Simple Kinetic Theory Research Articles

Thermal transpiration correction in capacitance manometers

Capacitance manometers with sensors maintained at temperatures above ambient show a non-linearity in their pressure response. It is shown that the magnitude of this effect is consistent with the thermal transpiration effect calculated from simple kinetic theory. In addition, good agreement is found with the empirical model of Takaishi and Sensui 5. This model provides a simple method of calculating the response of a capacitance manometer, for a given gas, from a previous calibration with any gas.

The physics of “falling curtain” dry magnetic separation

The separation process in a “falling curtain” of particles is investigated in detail. Each particle experiences gravity, air drag and magnetic forces, as well as collisions with other particles. A simple kinetic theory model is used to model these processes and the separation distance between two different minerals is calculated. The maximum throughput of a superconducting magnet can be as high as 10 tons/hour per meter of effective magnet length, with a recovery in excess of 90%.

Observation of a new thermal wave in a planar superfluid helium layer

The existence of a new thermal wave in He II has been experimentally confirmed in a channel formed between two plane-parallel glass plates. The thermal wave is the limiting case of second sound in narrow channels under the condition that the channel width is small compared to the penetration depth of a viscous wave. It is a strongly attenuated temperature or entropy wave, which is coupled to pressure oscillations, and it shows dispersion. The phase velocity of this wave mode was determined in dependence on the frequency, the channel width, and the temperature. At temperatures between 1.1 K and the $\ensuremath{\lambda}$ point, the results are in very good agreement with a thermohydrodynamic theory. Below 1.1 K the phase velocity is affected by mean-free-path effects of the elementary excitations, and deviations from this theory occur. They can be described by a simple kinetic theory.

A simple kinetic theory calculation of terrestrial atomic hydrogen escape fluxes induced by charge exchange collisions

A simple kinetic theory model is presented for the calculation of atomic hydrogen escape fluxes from earth induced by charge exchange collisions with hot protons. An analytical expression is derived for the nonthermal flux in terms of atmospheric and dynamical variables. The results, which indicate an increase in the nonthermal flux with decreasing exospheric temperature, are in good agreement with the earlier estimates by Bertaux (1975).

Calculation of the integrated sticking coefficient from measurements of the force exerted on a substrate during the deposition of a thin film from an atomic beam

During the growth of a thin film on a substrate by deposition from an atomic beam, momentum is transferred to the substrate by the condensation and partial re-evaporation of the beam atoms. This paper derives a mathematical description of that momentum transfer in terms of simple kinetic theory. If the force exerted by the beam on the substrate can be measured as a function of time, this description allows the integrated sticking coefficient for the deposition process to be calculated.

Generalized reorientation cross section for cylindrically symmetric velocity distributions

Generalized reorientation cross sections are derived for the case of atom–molecule collisions where the molecules initially have a velocity distribution cylindrically symmetric about an axis in the laboratory reference frame. This spatial ordering of the velocity can come about, for instance, by exciting molecular electronic states with a light source whose linewidth is much narrower than the Doppler-broadened absorption line. A simple kinetic theory can be set up in terms of state multipoles that are not completely irreducible; the resulting reorientation cross sections are only slightly more complex than the cross sections occurring in a spherically symmetric velocity field. Two approximations are investigated: a McGuire–Kouri mj-conserving model and a semiclassical model where the orientation of the rotation plane is conserved. The import of the generalized cross sections for several types of experiment and the applicability of the approximate models are discussed.

Theory of Solid-Liquid Interface and Crystal Growth

The equilibrium properties of solid-liquid interface are investigated based on multi-level model (MLM) by Temkin. The simple expression is derived to the shape of the interface. The surface tension is obtained, giving rise to the lattice resistance to the motion of the interface. Simple kinetic theory for the propagation of the interface in nonequilibrium state is introduced. The propagating velocity of the interface is derived within linear approximation. The result is in agreement with that of the computer experiment qualitatively.

The flow of rarefied gases through long tubes of circular cross‐section

AbstractA brief review is presented of various models of rarefied gas flow in long tubes. The complex treatments based on the Boltzmann equation provide only numerical solutions for the transition region unless some arbitrary assumptions are made, while those based on the traditional approach of simple kinetic theory have usually involved empiricism to a greater or lesser extent. An analytic expression is derived here based on a physically realistic model, making use of simple kinetic theory and containing no arbitrary assumptions. The model is completely predictive and adequately describes the flow in long tubes over the entire pressure range, from free‐molecule to continuum laminar flow, and also predicts the “Knudsen minimum” in the transition region. The concept of a “geometric mean free path” is introduced and appears to be useful in analyzing rarefied gas dynamics in a confined space. A relation is also obtained for the viscosity coefficient in the transition region.

TREATMENT OF THE NONEQUILIBRIUM VAPOR MOTION NEAR AN EVAPORATING INTERPHASE BOUNDARY

Strong evaporation problems are characterized by the nonequilibrium vapor motion near the interphase boundary. The solution of this nonequilibrium region, known as Knudsen layer, requires the use of kinetic theory. Kinetic equations have been solved numerically for a plane evaporation problem. Numerical solutions have led to the establishment or the validity of a simple kinetic theory approach to calculate the jump conditions across the Knudsen layer and the net mass, momentum, and heat fluxes. This approach can be used together with the conventional continuum method to calculate How parameters at the outer edge of the Knudsen layer for heat transfer problems in which evaporation occurs at the interphase boundary.

Gas effusion - A relaxation process

A method based based on simple kinetic molecular theory and rate equations used in relaxation kinetics to demonstrate that gas effusion is a relaxation process.

Effects of ion dynamics on tearing modes

The eigenmode equations of several tearing modes are modified to include the ion dynamic terms, which are derived from a simple self-consistent ion kinetic theory. The stabilizing tendency of the ion acoustic term, noted previously by Bussac and co-workers, is confirmed, and the effect of an additional ion-electron friction term on the dispersion relation is discussed. Quantitative expressions for the change in mode frequency are given.

Molecular dynamics by neutron scattering in pure hydrogen and a mixture of hydrogen and argon gases

The inelastic scattering of 2.4 Å neutrons by two states of pure hydrogen and two states of a mixture of hydrogen and argon (at a similar density) have been studied. From these data relaxation times for the velocity auto-correlation function of each state are obtained and are compared to the predictions of a simple hard sphere kinetic theory. It is found that, although the relaxation time depends on the momentum transfer, for pure hydrogen the prediction is in general agreement with experiment. For the mixture the prediction is about 2.5 times larger than the measured values, which is attributed to the reduction in the 'persistence' of the velocity after a collision.

Dynamics of non-linear systems: The kink-phonon interaction

The interaction between non-linear elementary excitations (kinks) and phonons is examined, within the context of perturbation theory previously developed by Hasenfratz and Klein, for the case of theϕ4-model. It is demonstrated that the effect of a kink-phonon collision will be a shift in the kink's position, for which an analytical expression is given. It is conjectured that, as thermal phonons “collide” with the kink, the latter performs a purely diffusive motion. An estimate of the kink diffusion constant is given, based on a simple kinetic theory of kink-phonon collisions. The light scattering spectrum of a gas of non-interacting moving kinks with a thermal velocity distribution function is calculated; a central peak is found, whose structure reflects the kinks' diffusion.

Non-resonant absorption by a dilute gas of symmetric top molecules

A simple kinetic theory of non-resonant absorption by a dilute gas of symmetric top molecules is presented. Attention is focussed on the case where absorption occurs in the presence of static magnetic and electric fields. The macroscopic polarization of interest is found to behave differently in the two cases, but the lineshape has the same simple lorentzian form to a very good approximation. The predictions of the present theory agree with recent experimental observations, and the discrepancies of a previous kinetic theory are analysed and shown to be removable.

Molecular diffusivities of H2 16O, HD16O, and H2 18O in gases

Isotopic effects on the molecular diffusion coefficients of H2 16O, HD16O, and H2 18O have been determined by two independent methods. In the first one, the evaporation of liquid water under controlled laminar flow conditions was investigated. In the second one, the transport of water vapor through a diffusion tube was measured. The molecular diffusion coefficient of natural water vapor in nitrogen was redetermined. At 21 °C and P=760 Hg mm, D=0.244±0.004 cm2/sec. For the isotopic molecules we have DHD16O/DH216O=0.9757±0.0009 and DH218O/DH216O=0.9727±0.0007. Agreement between the data obtained in the pure gas phase experiment and the two-phase experiment shows that the condensation coefficients of the isotopically substituted molecules are identical. Interpretation of the isotopic effects on molecule diffusivities indicates that the relative mass differences between H2 16O, HD16O, and H2 18O alone cannot account for the experimental results. This is more important for the D–H substitution in which the asymetric molecule HD16O is formed. Qualitatively, the displacement of the center of gravity of the molecules H2 16O and HD16O in this substitution can explain the observed effect. Interpretation of these isotopic effects in terms of simple kinetic theory of gases indicates that for rigid spherical molecule models with diameters Γ we have the relation ΓH218O<ΓH216O<ΓHD16O. We calculate from the experimental data ratio of the coefficients of diffusion of the three isotopic molecules in air DHD16O/DH216O=0.9757±0.0009 and DH218O/DH216O=0.9727±0.0007.

Divanadium

The metal concentration and matrix conditions which favor the dimerization of vanadium atoms to divanadium molecules are quantitatively assessed using optical spectroscopy. A simple kinetic theory is presented which enables small metal clusters to be identified in the presence of atomic species. This approach makes use of the fact that a metal atom being deposited is capable of diffusing either on the matrix surface or within a narrow region (the reaction zone) near the matrix surface before its kinetic energy is dissipated sufficiently to immobilize it. The surface diffusion pathway is found to predominate over the statistical generation of dimers. The kinetic result, which suggests that V2 is formed on the matrix surface rather than in the gas phase, is also borne out by the intriguing observation that for a given metal deposition rate the dimer-to-monomer ratio decreases as one increases the atomic weight of the noble gas used to isolate them, with Ar giving the most V2 and Xe the least. Careful concentration experiments in Ar, Kr, and Xe matrices permit the uv–visible transitions of V2 to be identified and the extinction coefficient ratio εV/εV2 to be determined. A qualitative molecular orbital description of V2 is presented in the light of iterative extended Hückel calculations. These computations suggest that high spin divanadium has a strong metal–metal bond which is mainly 4s in character with only small contributions from the degenerate dxz,yz π-bonding set. Visible absorptions observed in the 600–450 nm region are tentatively assigned to electronic transitions localized mainly between the V–V σ-bond and the d-orbital manifold.

Magnon-drag Peltier effect in a Ni-Cu alloy

Peltier-effect measurements to an accuracy of 1% have been made on ${\mathrm{Ni}}_{66}$${\mathrm{Cu}}_{34}$ and ${\mathrm{Ni}}_{69}$${\mathrm{Fe}}_{31}$ at 1.3-4.2 K and magnetic fields to 5.5 T. The Peltier coefficient $\ensuremath{\pi}$ is proportional to ${T}^{2}$ as expected for electron diffusion. However, the absolute value of $\ensuremath{\pi}$ decreases by 7% in Ni-Cu and 4% in Ni-Fe when the field is increased from just above ferromagnetic saturation to 5.5 T, at 4.2 K. This decrease is consistent with a magnon-drag contribution to the Peltier coefficient, which is quenched by the field, at least in the case of Ni-Cu. The magnitude of the contribution, when combined with Hall data, indicates that the magnon gas drifts at a speed close to that of the $4s$ electron gas. Using a simple kinetic theory this implies that magnons relax faster on $4s$ electrons than on impurities. Interpretation of Ni-Fe data is not so clear.

Ice Clouds at the Summer Polar Mesopause

Abstract Recent satellite observations have shown the existence of a persistent layer of light-scattering particles in the vicinity of the polar mesopause during the summer. The suggestion has been made that this layer consists of ice particles, and that noctilucent clouds are a sporadic manifestation of the layer near its low-latitude edge. The consequences of this proposal in terms of the water vapor content of the mesosphere are explored in this paper through the development of a model for such a cloud, in which the water vapor mixing ratio is assumed to be 1 to 10 ppm at 60 km, and the temperature is assumed to drop to values well below 140 K at the mesopause. Water vapor is transported upward by eddy diffusion, and is photodissociated by solar ultraviolet radiation. Sublimation nuclei of radius 10A are assumed to exist in the vicinity of the mesopause, and the growth of the ice particles and their terminal speed of descent are calculated from simple kinetic theory considerations. The results indicate...

On the negative longitudinal magnetoresistance for a thin wire

Abstract A simple kinetic theory is described for the negative longitudinal magnetoresistance of a thin wire.

A theoreticol and experimental study of the centrifugal molecular still

AbstractA mathematical model of the centrifugal molecular still has been derived based on a fully developed profile, but negligible normal and tangential velocity components. Thermal gradients, film thicknesses, and evaporation rates calculated from this mathematical expression correlate well with reported literative values as well as with the present data.Mean distillation rates were measured for five pure liquids on a centrifugal still with an effective evaporating surface area of 100 sq. cm. These experimentally obtained rates for liquids exhibiting ideal behavior agreed quite well with theoretical values predicted on the basis of simple kinetic theory. In the case of an associated liquid, however, rate measurements were found to be only 53 to 90% of the theoretical value. Although these low values tend to support the concept of an evaporation coefficient as a true molecular property, there wasevidence that surface irregularities could have accounted for all or at least part of the discrepancy noted.