalysts, filtration, etc...). A program computing effective diffusivities in the bulk, Knudsen and transition regimes has been designed and tested, which uses a Monte-Carlo mean-square-displacement algorithm. The porous medium has been represented from a special interpretation of a computer 3D discretized image. Simulations were carried out in a typical case of complex structured porous medium: a stacking of tissues (e. g. 2D woven fiber preform for CVI-densified composite materials). The results are presented as tortuosity factors, i.e. deviations from an equivalent medium made of straight cylindrical pores. The evolution of the diffusivities with the geometrical parameters of the tissues, and with the stacking mode has also been studied. It appears that the perpendicular diffusivity is closely related to the proportion of matching holes between different layers of tissue. The intermediate regime appears for Knudsen numbers lying between 100 and 10 -1 . In this domain, the Bosanquet formula only gives a good description if the Knudsen number is multiplied by a factor γ = 1/4. This phenomenon had been reported, to a lesser extent, for unidirectional random fiber packings.

Flow induced around a sphere with a non-uniform surface temperature in a rarefied gas, with application to the drag and thermal force problems of a spherical particle with an arbitrary thermal conductivity

Abstract: A flow induced around a sphere with a non-uniform surface temperature in a rarefied gas is investigated using the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition. With the aid of the accurate and efficient numerical method developed by the authors with Aoki, the behaviour of the gas (the velocity distribution function as well as macroscopic variables and force on the sphere) is clarified for the whole range of the Knudsen number. In addition, the solutions of the drag and thermal force (thermophoresis) problems of a spherical particle with an arbitrary thermal conductivity are obtained by appropriate superpositions of the present solution and those of a sphere with infinite thermal conductivity, obtained by the authors with Aoki. The resulting thermal force is compared with various experimental data.

Knudsen diffusion in porous catalysts with a fractal internal surface

Abstract: Porous amorphous catalysts often have a fractal internal surface down to molecular scales. The movement of gas molecules inside the narrow channels that constitute all or most of the pore space, is mainly hindered by collisions with the surface, rather than with each other: Knudsen diffusion, rather than bulk molecular diffusion is then the main diffusion mechanism. The influence of the fractal surface morphology on the Knudsen diffusivity is investigated. A momentum transfer technique leads to a smooth field approximation for the Knudsen diffusivity. The dependence of the surface accessibility on the size of the molecules causes the Knudsen diffusivity of a molecule to depend on its effective diameter. Because the previous method assumes a uniform surface accessibility, a first-passage time technique is developed, which accounts for the true accessibility distribution over the surface. The problem is solved analytically and the result is a simple expression of the Knudsen diffusivity. Extensions of this technique to other problems in catalysis and to other fields are discussed. Once a property, like the Knudsen diffusivity, is known for a medium with smooth walls, the method developed here allows us to calculate the same property for a medium with fractal walls.

Thermal bifurcation of scrape‐off layer plasma and divertor detachment

Abstract: Models to investigate the main features of plasma–neutral interactions in the recycling region of a tokamak divertor are developed for the two opposite extremes of fluid and Knudsen neutrals. Both neutral models show that a reduction of the heat flux into the hydrogen recycling region below a critical value leads to bifurcation (or rapid change) of the plasma parameters near the target. This bifurcation causes behavior in the scrape‐off layer, which is in agreement with the following main features of detached divertor regimes in current tokamak experiments: (i) strong decrease of the plasma temperature near the target, (ii) plasma pressure drop in the recycling region, and (iii) strong decrease of the target heat load and plasma flux onto the target. It is also shown that in the Knudsen limit, the neutral density in the divertor region cannot exceed a maximum density, which is of the order of 1–2×1013 cm−3 for current experiments.

Evaporation of a rarefied gas from a cylindrical condensed phase into a vacuum

Abstract: Steady evaporating flows from a cylindrical condensed phase into a vacuum are studied on the basis of kinetic theory. The behavior of the gas (the velocity distribution function as well as the density, velocity, and temperature) is analyzed numerically in detail for the whole range of the Knudsen number defined by the condition of the condensed phase. The discontinuity of the velocity distribution function in the gas, a typical behavior of the gas around a convex body, is analyzed accurately. The flow is highly in nonequilibrium over the whole field except for very small Knudsen numbers. The behavior of the far field from the cylinder, proper to each Knudsen number, differs markedly from that of corresponding flow [Phys. Fluids A 5, 1491 (1993)] from a spherical condensed phase, universally of free molecular type. The height of the velocity distribution function and the temperature of the gas vanish at infinity, without freezing at finite values, except in the free molecular flow.

Direct simulation Monte Carlo calculation of a jet interaction experiment

Abstract: This study deals with the development of a methodology for numerically simulating the interaction of a reaction control system (RCS) jet with a low-density external flow. A European Space Agency experiment was chosen as a test case, since it provided experimental data that could validate some of the numerical results. The initial approach was to focus on several subproblems having direct relevance to the full interaction problem. This enabled different numerical methods to be investigated separately and validated for each part of the interaction problem. In this manner, the best methodology for solving the full interaction problem was developed. The subproblems considered in this study included typical RCS nozzle and plume flows, a flat plate at zero incidence, and the flow past the experimental test model without the control jet firing. Once these calculations were completed, a simulation was performed of the test model with the control jet operating at the experimental density. The results from this final simulation were compared with experimental measurements. Nomenclature = reference diameter, m = Knudsen number at nozzle throat = Knudsen number at nozzle lip = Mach number = number density, molecules/m3 = freestream number density, molecules/m3 = pressure, Pa = Reynolds number T^ef = reference temperature, K 7"waii = temperature of nozzle wall T^ = freestream temperature, K X, Y, Z = Cartesian body coordinates p , - density, kg/m3 Poo = freestream density, kg/m3 Kn\ip M

Effects of roughness orientations on thin film lubrication of a magnetic recording system

Abstract: In this paper, the relations expressing the effects of roughness orientations and molecular mean free path on the roughness-induced flow factors are derived. Such consideration of the effects of roughness orientation on bearing performance is necessary when rotary actuators are used in magnetic recording systems. Using the perturbation approach and the coordinate transformation, the flow factors are derived and expressed as functions of the roughness orientations, the Peklenik numbers, the standard deviations of roughness heights of each surfaces, the inverse Knudsen number and the film thickness ratio of the lubrication film, where h/ sigma is the ratio of average film thickness to standard deviation of the composite roughness. Two orientation coefficients are proposed to reveal the combined effects of Peklenik number and orientation angle and the change of flow factors is analysed as the orientation coefficients vary. Finally, the static performance of a magnetic recording head flying above a rotating disc under the ultra-thin-spacing condition is analysed with roughness and rarefaction effects taken into account. The effects of surface characteristics of the moving surface on load capacity are more significant than those of the stationary surface.

Gas and solute diffusion coefficients in pore networks and its description by a simple capillary model

Abstract: Among the different geometrical descriptions of the pore networks of porous materials, a common one is that of cylindrical pores arranged on a regular lattice. Lattice calculations of diffusivities and other transport parameters are expected to gain increasing interest, both because of their tractability and because of continuing developments in techniques for characterizing porous solids in terms of models of this type. In this study we consider two approaches to the prediction of the apparent molecular and Knudsen diffusivities of diluted simple-cubic lattices: the MC-REMA method of Zhang and Seaton, which explicitly incorporates the geometry and connectivity of the network and is known to give accurate results, and the simple capillary model of Mualem and Friedman, which is computationally very fast. The MC-REMA calculations show that the diffusion coefficients increase both with increasing coordination number and decreasing coefficient of variation of the pore-size distribution. The influence of the coordination number,Z, is found to be more pronounced for small values ofZ, while the effect of the width of the pore-size distribution is less significant at both extremes of highly uniform and highly distributed pore sizes. The simple capillary model of Mualem and Friedman is shown to give a good representation of the accurate MC-REMA results, after correlating a single adjustable parameter toZ and the coefficient of variation of the pore-size distribution.

Heat conduction through a rarefied gas between two rotating cylinders at small temperature difference

Abstract: Numerical calculations of heat transfer between two coaxial rotating cylinders at a small temperature difference are carried out over wide ranges of the Knudsen number and the angular velocity The calculations have been performed based on the S-model of the Boltzmann equation by the discrete velocity method It has been confirmed that in a rotating gas a radial temperature gradient causes both radial and tangential heat fluxes Also, it has been found that the radial heat flux is affected by the rotation

Numerical analysis of hypersonic low-density scramjet inlet flow

Abstract: Hypersonic low-density flow around a two-dimensional scramjet inlet model has been analyzed using the direct simulation Monte Carlo (DSMC) method. The predominant features of hypersonic flows, such as a thick viscous layer due to the low-density fluid together with shock-boundary-layer interaction and shock impingement as well as shock-induced separation, are encountered in this type of flowfield. Three hypersonic flowfields with different degrees of rarefaction are investigated. The freestream Knudsen numbers of the flowfields based on the height of the duct passage are in the range of 0.02-0.12. Conventional continuum gasdynamics based on the concept of a local equilibrium may not be adequate to describe this type of flowfield accurately. The pressures obtained by the DSMC simulation are compared with available experimental data. Good agreement is obtained with previous experimental data and with theoretical solutions for similar wedge flow cases near the leading edge of the ramp centerbody. Good agreement is observed with the experimental data of Minucci and Nagamatsu except for some discrepancies, especially in the lower-density cases, which may be partially attributed to three-dimensional effects and/or to experimental uncertainty.

IR emission spectroscopy of silica aerogel

Abstract: A spectral method (infrared emission spectroscopy) to characterize thermal properties of silica aerogel is described. It provides spectral information on heat flow. An emission chamber permitted measurement of thermally emitted radiation due to an applied temperature gradient. Different boundary emissivities and different pressure conditions can be applied, so that the Knudsen effect can be observed. A rigorous numerical treatment of the underlying heat transport mechanism was necessary for a correct interpretation of the measured data. Internal parameters of the aerogel sample had to be modelled in an adequate way (incorporation of the Knudsen effect, modelling of the spectral absorption coefficient with the help of effective medium theories). Measurements and computer simulations of the thermally emitted radiation are presented. The influence of the Knudsen effect on the emission spectra of the aerogel was studied. Analysis of emission spectra in combination with an integral measurement of the total heat flow in principle allows a fit of the internal aerogel parameters, i.e., the mean pore size of the samples, the thermal conductivity of the silica skeleton and the spectral absorption coefficient.

Asymptotic Analysis of Ultra-Thin Gas Squeeze Film Lubrication for Infinitely Large Squeeze Number (Extension of Pan’s Theory to the Molecular Gas Film Lubrication Equation)

Abstract: Ultra-thin gas squeeze film characteristics are analyzed by extending Pan's asymptotic theory for infinite squeeze number to the molecular gas film lubrication equation which was derived from the linearized Boltzmann equation and is valid for arbitrary Knudsen numbers. The generalized asymptotic method is shown to solve the boundary value equation which contains the flow rate coefficient as a function of the product of pressure P and film thickness H. Numerical results are obtained for a circular squeeze film. The PH ratio and the load carrying capacity ratio to those of continuum flow both decrease when the average film thickness is less than several microns because of molecular gas effects

Theory of free boundary step coverage in chemical vapor deposition

Abstract: A new theory of chemical vapor deposition (CVD) with variable diffusion coefficient describes the time evolution of the free surface of a film to closure on trench walls. The diffusion coefficient decreases with the distance from the mouth and with time as the trench is closed by film formation, and it reduces to the conventional continuum value at high pressure. However, the authors predict higher rates of transport than by Knudsen diffusion at low pressure in small features as do ballistic transport calculations. The shape of the film and its uniformity depend on the Damkoehler number (Da), the aspect ratio (A), and the Knudsen number ({lambda}{sub 1}) for a first order surface reaction. Free boundary solutions were obtained to closure for various values of these parameters, and the step coverage at closure is correlated well by two dimensionless numbers, DaA{sup 2} and {lambda}{sub 1}, over a wide range of reactor pressures (10{sup {minus}2}--760 Torr). The generalized correlation of the figure of merit for step coverage in the tetraethyl orthosilicate--ozone agrees well with the experimental results. The feature scale model, coupled with commercial reactor models through the diffusive flux of reactant at the wafer surface, enables gap filling/step coverage to bemore » determined as a function of process conditions.« less