Über die Kraft eines inhomogenen Gases auf kleine suspendierte Kugeln

Waldmann, L.

doi:10.1515/zna-1959-0701

Cited by 258 publications

(81 citation statements)

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“…For the present case where the particle is in the free-molecular regime (i.e., the velocity distribution function of gas molecules hitting the particle is not appreciably altered by the presence of the particle), an elementary kinetic approach can be used. Following the classic derivation of Waldmann (1959), the net thermophoretic force is found directly by calculating the net rate of momentum transferred to the particle by the impinging and re ected molecules. In Waldmann's work, the incoming molecules were represented by an analytical Chapman-Enskog distribution, characteristic of a near-equilibrium gas sustaining a temperature gradient.…”

Section: Green's Function Methods For Particle Force Calculationsmentioning

confidence: 99%

“…D 0). Waldmann (1959) derived an expression for the thermophoretic force in the free-molecular particle limit (Kn R ! 1), but where the system is continuum (Kn L !…”

Section: Gas Heat Flux and The Thermophoretic Forcementioning

confidence: 99%

“…Important reviews of this case include those by Loyalka (1992), Bakanov (1991), Fuchs (1982), Talbot et al (1980), and Waldmann and Schmitt (1966). Of particular importance here is Waldmann's expression (Waldmann 1959;Waldmann and Schmitt 1966) for the thermophoretic force on a free-molecular particle (Kn R ! 1) in a continuum gas described by a rst-order approximation Chapman-Enskog molecular velocity distribution function.…”

Section: Introductionmentioning

confidence: 99%

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Thermophoresis in Rarefied Gas Flows

Gallis¹,

Rader²,

Torczynski³

2002

Aerosol Science and Technology

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Numerical calculations are presented for the thermophoretic force acting on a free-molecular, motionless, spherical particle suspended in a rare ed gas ow between parallel plates of unequal temperature. The rare ed gas ow is calculated with the direct simulation Monte Carlo (DSMC) method, which provides a timeaveraged approximation to the local molecular velocity distribution at discrete locations between the plates. A force Green's function is used to calculate the thermophoretic force directly from the DSMC simulations for the molecular velocity distribution, with the underlying assumption that the particle does not in uence the molecular velocity distribution. Perfect accommodation of energy and momentum is assumed at all solid/gas boundaries. Earlier work for monatomic gases (helium and argon) is reviewed, and new calculations for a diatomic gas (nitrogen) are presented. Gas heat ux and particle thermophoretic forces for argon, helium, and nitrogen are given for a 0.01 m spacing between plates held at 263 and 283 K over a pressure range from 0.1 to 1000 mTorr (0.01333 -133.3 Pa). A simple, approximate expression is introduced that can be used to correlate the thermophoretic force calculations accurately over a wide range of pressures, corresponding to a wide range of Knudsen numbers (ratio of the gas mean free path to the interplate separation).

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Section: Green's Function Methods For Particle Force Calculationsmentioning

confidence: 99%

“…D 0). Waldmann (1959) derived an expression for the thermophoretic force in the free-molecular particle limit (Kn R ! 1), but where the system is continuum (Kn L !…”

Section: Gas Heat Flux and The Thermophoretic Forcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermophoresis in Rarefied Gas Flows

Gallis¹,

Rader²,

Torczynski³

2002

Aerosol Science and Technology

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“…For the free-molecule regime (Kn 1), Waldmann (1959) derived an expression for the thermophoretic force that is still considered to be very reliable. He also derived an expression for the free-molecule drag force on a sphere, although the same result had been obtained much earlier by Epstein (1924).…”

Section: Early Analytical Theoriesmentioning

confidence: 99%

“…Theories were readily forthcoming from Epstein (1929) for the continuum regime (Kn 1), Brock (1962) for the slip-flow regime (Kn ∼ 0.1), and Waldmann (1959) for the free-molecule regime (Kn 1). Unsurprisingly, however, the transition regime proved much more difficult to model.…”

Section: Introductionmentioning

confidence: 99%

Thermophoresis of a Spherical Particle: Reassessment, Clarification, and New Analysis

Young

2011

Aerosol Science and Technology

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The thermophoretic force acting on a spherical particle depends on the Knudsen number and the particle-to-gas thermal conductivity ratio, and it can be estimated using various analytical and numerical methods for solving the Boltzmann equation. A substantial body of experimental data also exists. Nevertheless, the situation is not as clear as it might be and this article assesses the current predictive capabilities. First, some issues of nondimensionalization and data presentation are discussed. Then, the Grad 13-moment (G13) method of solution is examined in detail, and it is shown how the method generates a hierarchy of expressions for the thermophoretic force at low Knudsen number including all the well-known results. The non-Navier-Stokes-Fourier thermal stress and pressure-driven heat flux and their relation to the phenomenon of reversed thermophoresis are discussed. Theories of thermophoresis at arbitrary Knudsen number are then examined and it emerges that there are essentially only two theories extant. The available experimental measurements of the thermophoretic force and velocity are compared with these theories. Finally, it is shown that the G13 solution can be adapted to provide an interpolation formula for the transition regime, which gives a good approximation for practical calculations and is quantitatively very different from the commonly used prescription.

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Air Pollution Control Methods

Crocker

2000

Kirk-Othmer Encyclopedia of Chemical Technology

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Air pollution may be rendered less harmful by reducing the concentration of contaminants, the exposure time, or both. Selection of pollution control methods is generally based on the need to control ambient air quality in order to achieve compliance with standards for criteria pollutants, the need to reduce emission to the atmosphere of a hazardous air pollutant, or in the case of nonregulated contaminants, to protect human health and vegetation. There are three elements to a pollution problem: a source, a receptor affected by the pollutants, and the transport of pollutants from source to receptor. Modification or elimination of any one of these elements can change the nature of a pollution problem. The classes of pollutants include gases and particulates; odors are often discussed separately. To achieve air pollution control, reliable measurements are needed to quantify both the pollutant concentration and the contribution of individual sources. These data are necessary for designing control equipment, for monitoring emissions, and for maintaining acceptable ambient air quality. Two categories of measurement techniques are ambient and source measurement. Ambient sampling may help to establish and operate a pollution alert network, monitor the effect of an emission source, predict the effect of a proposed installation, locate the source of an undesirable pollutant, or obtain permanent sampling records for legal action or for modifying regulations. Source sampling problems are distinct from those of ambient sampling. Source gas may have a high temperature or contain high concentrations of water vapor or entrained mist, dust, or other interfering substances. Typical objectives of source sampling are demonstrating compliance with regulations, obtaining emission data, and determining the need for maintenance of process or control equipment. The Clean Air Act in 1990 has three areas of emphasis: acid rain reduction in the northeastern United States; severe limitation on atmospheric emissions of 189 chemicals on the hazardous or Toxic Substance list; and tightened regulations on vehicular exhaust (ozone compliance and smog reduction). Five methods are available for controlling gaseous emissions: absorption, adsorption, condensation, chemical reaction, and incineration. Atmospheric dispersion from a tall stack is now less viable. Adsorption is desirable for contaminant removal down to extremely low levels. Condensation is best for substances having rather high vapor pressures. Incineration is used to remove organic pollutants and small quantities of H 2 S, CO, and NH 3 . Specific problem gases such as sulfur and nitrogen oxides require combinations of methods. Major sources of sulfur dioxide are the combustion of sulfur‐containing fossil fuels, sulfur recovery from petroleum processing, and pulp and paper manufacture. Combustion emissions are controlled by substituting a low sulfur fuel source, by fuel desulfurization and refining, and by sulfur removal either in the combustion process or from the flue gas. Major sources of nitrogen oxide emission are nitrogen fixation during high temperature combustion, nitric acid manufacture and concentration, and vehicular emissions. NO formation in combustion may be reduced by maintaining low excess air, employing two‐stage combustion, flue gas recirculation, and burner placement. The removal of particles (liquids, solids, or mixtures) from a gas stream requires deposition and attachment to a surface. Devices for particle collection by filtration can be divided into three categories: cloth filtration, paper and mat filters, and in‐depth aggregate bed filtration. Scrubbers can be highly effective for both particulate collection and gas absorption. Scrubbers make use of a combination of particulate collection mechanisms. Wet‐scrubber collection efficiency may be unexpectedly enhanced by particle growth. Vapor condensation produced by cooling, can lead to particle growth or agglomeration.

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Über die Kraft eines inhomogenen Gases auf kleine suspendierte Kugeln

Cited by 258 publications

References 0 publications

Thermophoresis in Rarefied Gas Flows

Thermophoresis in Rarefied Gas Flows

Thermophoresis of a Spherical Particle: Reassessment, Clarification, and New Analysis

Air Pollution Control Methods

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