Showing papers on "Knudsen number published in 2001"

Mass flow and tangential momentum accommodation in silicon micromachined channels

Abstract: High-precision experimental results are reported showing the tangential momentum accommodation coefficient (TMAC) for several gases in contact with single-crystal silicon to be less than unity. A precise and robust experimental platform is demonstrated for measurement of mass flows through silicon micromachined channels due to an imposed pressure gradient. Analytic expressions for isothermal Maxwellian slip flows through long channels are used to determine the TMAC at a variety of Knudsen numbers. Results from experiments using nitrogen, argon and carbon dioxide are presented. For all three gases the TMAC is found to be lower than one, ranging from 0.75 to 0.85.

Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime

Abstract: In hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices, the local Knudsen number lies in the continuum–transition regime Navier–Stokes equations are not adequate to model these flows since they are based on small deviation from local thermodynamic equilibrium To model these flows, a number of extended hydrodynamics or generalized hydrodynamics models have been proposed over the past fifty years, along with the direct simulation Monte Carlo (DSMC) approach One of these models is the Burnett equations which are obtained from the Chapman–Enskog expansion of the Boltzmann equation [with Knudsen number (Kn) as a small parameter] to O(Kn2) With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with the Burnett model As a result, several improvements to the conventio

On fluid/wall slippage

Abstract: Certain (non polymeric) fluids show an anomalously low friction when flowing against well chosen solid walls. We discuss here one possible explanation, postulating that a gaseous film of small thickness h is present between fluid and wall. When h is smaller than the mean free path l of the gas (Knudsen regime) the Navier length b is expected to be independent of h and very large (microns).

Fluid flow in nanopores: An examination of hydrodynamic boundary conditions

Abstract: Steady-state Poiseuille flow of a simple fluid in carbon slit pores under a gravity-like force is simulated using a realistic empirical many-body potential model for carbon. In this work we focus on the small Knudsen number regime, where the macroscopic equations are applicable, and simulate different wetting conditions by varying the strength of fluid–wall interactions. We show that fluid flow in a carbon pore is characterized by a large slip length even in the strongly wetting case, contrary to the predictions of Tolstoi’s theory. When the surface density of wall atoms is reduced to values typical of a van der Waals solid, the streaming velocity profile vanishes at the wall, in accordance with earlier findings. From the velocity profiles we have calculated the slip length and by analyzing temporal profiles of the velocity components of particles colliding with the wall we obtained values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall.

Effects of surface roughness on self- and transport diffusion in porous media in the knudsen regime

Abstract: The effect of surface roughness on Knudsen diffusion in nanoporous media is investigated by means of dynamic Monte Carlo simulations in three-dimensional rough fractal pores. These simulations yield new insight and explain a number of apparent inconsistencies by revealing a striking difference between the roughness dependence of transport diffusion and gradientless (self- or tracer) diffusion. Both analytical and simulation results show a significant roughness dependence of self-diffusion in the Knudsen regime. Transport diffusion, on the other hand, is roughness independent, as the fluxes do not depend on the detailed residence time and molecular trajectories.

Unified solutions to classical flow problems based on the BGK model

Abstract: A version of the discrete-ordinates method is used to solve in a unified manner some classical flow problems based on the Bhatnagar, Gross and Krook model in the theory of rarefied-gas dynamics. In particular, the thermal-creep problem and the viscous-slip (Kramers') problem are solved for the case of a semi-infinite medium, and the Poiseuille-flow problem, the Couette-flow problem and the thermal-creep problem are all solved for a wide range of the Knudsen number.

Heat transfer in microchannel devices using DSMC

Abstract: The heat transfer characteristics of supersonic flows in microchannels is studied using direct simulation Monte Carlo (DSMC) method. The velocity components and the spatial coordinates of the simulated particles are calculated and recorded by using a variable-hard-sphere (VHS) collision model. The effects of Knudsen number (Kn) on the heat transfer of the microchannel flows are examined. The results show that the magnitude of the temperature jump at the wall increases with increasing Kn. The heat transfer to the isothermal wall is found to increase significantly with Kn. The possible causes for the increase of wall heat transfer are discussed.

A rarefied gas flow caused by a discontinuous wall temperature

Abstract: A flow of a rarefied gas caused by a discontinuous wall temperature is investigated on the basis of kinetic theory in the following situation. The gas is confined in a two-dimensional square container, and the left and right halves of the wall of the container are kept at different uniform temperatures, so that the temperatures of the top and bottom walls are discontinuous at their respective middle points. External forces are assumed to be absent. The steady flow of the gas induced in the container by the effect of the discontinuities is analyzed numerically on the basis of the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The features of the flow are clarified for a wide range of the Knudsen number. In particular, it is shown that, as the Knudsen number becomes small (i.e., as the system approaches the continuum limit), the maximum flow speed tends to approach a finite value, but the region with appreciable flow shrinks to the points of discontinuity; thus, the overall flow in the container vanishes nonuniformly in the continuum limit. The behavior of the molecular velocity distribution function is also investigated in detail.

The ghost effect in the continuum limit for a vapor–gas mixture around condensed phases: asymptotic analysis of the boltzmann equation

Abstract: A binary mixture of a vapor and a noncondensable gas around arbitrarily shaped condensed phases of the vapor is considered. Its steady behavior in the continuum limit (the limit where the Knudsen number vanishes) is investigated on the basis of kinetic theory in the case where the condensed phases are at rest, and the mixture is in a state at rest with a uniform pressure at infinity when an infinite domain is considered. A systematic asymptotic analysis of the Boltzmann equation with kinetic boundary condition is carried out for small Knudsen numbers, and the system of fluid-dynamic type equations and their appropriate boundary conditions that describes the behavior in the continuum limit is derived. The system shows that the flow of the mixture vanishes in the continuum limit, but the vanishing flow gives a finite effect on the behavior of the mixture in this limit. This is an example of the ghost effect discovered recently by Sone and coworkers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996);...

Application of a parallel DSMC technique to predict flow characteristics in microfluidic filters

Abstract: Using a parallel implementation of the direct simulation Monte Carlo (DSMC) method, periodic MEMS microfilters are studied in detail. The dependence of the flow characteristics on geometry, Knudsen number, pressure difference, spacing between the filter elements, and accommodation coefficients are investigated. By comparing DSMC results with the widely used analytical formulas, the validity range of the analytical approaches is evaluated. The simulation results show that velocity slip exists both on the filter channel walls and on the filter membrane and results in an increased flow rate. Velocity slip increases strongly with decreasing accommodation coefficients. For long channels, this results in a strong increase in flow rate; whereas for short channels, the increase in flow rate is limited. For the filter separations considered in this paper, we observe that separation between filter channels does not influence the flow rate within each channel.

Modelling transport mechanism through a porous partition

Abstract: The physical nature of water flow, in vapour phase, through the pores of a microporous partition has been studied according to the possibilities suggested by the Kinetic Theory of Gases. A method is proposed that permits to decide which is the most reasonable possibility for the transport mechanism. In order to check the proposed model, the phenomenon of membrane distillation has been studied with four commercial membranes, in different experimental conditions. The influence of some relevant parameters, such as mean temperature and stirring rate, has been considered. Tile quantitative influence of the unstirred boundary layers, adjoining both faces of the membrane, has been taken into account. The calculations show that, apparently, the water flux is composed of two contributions: a Knudsen type flux plus a diffusive one.

A numerical investigation of low reynolds number gaseous slip flow at the entrance of circular and parallel plate micro-channels

Abstract: Key words: Hydrodynamic development length, Knudsen number, Micro-channels, Non-continuum flow, Rarefied gas dynamics, Slip flow.Abstract. Rapid progress in Micro-Electro-Mechanical Systems (MEMS) technology duringthe last decade has led to the development of an increasing number of micro-scale deviceswhich involve the manipulation of fluids. An emerging issue in MEMS research, however, isthe realisation that the fluid mechanics at such small scales is not necessarily the same as thatexperienced in the macroscopic world. For example, one of the major difficulties in predictingthe transport of gases through micron-sized channels can be attributed to the fact that thecontinuum flow hypothesis in the Navier-Stokes equations begins to break down when thedimensions of the channel are comparable to the mean free path of the molecules. Under suchconditions, the gas can no longer be regarded as being in thermodynamic equilibrium and avariety of non-continuum or rarefaction effects are likely to be exhibited. Velocity profiles,mass flow rates and boundary wall shear stresses are all influenced by the non-continuumregime. In addition, the length of the hydrodynamic development region at the entrance to achannel may also be affected.The present work forms part of a larger study into microfluidic modelling techniques andexamines the role of the Reynolds number and Knudsen number on the hydrodynamicdevelopment length at the entrance to circular and parallel plate micro-channels. Numericalsimulations are carried out over a range of Knudsen numbers covering the continuum andslip-flow regimes ().0Kn0.1≤≤ The results suggest that rarefaction has only a marginaleffect on the development length in circular pipes. However, in the case of the parallel-plategeometry, entrance development lengths at the upper limit of the slip-flow regime are shownto be almost 25% longer than the corresponding continuum solution.

A Particle-Only Hybrid Method for Near-Continuum Flows

Abstract: EPSM is a particle simulation method for the simulation of the Euler equations. EPSM is used here as part of a hybrid EPSM/DSMC method for the simulation of near continuum flows. It is used where the flow gradients are not large and the flow is expected to be in an equilibrium state. The gradient of local mean free path has been used to detect those regions where EPSM can be invoked. Results are presented for the unsteady flow of a gas in a shock tube with Knudsen numbers in the initial state of 0.01 and 0.002 either side of the diaphragm (based on the length of the initial low-pressure region). The results for the hybrid method are very close to those for pure DSMC. The execution speed of the hybrid code is 1.75 times that of standard DSMC.

Experimental estimate of energy accommodation coefficient at high temperatures.

Abstract: The energy accommodation coefficient (EAC), which is used to characterize gas-surface interactions, was experimentally estimated at high temperatures. A method utilizing laser irradiation to heat up nanoparticles that are generated in a flame was proposed. From the obtained dependence of particle temperature upon laser power, the EAC was derived to be approximately equal to 0.005, which agrees nicely with our recent rigorous theoretical result. It indicates that the efficiency of heat transfer between gas and particles is sufficiently small in high temperature system at large Knudsen numbers.

Continuum description of rarefied gas dynamics. II. The propagation of ultrasound.

Abstract: The equations of fluid dynamics developed in Paper I [X. Chen, H. Rao, and E. A. Spiegel, Phys. Rev. E 64, 46308 (2001)] are applied to the study of the propagation of ultrasound waves. There is good agreement between the predicted propagation speed and experimental results for a wide range of Knudsen numbers.

Continuum description of rarefied gas dynamics. I. Derivation from kinetic theory

Abstract: We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas As in the works of Hilbert, of Chapman, and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulas at each order by using results from previous orders In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process dependent and our heat current depends on the gradients of both temperature and density On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity

Mathematical modeling of vapor-plume focusing in electron-beam evaporation

Abstract: A Monte Carlo model of titanium evaporating from a disk surface shows that collisions between evaporant atoms give rise to plume focusing from the ideal cosine distribution to a cos n distribution, as has been widely reported in experiments. Further, it is shown that under conditions in which hardsphere models are accurate, the cosine power of the distribution (which indicates the extent of focusing) and the fraction of evaporant atoms which recondense at the source are both universal functions of an effective local Knudsen number for the source, which can be empirically fitted to a simple functional form. This function leads to the property that, for a given total evaporation rate, a smaller and more intense vapor source gives rise to more focusing than a broader source. Ring sources are also modeled, and, for a given ratio of ring thickness to outer radius, these also show a dependence of the cosine power and recondensation fraction on the local Knudsen number.

Thermodynamic Activity Measurements with Knudsen Cell Mass Spectrometry

Abstract: Coupling the Knudsen effusion method with mass spectrometry has proven to be one of the most useful experimental techniques for studying the equilibrium between condensed phases and complex vapors. The Knudsen effusion method involves placing a condensed sample in a Knudsen cell, a small "enclosure", that is uniformly heated and held until equilibrium is attained between the condensed and vapor phases. The vapor is continuously sampled by effusion through a small orifice in the cell. A molecular beam is formed from the effusing vapor and directed into a mass spectrometer for identification and pressure measurement of the species in the vapor phase. Knudsen cell mass spectrometry (KCMS) has been used for nearly fifty years now and continues to be a leading technique for obtaining thermodynamic data. Indeed, much of the well-established vapor specie data in the JANAF tables has been obtained from this technique. This is due to the extreme versatility of the technique. All classes of materials can be studied and all constituents of the vapor phase can be measured over a wide range of pressures (approximately 10(exp -4) to 10(exp -11) bar) and temperatures (500-2800 K). The ability to selectively measure different vapor species makes KCMS a very powerful tool for the measurement of component activities in metallic and ceramic solutions. Today several groups are applying KCMS to measure thermodynamic functions in multicomponent metallic and ceramic systems. Thermodynamic functions, especially component activities, are extremely important in the development of CALPHAD (Calculation of Phase Diagrams) type thermodynamic descriptions. These descriptions, in turn, are useful for modeling materials processing and predicting reactions such as oxide formation and fiber/matrix interactions. The leading experimental methods for measuring activities are the Galvanic cell or electro-motive force (EMF) technique and the KCMS technique. Each has specific advantages, depending on material and conditions. The EMF technique is suitable for lower temperature measurements, provided a suitable cell can be constructed. KCMS is useful for higher temperature measurements in a system with volatile components. In this paper, we briefly review the KCMS technique and identify the major experimental issues that must be addressed for precise measurements. These issues include temperature measurements, cell material and cell design and absolute pressure calibration. The resolution of these issues are discussed together with some recent examples of measured thermodynamic data.