Mean Thermal Speed Research Articles

Lattice Boltzmann approach for the simulation of rarefied gas flow in the slip flow regime

For rarefied gas flows in micro-devices, the rarefaction effect becomes significant and the slip at the solid wall becomes an important flow feature. The lattice Boltzmann equation (LBE) method has been used to simulate rarefied gas flows in micro-systems and proved its accuracy in capturing rarefied effect. However, the results of previous studies are not in accordance with each other even though they were started from the same governing equation to solve the same problem, and show only qualitative agreements with those of experimental or analytic approaches. The discrepancies of the results come from the boundary condition and the relation between Knudsennumber and relaxation-time. In this work, the best combination of LBE approach, which employs an equilibrium wall boundary condition and a Knudsen-number-relaxation-time relation derived using the viscosity-based mean free path and mean thermal speed, is suggested. The results of the simulations are compared with the analytic solutions. The present 2D results of microchannel and oscillatory shear-driven gas flows are in excellent agreement with the analytical solution. The results of 3D microchannel flow are also compared with the analytic solutions, and are in good agreement.

Ion Mobilities in Diatomic Gases: Measurement versus Prediction with Non-Specular Scattering Models

Ion/electrical mobility measurements of nanoparticles and polyatomic ions are typically linked to particle/ion physical properties through either application of the Stokes-Millikan relationship or comparison to mobilities predicted from polyatomic models, which assume that gas molecules scatter specularly and elastically from rigid structural models. However, there is a discrepancy between these approaches; when specular, elastic scattering models (i.e., elastic-hard-sphere scattering, EHSS) are applied to polyatomic models of nanometer-scale ions with finite-sized impinging gas molecules, predictions are in substantial disagreement with the Stokes-Millikan equation. To rectify this discrepancy, we developed and tested a new approach for mobility calculations using polyatomic models in which non-specular (diffuse) and inelastic gas-molecule scattering is considered. Two distinct semiempirical models of gas-molecule scattering from particle surfaces were considered. In the first, which has been traditionally invoked in the study of aerosol nanoparticles, 91% of collisions are diffuse and thermally accommodating, and 9% are specular and elastic. In the second, all collisions are considered to be diffuse and accommodating, but the average speed of the gas molecules reemitted from a particle surface is 8% lower than the mean thermal speed at the particle temperature. Both scattering models attempt to mimic exchange between translational, vibrational, and rotational modes of energy during collision, as would be expected during collision between a nonmonoatomic gas molecule and a nonfrozen particle surface. The mobility calculation procedure was applied considering both hard-sphere potentials between gas molecules and the atoms within a particle and the long-range ion-induced dipole (polarization) potential. Predictions were compared to previous measurements in air near room temperature of multiply charged poly(ethylene glycol) (PEG) ions, which range in morphology from compact to highly linear, and singly charged tetraalkylammonium cations. It was found that both non-specular, inelastic scattering rules lead to excellent agreement between predictions and experimental mobility measurements (within 5% of each other) and that polarization potentials must be considered to make correct predictions for high-mobility particles/ions. Conversely, traditional specular, elastic scattering models were found to substantially overestimate the mobilities of both types of ions.

Hydrodynamic interactions between two equal spheres in a highly rarefied gas

This paper describes hydrodynamic interactions between two spherical particles having equal radii, a, and translating with velocities U1 and U2 in a highly rarefied gas. The center-to-center distance between the two spheres is aχ. The gas is at rest far from the two particles. The spheres move with speeds that are much smaller than the mean thermal speed of the gas molecules so that the Mach number, M≡max(U1,U2)/c̄, characterizing the deviation from equilibrium is much less than one. Here c̄ is the mean thermal speed of the gas molecules. Gas molecules are assumed to be diffusively reflected from the particle surfaces. Our analysis is confined to the case where the particle Knudsen number is very large, i.e., Kno≡λo/a→∞, λo being the mean free path of the gas far from the two particles. We first study the free-molecular drag on the two sphere configuration for arbitrary translations of the spheres. For small Mach number, the general time-dependent, nonlinear problem may be approximated by a quasisteady, linear problem in which the spheres are held fixed and molecules reflected from each sphere have a modified Maxwell–Boltzmann distribution of velocities. A standard integral equation formulation based on flux balances at the particle surfaces is then employed to calculate the drag force acting on the spheres. The results obtained can be used as leading estimates for the forces acting on the spheres when Kno≫1 and 2⩽χ≪Kno. We then consider the case where the flow in the vicinity of each sphere is nearly free-molecular, but the flow in the O(aχ) space between the spheres is nearly continuum in nature. In this limit, the flow in the gap between the spheres is studied using the method of reflections. This approach can be used for arbitrary Kno provided Kno≪χ≪Kno M−1. The leading correction to the drag force due to the hydrodynamic interactions between the spheres when Kno≫1 is obtained. In all cases studied, the temperature of the two spheres is assumed to be the same as that of the surrounding gas.

Preacceleration in collapsing magnetic neutral sheets and anomalous abundances of solar flare particles

Levine's (1974) concept of a collapsing magnetic neutral sheet which can accelerate ambient protons to several times the mean thermal speed, provided that the collapse time scale is shorter than the proton Coulomb loss time, is applied to heavier elements in an investigation of the composition of the particles which can be accelerated by such a sheet. Tables of ionization equilibrium are combined with the thermal structure of a constant pressure loop in order to calculate phi<SUB>x</SUB> (the fraction of an element x which is accelerated) of 18 heavy elements, from carbon to nickel which satisfy a maximum-ionization criterion. Normalizing phi<SUB>x</SUB> to oxygen, it is found that relative to the composition of the ambient materials, C and N can be depleted by factors of up to 2-10, while other heavy elements, along with hydrogen, are enhanced. The numerical results obtained are qualitatively similar to anomalous abundances reported among solar flare particles.

Measurement of a Total Atomic-Radiator-Perturber Scattering Cross Section

From work on the $2S\ensuremath{-}2{P}_{\frac{1}{2}}$ transition of atomic $^{7}\mathrm{Li}$, perturbed by noble gases, and use of the photon-echo technique, the first measurement of a total atomic-radiator-perturber scattering cross section is reported. The phase-changing, inelastic, and velocity-changing aspects of collisions contribute to this cross section, which is significantly larger than the corresponding pressure-broadening cross section. Typical velocity changes are found to be roughly one percent of the mean thermal speed.

Orbiting molecular‐beam laboratory

The composition of the atmosphere within the planned orbital envelope of the Space Shuttle (200–1000 km) and the velocity necessary to maintain a stable orbit within that envelope (∠8 km s−1) provide unique conditions for forming a high‐purity, moderate energy beam (∠5 eV) of atomic oxygen. At 500 km for example, atomic oxygen comprises approximately 90% of the atmosphere with the remaining 10% being primarily helium. Since the mean thermal speed of the ambient atomic oxygen is substantially less than the orbital speed, a high‐purity beam can be generated by sweeping through the gas with a series of beam‐forming truncated conical shells. Further, molecular shielding provides a low‐density background inside the conical shells (∠103 cm−3) within which the beam is formed. The characteristics of the beam, including energy distribution, flux, and purity variation with orbital altitude and methods for lowering the mean energy, are presented. The approach to forming the beam, the planned apparatus, modes of deployment (attached to the Shuttle or as a free flyer), operational capabilities, measurement capabilities, and attitude control requirements, are also discussed. Finally, a number of gas–surface interaction experiments that have been proposed for this laboratory are discussed.

Rapidly rotating stars with optically thin stellar winds

view Abstract Citations (33) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Rapidly rotating stars with optically thin stellar winds. Marlborough, J. M. ; Zamir, M. Abstract The analysis of Cassinelli and Castor, concerning the role of the radiation field in the heating, cooling, and transfer of momentum to the atmospheres of early-type stars, is extended to the case of rapidly rotating stars in general, and of Be stars in particular. The general equations for steady flow are presented and the solution discussed for flow in the equatorial plane and in the region near the pole under the assumptions of an optically thin wind and radially streaming radiation. Limiting values for the ratio of velocity of escape to mean thermal speed at the sonic point are obtained if transonic flow is to occur. The observational evidence presently available is considered and is shown to support the theoretical predictions. Publication: The Astrophysical Journal Pub Date: January 1975 DOI: 10.1086/153314 Bibcode: 1975ApJ...195..145M Keywords: B Stars; Early Stars; Optical Thickness; Radiation Effects; Stellar Rotation; Stellar Winds; Electron Scattering; Far Ultraviolet Radiation; Momentum Transfer; O Stars; Radiant Cooling; Transonic Flow; Ultraviolet Spectra; Astrophysics full text sources ADS |

Ion velocity distributions in the auroral ionosphere

For application to studies of the auroral ionosphere we have calculated the velocity distribution of the ions in a weakly-ionized plasma subjected to crossed electric and magnetic fields. We have retained enough terms in the series expansion of the distribution to enable us to determine under what conditions departures from the Maxwellian form become significant and what the nature of these departures is, but we cannot calculate precise values of the distribution function when the departures are large. Departures are negligibly small under conditions appropriate to the auroral ionosphere at low altitudes, where the ion-neutral collision frequency is much larger than the ion cyclotron frequency. At altitudes above about 120 km, however, the magnitude of the departures varies little with altitude. Electric fields greater than 25 mV m −1 cause departures from the Maxwellian distribution that are greater than 20 per cent at random velocities equal to or greater than twice the mean thermal speed of the ions. Under almost all conditions we find that the distribution is depleted in ions moving parallel to the magnetic field relative to those moving perpendicular, an effect that might be detectable in ionospheric measurements of ion temperature.

Structure of Evolving Ion-Acoustic Fronts in Collisionless Plasmas

Exact analytic solutions are obtained to the linearized, two-species Maxwell-Vlasov equations for the evolution of an initial step-function density discontinuity in an initially neutral, collisionless plasma. These solutions have been evaluated numerically for hydrogen plasmas with starting temperature ratios 0 ≤ θ = Te/Ti ≤ 30, for times 0 ≤ τ = ωpit ≤ 100, and over distances into the original low-density region 0 ≤ η = x/Ait ≤ 12, where Ai is the mean thermal speed of ions. For τ ≪ 1 both species simply free stream. By late times (τ ≳ 30) quasineutrality of the perturbation has been established, and it is found that: (1) the ion profiles for θ ≲ 1 exhibit the appearance of free streaming at an enhanced ion temperature, suggesting that the strong Landau damping usually attributed to the low-θ limit might better be termed “ambipolar free streaming,” (2) for θ ≃ 5 they are self-similar and monotonic with a steep leading edge near η = θ1/2 followed by a broad, arched trailing edge accounting for half the density rise, and (3) for θ ≳ 30 they have a steep but spreading leading edge near θ1/2 and general resemblance to the integrated Airy function profile obtainable through a moment equation treatment retaining only the last damped collective mode.

Experimental Investigation of the Normal Modes in a Warm Cylindrical Plasma

Experimental observations of the normal modes in a cylindrical plasma without external excitation is presented. The experimental results compare favorably with theory. Measurement of the high-frequency electromagnetic field outside of the plasma and its spectrum lead to a method of measuring the electrostatic oscillations spectrum in a plasma without perturbing it in any way. Exact measurement of the emission profile at the plasma frequency can give information about the mean thermal speed of the electrons without any assumption about their distribution function.

The growth and decay of resonant plasma oscillations excited by a small pulsed dipole

The application of integration by the method of stationary phase to resonant oscillations excited by a small pulsed dipole is outlined. Both the growth and the decay of the oscillations near the plasma frequency are determined by this method at a fixed distance from the dipole, first in the absence and then in the presence of an external magnetic field. It is shown that Landau damping must be taken into account in the calculation of the growth but not of the decay. The oscillations are shown to spread out with a speed that is about half the mean thermal speed of electrons.Only the decay, not the growth, of the oscifiations near harmonics of the cyclotron frequency can be calculated by the same method. It is shown, moreover, that the amplitude, calculated for an observation point that moves away with sateffite velocity in an ionospheric environment, is only valid for time delays longer than about a minute. Such a result is therefore of no practical interest because the resonances observed from sateffites only last a few milliseconds. The erroneous nature of using such a result and the need for a different approach, such as that used in earlier work by the first author, are thus demonstrated.

Kinetic Theory of Weak Shock Generation by an Impulsively Started Piston

The impulsive piston problem is examined for an early period before nonlinear effects acquire significance. It is assumed that the velocity of the piston is well below the mean thermal speed, that specular reflection occurs at its surface, and that the linearized isothermal Bhatnagar-Gross-Krook equation governs the gas dynamics. With the aid of Fourier and Laplace transforms an exact solution to this equation and also asymptotic solutions for times short and long as compared to a mean free time are derived. At the earliest times a “relative steepening” of the density profile near the isothermal sound speed is observed. Much later a Navier-Stokes shock-type profile is achieved, but, in addition, a careful analysis predicts the presence of a “transient Knudsen layer” near the piston joined smoothly to an extremely weak “kinetic precursor disturbance” far ahead of the shock. Discussion is given to the influence of the chosen kinetic model equation and boundary condition on these results.

On the theory of charging of aerosol particles by unipolar ions in the absence of an applied electric field

Abstract The charging of aerosol particles by unipolar ions in a gaseous medium and in the absence of an applied electric field has been analyzed from the standpoint of the kinetic theory and compared with theories based upon the macroscopic diffusion of ions and experimental data. It is shown that the quasi-steady charging rate can be expressed by the simple equation, d γ d τ = e −γ , where γ is a dimensionless particle charge and τ is a dimensionless particle charging time. The particle charging rate is shown to be unaffected by the mean free path of the ions, and hence by pressure. The theoretical equation shows good agreement with the experimental data when the mean thermal speed of the ions is taken as 1.18 × 104 cm./sec., which corresponds to a molecular weight of 460 for the corona ions used in the charging experiments. It is also shown that the theory based upon the solution of the continuous macroscopic diffusion equation for ions cannot be applied to the electrical charging of aerosol particles in the micron and submicron size range because of the low concentration of ions normally encountered and the essentially discontinuous nature of the charging process.

Optimum estimation of satellite trajectories including random fluctuations in drag

length is in the order of several centimeters. The introduction of two-stream functions makes it possible to include the satellite speed in the self-consistent equations. This analysis determines the potential field around a moving satellite, which is shown not to have spherical symmetry. Furthermore, the determined potential field is significantly associated with the calculation of Coulomb drag, as indicted in Eq. (15). Two-stream instability predicts a long wake trail behind the satellite and high frequency of oscillation which agrees with the fact. By using the actual data of Explorer VIII and the data of the upper atmosphere (satellite speed = 7.4 X 10 m/sec), the mean thermal speed of electrons = 2.06 X 10 m/sec at the altitude of 1000 km, the mean thermal speed of ions = 1.20 X 10 m/sec, and the temperature = 1100 °K; Eq. (13) then gives as tagnation potential of — 0.156 v as compared with the actual measurement of —0.15 v. Of course, the agreement of the surface potential with the experimental one is not a test of the potential distribution, but only of Eq. (13) and, to a lesser degree, of the assumption concerning the surface interaction. However, the interpretation of Explorer VIII data supports qualitatively the nonspherical potential field. References

Nonexistence of Quiescent Plasma States in Ion Propulsion

The problem of neutralizing an ion beam is analyzed within the framework of a one-dimensional collision-free theory. The character of steady-state solutions obtained depends upon the ratio between the mean thermal speed of the electrons and the ion velocity. When the ions are faster, excess electrons are returned to their source from a finite distance behind the electron emitter and the flow of charges is unidirectional (beam-like) further downstream. When the electrons are faster, a ``floating target'' must be postulated downstream to intercept electrons and ions at equal rates and to return excess electrons to the emitter. In this case the flow pattern of the electrons is ``plasma-like.'' Both beam-like and plasma-like states are found to be unstable with respect to small perturbations. Thus the plasma driving a space vehicle cannot be in a quiescent state.

Interaction between Plasma Oscillation and Radiation Field I; Radiation Damping of Plasma Oscillation

The interaction mechanism between plasma oscillation and radiation field in high temperature plasma is discussed with quantum mechanical treatment in the absence of external magnetic field. The radiation damping of plasma oscillation is evaluated and compared with the Landau damping, mode-coupling damping and collision damping. The radiation damping is much larger than the Landau damping in the range of wave vector of plasma oscillation k < k D /7 and is smaller than the mode-coupling damping by the order ( v T / c ) 3 for all range of k , where k D is the Debye cut-off wave vector, v T is the mean thermal speed of electrons and c is the light velocity.

Induced Oscillations in a Rarefied Plasma in a Magnetic Field

The excitation of collective plasma motion by a small charged object moving through a low-density unbounded plasma in an external uniform, static magnetic field is considered. The energy loss per unit path length due to the excitation of collective plasma motion is found as a function of magnetic field strength for an arbitrary angle between the velocity of the object and the field direction. It is assumed throughout this paper that the ion temperature is zero and the velocity of the charged object is small compared to the mean thermal electron speed.

An elementary theory of thermal and pressure diffusion in gaseous binary and complex mixtures: I. General theory

A general treatment of the problem of thermal and pressure diffusion has been given. Equations for thermal and pressure diffusion factors as well as for thermal and pressure diffusion ratios are deduced. Two kinds of free paths have been considered, one related to number density transfer and the other one to mean thermal speed transfer. The ratio of these two free paths depends on the hardness of the molecules.

An elementary theory of thermal and pressure diffusion in gaseous binary and complex mixtures: II. Binary mixtures with experimental comparison

The general treatment of thermal and pressure diffusion given in a preceding paper has been worked out for binary mixtures, by making particular assumptions on the mean free paths, l k and l k ′, for number density and for mean thermal speed transfer respectively. The resulting equations can be easily applied in practice and account for most characteristics of thermal diffusion. It is shown that the inverse of the thermal diffusion factor is linearly dependent on concentrations, to a first approximation, except for the unusual cases to which a change of sign of the thermal diffusion factor with concentration may occur. Such linear dependence has been confirmed by experiments and is also observed for Chapman's r.e.s. first approximation.

The Scattering of Electromagnetic Waves by Plasma Oscillations

Theory of plasma oscillation is applied to the problem of the scattering of -1000Mc waves in the E layer of the ionosphere. It is assumed that a region of the ionosphere having an irregular or turbulent character contains “oscillating domains” or “coherent units” in which free electrons perform synchronous oscillations. These domains are shown to be effective in scattering waves of frequencies ∼(c/v) ωp, where ωp is the plasma frequency, v the mean thermal speed of electrons, and c the velocity of light. A rough estimate indicates that the scattered wave may be observable for a proper setup in the experiment, and that its angular dependence is (sin 1/2 0)-1, 0 being the scattering angle.