Knudsen Effect Research Articles

Effect of pore structure, randomness and size on effective mass diffusivity

AbstractThe effective mass diffusivity 〈 Dm 〉 of large specific surface area catalytic porous coatings is analyzed using 2‐D network models of connecting arms and verified experimentally for a multiple pore length scale coating layer. The network model includes effects of variation in the lattice randomness (Voronoi tessellation in the form of Delaunay lattice triangulation), pore coordination number, pore size (Knudsen effect), and pore‐size distribution on the predicted 〈 Dm 〉. The effect of pore poisoning, resulting in a pore blockage, is analyzed. Correlations for the porosity and pore‐blockage dependency of 〈 Dm 〉, as well as relationships for the pore size (low‐dimensionality) and multiple pore length scale effects, are also discussed. An experiment performed on a catalytic converter washcoat segment (represented by three pore length scales) placed on an otherwise impermeable wall of an electrochemical sensor shows a good agreement with the predicted 〈 Dm 〉 based on a multiple pore length scale medium with parallel diffusion paths.

Contribution of Phonon Drag to the Knudsen Effect in the Superfluid Mixtures of Helium Isotopes

Contribution of phonon drag to the Knudsen effect in 3 He- 4 He mixtures is studied. A set of the model kinetic equations for 3 He-quasiparticles and phonons is solved. The effect of non-equilibrium in the phonon system on the formation of the steady state of 3 He- 4 He mixture in restricted geometry is investigated.

In situ rock salt permeability measurement for long term safety assessment of storage

Abstract A field test was carried out in the Amelie Mine owned by Mines de Potasse d'Alsace (MDPA, France) for the purpose of measuring rock salt permeability away from underground facilities. The selected salt bed is about 1 m thick and located 16 m away from the gallery floor. The permeability was measured by means of nitrogen and saturated brine injection. Theoretical studies indicated that in order to control the `disturbing effects' (thermal effects, chemical reaction between halite and brine), the work should be done at constant temperature and pressure. The field experiment results confirm that rock salt is permeable to gas and brine, even relatively far from underground openings. The measurements of the tests with brine were interpreted satisfactorily by a model based on Darcy's law, with an intrinsic permeability value of 2×10 −21 m 2 and an initial pore pressure value of 1 MPa. Interpretation of the measured gas flow rate shows that: (a) after brine percolation, the capillary pressure effect is significant and (b) gas migration in salt is not controlled by Darcy's law; the Knudsen effect and partial saturation may play an important role.

Size effect in impuriton gas of 3He–4He superfluid mixture

The flow of quasiparticle gas under the action of gradients of thermodynamic quantities in a volume filled with a powder (crocus) is considered. The exact solution of the kinetic equation is obtained in terms of the matrix elements of the collision integral for quasiparticles and partial cross sections of quasiparticles scattering by crocus. The condition describing a steady nonequilibrium state of the quasiparticle gas in a volume filled with a porous material is determined. The obtained results are valid for arbitrary relations between the frequencies of collisions of quasiparticles with one another and with powder particles. The Knudsen effect in a degenerate quantum gas is studied, and the transition from the Knudsen to hydrodynamic flow of quasiparticle gas is analyzed. The steady nonequilibrium state of the impuriton gas in the 3He–4He superfluid mixture is investigated in a confined geometry.

Knudsen effect in gas of impuritons of3 He−4 He superfluid mixtures

Knudsen effect in the gas of impurity excitations (impuritons) of3He−4He superfluid mixtures was studied by theory with account of the interaction between quasiparticles and deviation of those dispersion law from quadratic one. The conditions under which the Knudsen effect in typical experimental device can be observed are discussed. Such a device consists of two vessels filled with superfluid mixtures at different temperatures and concentrations and connected by the set of narrow capillaries. Using the solution of kinetic equations the relations between temperatures and concentrations were found at stationary conditions. The influence of geometry and size of capillaries on Knudsen effect are investigated.

IR emission spectroscopy of silica aerogel

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.

Untersuchungen zur Trennung von Gasen an mikroporösen Membranen

AbstractStudies of Gas Separation on Microporous Membranes. The composition of Gas Mixtures can be influenced with the aid of microporous membranes by exploitation of the Knudsen effect. The components of lower molecular mass are enriched in the permeated gases while the components of higher molecular mass are concentrated in the retained gases. The best separation is achieved at higher Knudsen numbers. The maximum achievable separation factor is limited by the molecular mass ratio. Hence the gas components in the permeate can be enriched or depleted but never completely separated. In the present experiments, separation factors up to 1.39 and enrichment factors up to 1.10 were attained. However, these values should be substantially improved on use of surface modified porous membranes. Use of ceramic membrane materials permits use of this separation mechanism at very high temperatures.

Hydrodynamic electron flow in high-mobility wires.

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.

Simulation of heat and momentum transfer in complex microgeometries

In this article we present a time-accurate computational model based on the slip-flow theory to simulate momentum and heat transport phenomena in complex microgeometries, encountered in typical components of microdevices such as microcapillaries, microvalves, microrotors, and microbearings. In the first part, we present extensions to the classical Maxwell/Smoluchowski slip conditions to include high-order Knudsen number effects as well as to take into account the coupling of momentum and heat transfer through thermal creep and viscous heating effects. The numerical method is based on the spectral element technique; validation of the method is obtained by comparison of the numerical simulation results in simple prototype flows (e.g., channel slip-flows) with analytical results. Reduction of pressure drop in microchannels, reported in similar experimental studies, is investigated using slip-flow theory and simulations. In the second part, we consider model inlet flows and a slip-flow past a microcylinder. The effect of slip-flow on skin friction reduction and associated increase in mass flow rate as well as the variation of normal stresses is investigated as a function of Knudsen number. Finally, the effect of compressibility is examined and possible extensions of the current model to take into account such effect are discussed.

Molecular Dynamics Computer Simulations of Diffusion in Porous Silicates

ABSTRACTIn this work a newly developed dual control volume grand canonical molecular dynamics technique simulates the diffusion of gas in a cylindrical pore. This allows spatial variation of chemical potential and hence an accurate simulation of steady state pressure driven diffusion. The molecular sieving nature of imicroporous imogolite models and the Knudsen effect are discussed and compared with experimental data.

A unified approach to plasma-particle heat transfer under non-continuum and non-equilibrium conditions

A model for the heat transfer from a stationary, infinite plasma to a particle is developed so as to include rarefaction effects over the entire range of Knudsen numbers, and thermal and chemical nonequilibrium in the vicinity of the particle surface. The overall heat transfer rate is obtained by separately determining the contributions due to heavy species conduction and to energy transport by ion flow to the particle surface. Knudsen effects are accounted for by means of Sherman's interpolation formula for the conduction problem and its equivalent in electrostatic probe theory for the ion transport to the surface. Results are presented for argon plasmas in the pressure range 0.1–1 atm, and for particle sizes in the range 10–100 μm.

Particle heating in a thermal plasma

Abstract

Ballistic charge-carrier transport in semiconductor point contacts.

Investigations of Joule heat generated in the vicinity of well-defined semiconducting microcontacts indicate the existence of a Knudsen effect in solids, in analogy to the Kundsen flow in gases, provided the contact diameter is sufficiently small compared to the mean free path of the carriers. The Joule heat is produced asymmetrically in the downstream part of the constriction, independently of the semiconducting material, type of electronic carrier, and carrier doping. Our experiments with n-type Si, p-type Si, and n-type GaAs show that this dimensionality effect is a general phenomenon in reduced geometries and that ballistic carrier transport is intimately correlated with asymmetric heat production.

Particle-gas mass transfer under plasma conditions

A simple analytical method is proposed for particle-gas mass transfer calculations under plasma conditions. This method, called the Z-potential method, fully accounts for the temperature variation of the gas transport properties while permitting use of the convenient isothermal expression Sh = 2.0. The Z-potential approach is also found to be extremely useful in ascertaining the Knudsen discontinuum effect on mass transfer between the plasma gas and a small particle. A predictive model for the Knudsen effect, developed by combining the Z-potential approach with the jump theory, is illustrated in detail by means of a case study on a nitrogen plasma system.

Knudsen effect on plasma-particle mass transfer. I. Formulation and application to self-diffusion

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.

On the electron-electron contribution to the low-temperature electrical resistivity of thin wires

The authors present, within the framework of the linearised Boltzmann equation and for a metal with a spherical Fermi surface, a theoretical analysis of the electrical resistivity of wires in the presence of normal electron-electron scattering, Umklapp electron-electron scattering and electron-impurity scattering when surface effects are not negligible. They give both approximate analytic and exact numerical results which, besides showing the general behaviour of the electrical resistivity with varying temperature, are able to explain from first principles of the Gurzhi effect and the Knudsen effect in metals. A comparison of the theoretical results with recent experimental data on the electrical resistivity of thin wires of potassium shows very satisfying agreement from both a qualitative and a quantitative point of view.

Effect of electron-electron scattering on the anomalous surface impedance

An analysis of the contribution of normal electron-electron scattering to the anomalous surface impedance is presented. It is shown that in addition to the negative Black-Mills term, there also exists a large positive term due to the Knudsen effect. The authors find that the sum of the two terms is positive and in good agreement with the recent data of Love et al. (1982) on the anomalous surface impedance of Cu and Al.

Effect of Pressure on Heat Transfer to a Particle Exposed to a Thermal Plasma

This study is concerned with the effect of reduced pressure on heat transfer to particulate matter injected into a thermal plasma. Reduced pressures in conjunction with the high temperature in a thermal plasma lead to a strong increase of the mean free path in the plasma, and therefore, the Knudsen effect plays an important role in this situation. Based on the heat-conduction-potential jump approach, calculated data are presented for small spherical particles, typical for applications in plasma processing (for example, plasma spraying) and in plasma chemistry. The Knudsen effect severely reduces the heat flux to a particle, even for larger particles (up to 100 μm) at reduced pressures. For small particles (<10 μm) this effect is even felt at atmospheric pressure.

Low-temperature physics: Knudsen effects in liquid helium

Low-temperature physics: Knudsen effects in liquid helium

Behavior of small particles in a thermal plasma flow

In this paper computational results are presented which reveal the effects of the Knudsen number on heat transfer and drag of small particles in a flowing thermal argon plasma. The Knudsen number is restricted to moderate values so that “temperature jump” and “velocity slip” conditions may be employed, and for the governing equations the continuum approach remains valid. It is shown that the ratio of the heat fluxes with and without the Knudsen effect is almost identical to the ratio obtained by the authors for the case of pure heat conduction. This fact is very important for modeling of the behavior of particles injected into an actual plasma reactor when the Knudsen effect has to be taken into account.