Showing papers on "Particle published in 1970"

The stress system in a suspension of force-free particles

Abstract: The purpose of the paper is to consider in general terms the properties of the bulk stress in a suspension of non-spherical particles, on which a couple (but no force) may be imposed by external means, immersed in a Newtonian fluid. The stress is sought in terms of the instantaneous particle orientations, and the problem of determining these orientations from the history of the motion is not considered. The bulk stress and bulk velocity gradient in the suspension are defined as averages over an ensemble of realizations, these averages being equal to integrals over a suitably chosen volume of ambient fluid and particles together when the suspension is statistically homogeneous. Without restriction on the type of particle or the concentration or the Reynolds number of the motion, the contribution to the bulk stress due to the presence of the particles is expressed in terms of integrals involving the stress and velocity over the surfaces of particles together with volume integrals not involving the stress. The antisymmetric part of this bulk stress is equal to half the total couple imposed on the particles per unit volume of the suspension. When the Reynolds number of the relative motion near one particle is small, a suspension of couple-free particles of constant shape is quasi-Newtonian; i.e. the dependence of the bulk stress on bulk velocity gradient is linear. Two significant features of a suspension of non-spherical particles are (1) that this linear relation is not of the Newtonian form and (2) that the effect of exerting a couple on the particles is not confined to the generation of an antisymmetrical part of the bulk stress tensor. The role of surface tension at the particle boundaries is described.In the case of a dilute suspension the contributions to the bulk stress from the various particles are independent, and the contributions arising from the bulk rate of strain and from the imposed couple are independent for each particle. Each particle acts effectively as a force doublet (i.e. equal and opposite adjoining ‘Stokeslets’) whose tensor strength determines the disturbance flow far from the particle and whose symmetrical and antisymmetrical parts are designated as a stresslet and a couplet. The couplet strength is determined wholly by the externally imposed couple on the particle; but the stresslet strength depends both on the bulk rate of strain and, for a non-spherical particle, on the rate of rotation of the particle relative to the fluid resulting from the imposed couple. The general properties of the stress system in a dilute suspension are illustrated by the specific and complete results which may be obtained for rigid ellipsoidal particles by use of the work by Jeffery (1922).

Dynamics of Dusty Gases

Abstract: This review deals with a certain restricted portion of the mechanics of heterogeneous media. The volume fraction of the solid-particle or droplet cloud is considered to be so small that the interaction between individual particles may be neglected or highly simplified. This limitation applies to the individual flow fields about the particles as well as to collisions, and to heat and mass transfer as well as to momentum exchange between phases. Under this circumstance, the problem of detailed transport processes between particles and gas may be treated independently of the complete dynamical problem, and this aspect, being a study of its own, will be suppressed to a considerable extent here. There are problems, such as the impact of particles on walls, the concentration separation in boundary layers or pipe flow, in which the distortion of the particle flow field due to a solid wall or another particle is the central physical issue. These problems therefore lie outside the scope of the review. On the other hand, the structure of shock waves, sound attenuation, and many flow-field problems can be treated within our present restrictions. The basic equations and exchange processes will be introduced first, together with the physical parameters that indicate the relative importance of the particle cloud and the limitations of the dusty-gas concept. Then several different problems will be discussed that lead to some of the significant results in the field and illustrate analytical techniques that have proven useful.

Hidden-Variable Example Based upon Data Rejection

Abstract: A deterministic local hidden-variable model is presented which describes the simultaneous measurement of the spins of two spin-\textonehalf{} particles which emerged from the decay of a spin-zero particle. In this model the measurement of the spin of a particle has one of three possible outcomes: spin parallel to the apparatus axis, spin antiparallel to the apparatus axis, or the particle goes undetected. It is shown that agreement with the predictions of quantum theory is obtained provided the experimenter rejects the "anomalous" data in which only one particle is detected. A reasonably model-independent lower bound to the fraction of undetected particles is also computed: It is found that in 14% of the decays or more, one or both of the particles will go undetected.

Theory of magnetic suspensions in liquid crystals

Abstract: The present paper discusses some properties of small, elongated particles suspended in a nematic or cholesteric phase, with low concentrations (typical volume fraction occupied by the particle f ≊ 10-3). We find that in most cases the particle axis should be locked and parallel to the local nematic axis n(r). If such colloidal suspensions could be made successfully with magnetic grains, it should be possible to prepare « ferronematics » or « ferrocholesterics », where locally all particles are magnetized in one direction (colinear to n), and also « compensated » materials with no spontaneous magnetization. These three types of samples should all show remarkable distorsions and phase changes in low external fields H. Similar effects are expected under electric fields with colloidal suspensions of polar rod molecules such as helical polypeptides.

The hyperbolic distribution of particle sizes

Abstract: Many natural collections of small particles, such as cosmic and terrestrial dust, mineral and organic particles suspended in sea water, and fine sediments, have a size distribution well formulated by the equation N = Kx−c, where N is the number of particles larger than size x and K and c are constants. A number of equations are derived for calculating the interesting parameters characterizing hyperbolic distribution, which are illustrated by new Coulter Counter measurements of dust and sea water. An appendix lists useful equations, generalized for different size parameters.

Mechanism of Inclusion Damage in Laser Glass

Abstract: The mechanism of inclusion damage in laser glass is associated with the temperature rise of particles, or surface regions of particles, relative to the surrounding glass. The particles of greatest concern are metallic, although at very high‐power levels ceramic inclusions containing large concentrations of highly absorbing ions can likewise result in failure. Solutions to the heat‐flow problems of a perfectly conducting sphere in a medium of finite conductivity and of the infinite composite solid indicate that temperatures of metal particles subject to a 20‐J/cm−2, 30‐nsec laser pulse can exceed 10 000°K for a range of particle sizes. These high temperatures produce stresses in the glass adjacent to the particles which can exceed the theoretical strength of the glass, and result in failure. The effects on the breakdown condition of flux level and pulse time, as well as the size, shape, thermal expansivity, and spectral emissivity of the particle, and the heat capacity and thermal conductivity of particle and glass are specified. Observations of damage morphologies are reported and related to the results of the calculations. A fatigue phenomenon is anticipated under certain conditions, and the phenomenon of phase separation is not expected to affect significantly the process of inclusion damage. Likely sources of metallic inclusion particles in laser glasses are considered, and melting conditions most suitable for their avoidance are discussed.

Effect of TiO2 on Initial Sintering of Al2O3

Abstract: Alpha alumina with additions of TiO2 sintered more rapidly than “pure” alumina. The rate of initial sintering increased approximately exponentially with titania concentration up to a percentage beyond which the rate of sintering remained approximately constant or decreased slightly with additional titania. The concentration which produces the maximum rate of sintering is thought to be the solubility limit of TiO2 in Al2O3. For alumina particles larger than about 2 μm, the kinetic process was mainly grain-boundary diffusion. With smaller particles, volume diffusion increased. The “solubility limit” increased with decreasing particle size, indicating an excess surface concentration of TiO2. The data may be interpreted in terms of a region of enhanced diffusion at the grain boundary that increases with TiO2 concentration. With small alumina particles, this region is large enough to become a significant portion of the volume of the particle, and the small particles appear to sinter by volume diffusion kinetics, but the diffusion coefficient corresponds to an enhanced diffusion coefficient.

Nematic Ordering of Hard Rods Derived from a Scaled Particle Treatment

Abstract: A fluid of hard rods is considered as a model for nematic liquid crystals. A direct application of the scaled particle approach results in an inconsistent thermodynamics. A simplified version which is consistent gives an integral equation for the orientational distribution which has the same form as that used by Onsager in the second virial approximation to the same problem. The coefficients, however, give finite density corrections which change his predicted order and density ratio at the transition in the direction of the experimental values.

Theory of plasma simulation using finite-size particles.

Abstract: The elementary properties of a plasma, in which the small‐separation force is smoothed from the Coulomb force, are developed. The modification is considered as being produced by spreading out the charge distribution of a particle to make a particle of finite size R (cloud). These clouds move freely through one another and interact through normal electromagnetic fields. A method to adapt point‐particle results for plasma oscillations, shielding, fluctuations, and collisions, is shown, and the modifications to these plasma properties discussed in detail. The relevance of these considerations to computer simulation of plasmas (in which some smoothing is a consequence of the numerical methods used and additional smoothing is sometimes added) is discussed. It is found that smoothing the short wavelength interaction can be used without destroying the desired physics, while suppressing collisional effects and noise at wavelengths < R which are exaggerated in simulation due to the use of far fewer particles than in a real plasma.

Filtration of particles from suspension by the american oyster crassostrea virginica.

Abstract: 1. Particle filtration by the oyster Crassostrea virginica was studied in the 1.0 to 12.0 µ size range in relation to naturally occurring particles and to kaolinite suspensions in filtered river water. 2. Oysters were held in troughs of flowing water under conditions similar to their natural environment. Particle number and volumes entering and leaving the troughs were enumerated using a Coulter electronic particle counter. Particle diameter was expressed as that of a sphere having a volume equal to the particle. 3. Results of the study were expressed as per cent of total particles removed in various size increments or in volumes removed over the same size range. 4. Oysters filtered naturally occurring particles in the 1.0 to 3.0 µ range with about one-third the efficiency as larger particles. Above 3.0 µ there was no change in efficiency with increasing particle size. For kaolinite particles, oysters removed particles in the 1.0 to 2.0 µ range with about half the efficiency as larger particles. Above this size there was no change. 5. When results are expressed in terms of per cent removal, the importance of the small sized particles is minimized. In terms of volume, particles in the 1.0 to 3.0 µ range constitute the largest single size fraction over the 1.0 to 12.0 µ range. 6. The consistent presence of an inflection point at a particle size around 2.0- 3.0 µ in the curve for per cent removed vs. particle size is an indication that the distance between adjacent latero-frontal cilia is the factor that determines the smallest particle size that can be completely retained by the oyster gill. 7. Presence of the inflection point is also interpreted as negating the existence of a mucous sheet over the gills, as suggested by MacGinitie (1941). 8. Particles in the 1.0 to 3.0 µ range may play an important role in the nutrition of oysters and other lamellibranchs. Their removal by these organisms may also be an important factor in sedimentary processes.

Particle deposition from turbulent air flow

Abstract: A theoretical model was developed to describe effectively the turbulent deposition of particles through the boundary layer adjacent to a deposition surface. Particle transport to the deposition surface is described by effective particle eddy diffusivities. Two innovations from published deposition models are incorporated into the new model. The first innovation is the discarding of the concept that the particle velocity at the start of free-flight is simply related to the rms air motion directed toward the deposition surfaces. The second is that particle eddy diffusivities are not the same as eddy diffusivities for air momentum as is generally assumed. In this study, the particle eddy diffusivities are back-calculated from the deposition data. From these calculations it is concluded that particle turbulent diffusivities are greater than those for air momentum transfer in turbulent flow.

Kramers Kronig analysis of the optical properties of small silver particles

Abstract: In order to complete a preceding paper the dielectric constantɛ of the particle material of small silver particles with diameters between 210 and 25 A is computed in the wavelength region 365≦λ≦455 nm from the measured spectra of thesmall particle plasma reasonance absorption. For this purpose a properKramers Kronig relation is derived, and is checked by applying to particles with Drude free electron gas. The results, concerning the silver particles, are that the real part ofɛ changes slightly, whereas the imaginary part is markedly enhanced (up to the ten-fold of the bulk values) if the particle size decreases. This size dependence ofɛ can quantitatively be described with thefree path effect within the accuracy of the measured values. Conversely, thebulk dielectric constant of silver is obtained by applying the free path effect to the measured dielectric constant of the small particles.

Settling velocities and vertical diffusion of particles in turbulent water

Abstract: A turbulent flow field that permits study of the kinematics of individual suspended particles has been produced in the laboratory. This paper considers the behavior in the vertical direction of particles 2 mm in diameter that have still-water terminal settling velocities ranging up to 4.0 cm/sec. The particle velocity frequency distributions are approximately Gaussian, and their root-mean-square values prove to be nearly independent of terminal fall velocity. In the majority of cases, particle diffusivity is greater than fluid diffusivity. The average velocity of fall determined by experiment in the various turbulent fields is reduced by as much as 30% below the corresponding still-water terminal fall velocity. A simple theoretical model predicts the fall velocity reduction due to a nonlinearity in the drag force. The model is then extrapolated to describe the behavior of quartz sand under field-scale turbulence conditions. It also predicts the time and distance required for such sand to reach terminal fall velocity in still water.

The deformation of single crystals of copper and copper-zinc alloys containing alumina particles - II. Microstructure and dislocation-particle interactions

Abstract: Electron microscope studies of deformed single crystals of Cu and Cu + Zn alloys of various compositions containing small alumina particles show that the dislocation structures generated and associated with the particles consist generally of prismatic loops, Orowan loops as well as prismatic loops in some brass alloys, and groups of dipoles. The formation of predominantly interstitial prismatic loops is explained in terms of a cross-slip mechanism controlled by the interstitial misfit strains around the particles. The transition from prismatic loop to prismatic plus Orowan loop structures in the brass alloys for Zn contents greater than ca . 20 wt % is considered to be due to the dependence of the activation energy for cross-slip on the stacking fault energy and to the solution hardening friction stress. In the Cu + 20% Zn alloys, measurements of the height of the loops and their numbers show that some dislocations by-pass the particles without forming loops. The mechanism of cross-slip leading to the formation of prismatic loops or ‘by-passing’ is discussed in some detail. The number of prismatic loops generated decreases with temperature. This fact is explained in terms of pipe or interface diffusion controlled climb of dislocations at the particles.

The scaled particle theory for mixtures of hard convex particles

Abstract: The excess volume and Gibbs free energy predicted by the scaled particle theory have been calculated for five binary systems of hard spheres, cubes, tetrahedra, ellipsoids and cylinders where the particles of the mixtures have the same shape but different sizes. At a fixed pressure, the excess volume was dependent on the shape of the particles involved, the temperature, pressure and size ratio of the particle. There appeared to be no equivalent sphere which could describe the equation of state and the mixing properties of the systems of non-spherical particles. The difficulties of extending the scaled particle theory to mixtures of different shaped particles are discussed and it is shown that the scaled particle theory is not thermodynamically consistent for these systems.

Calculated efficiencies of practical GaAs and Si solar cells including the effect of built-in electric fields

Abstract: The performance of GaAs solar cells has been calculated as a function of the doping levels, using practical values for the transport parameters Calculations show that surface recombination is a more probable cause than recombination in the junction region of the poor efficiencies obtained in practice Electric fields built into the cell by doping gradations may be used to reduce surface losses and produce an efficiency exceeding 20 per cent for a surface recombination velocity of 10 6 cm/sec This figure allows for the finite resistance of the surface layer, the effect of which is considered in detail for several cases Results for Si cells are also presented These are well in accord with the values obtained in practice For both materials consideration is given to the degradation brought about by particle bombardment

Effective Drag Coefficient for Gas-Particle Flow in Shock Tubes

Abstract: : Effective drag coefficients for flows of suspensions of spherical glass particles in air were derived from simultaneous measurements of pressure and particle concentration in the flow behind weak shock waves. Average particle diameters were 29 and 62 micrometers. The instantaneous concentration was determined by light scattering, and the results agree well with earlier shock-tube data based on streak records. They exhibit several unexpected features: the correlation between drag coefficient and Reynolds number is much steeper than the generally used 'standard' curve but approaches it at Reynolds numbers of several hundred; the correlation is independent of the particle concentration over the range of experiments, that is, for particle-to-gas flow rate ratios between 0.05 and 0.36; if the Reynolds number immediately behind the shock front is changed by varying the shock strength, the points move along the correlation, but if it is changed by changing the particle size, the entire correlation is shifted although to a smaller extent than would correspond to the direct effect of particle diameter on the Reynolds number. To account for the observations, a flow model is developed which allows for microscopic longitudinal and lateral perturbations of the particle motion that are the result of various causes, such as particle interactions with wakes of other particles, lateral forces caused by particle rotation, or electrostatic forces. (Author)

Rare‐Earth‐Compound Permanent Magnets

Abstract: Since the discovery of the extremely high magnetocrystalline anisotropy of YCo5 in 1966 there has been rapidly increasing interest in the development of cobalt‐rare‐earth intermetallic compounds as permanent magnet materials. The observed coercive forces are still only a small fraction of the anisotropy fields, and for some reason the coercive forces attainable with SmCo5 are larger than in other isostructural compounds with comparable anisotropy fields. A number of experiments have shown that the coercive force is very closely related to and can be profoundly influenced by the nature of the particle surface. The processing of these materials into magnets can be approached in several different ways, with due regard to the problem of chemical stability. The long‐range prospects of these materials may well be related to the improvement of the properties of compounds other than SmCo5 by influencing the factors that control the magnetization reversal process.

Free Conducting Particles in a Coaxial Compressed-Gas-Insulated System

Abstract: The effect of free conducting particles (FCPs) on the voltage-insulating performance of a short length of transmission line was quantitatively studied over the pressure range 0 to 300 psig for nitrogen and 0 to 125 psig for SF6. The FCPs were selected aluminum filings deliberately inserted into the concentric cylindrical (3"×10" dia.) electrode system. DC voltages of either polarity were produced by a Van de Graaff generator. The observed forms of interelectrode current included intermittent pulses or 'bursts', 'fireflies', steady corona, and sparks. Up to five-fold reductions in the current-onset voltage insulating strength resulted from the introduction of FCPs. For pressures up to 75 psig the sparking voltage in SF6 was 4 to 5 times higher than the sparking value in nitrogen. An electrostatic particle trap proved effective in reducing FCP-caused discharges. The dynamic equilibrium mechanism of 'fireflies' was studied in detail.

Size and Surface Effects on the Phonon Properties of Small Particles

Abstract: Measurements on thin films and surfaces have generated a need for a technique whereby one can calculate the phonon properties of small particles containing only a few hundred atoms. We have used moleculardynamic techniques to calculate the frequency distribution and various moments for five different particle configurations. Results are compared with the bulk solid. A model extending the Lennard-Jones and Devonshire cell model to surface environments is described. It is shown that this model replicates features of the more exact calculation. The frequency spectrum and various correlation functions are decomposed into contributions from the bulk, surface, and edge of a particle. The differences can be explained in terms of the local environment.