Measurement of the thermophoretic force by electrodynamic levitation: Microspheres in air

Li, Wanguang; Davis, E. James

doi:10.1016/0021-8502(95)00047-g

Cited by 91 publications

(30 citation statements)

References 34 publications

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“…Waldmann found that the thermophoretic force for this case is proportional to the particle area and the local gas translational heat ux, is inversely proportional to the mean molecular speed, and is independent of pressure. Experimental (Waldmann and Schmitt 1966;Li and Davis 1995a) and subsequent theoretical (e.g., Yamamoto and Ishihara 1988;Loyalka 1992;Beresnev and Chernyak 1995) studies support the Waldmann result.…”

Section: Introductionmentioning

confidence: 66%

“…Waldmann and Schmitt (1966) advocated the use of the translational part of the thermal conductivity, Equation (6), for polyatomic gases; they support this contention by comparison to experimental data (see also the recent work of Li and Davis (1995a)). The nal equality in Equation (9) states that the thermophoretic force is proportional to the translational component of the heat ux, q tr C .…”

Section: Gas Heat Flux and The Thermophoretic Forcementioning

confidence: 97%

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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: Introductionmentioning

confidence: 66%

Section: Gas Heat Flux and The Thermophoretic Forcementioning

confidence: 97%

Thermophoresis in Rarefied Gas Flows

Gallis¹,

Rader²,

Torczynski³

2002

Aerosol Science and Technology

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“…Takata et al (1993) noted that the solution for arbitrary could be expressed as a linear combination of the solution for → ∞ and that for a spherical particle with a given axisymmetric and sinusoidally varying surface temperature immersed in an infinite expanse of gas at temperature T 0 and pressure p 0 . They obtained Saxton and Ranz (1952), Figure 3 Castor oil in air 9.5 0.05-0.12 Schmitt (1959), Figure 6 Silicone oil in air 7.5 0.11-2.00 Schadt and Cadle (1961), Figure 1b TCP in air 10 0.14-0.76 Schadt and Cadle (1961), Figure 2b NaCl in air 322 0.20-1.49 Schadt and Cadle (1961), Figure 3 Hg in air 581 0.45-3.60 Jacobsen and Brock (1965), Figures 4 and 5 NaCl in Ar 300 0.06-0.67 Tong (1975), Figure 6 Al in He 1519 0.01-0.32 Davis and Adair (1975), Figure 5 Cork in Ar 2.5 0.05-1.80 Li and Davis (1995a), Figure 11 PSL in CO 2 10 0.10-3.50 Li and Davis (1995b), Figure 6 DOP in CO 2 12 0.05-4.20 Li and Davis (1995b), Figure 6 Glass in CO 2 75 0.12-4.00 Li and Davis (1995b), Figure 10 DOP in He 0.8 0.10-1.90…”

Section: Solutions Of the Original Bgk Equationmentioning

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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“…Fredlund (1938) attempted a systematic experiment to examine the effect of the temperature field upon a disk suspended on a balance. The thermophoretic force and the thermophoretic velocity are measured by several methods: Millikan cell (Rosenblatt & La Mer, 1946;Saxton & Ranz, 1952;Schadt & Cadle, 1961;Jacobsen & Brock, 1965), electrodynamic balance (Li & Davis, 1995a, 1995b, precipitation in a thermoprecipitator (Schadt & Cadle, 1957;Keng & Orr, 1966), jet technique (Kousaka et al, 1976;Prodi et al, 1979;Talbot et al, 1980), and deflection of a particle suspended by a small wire (Davis & Adair, 1975;Tong, 1975).…”

Section: Introductionmentioning

confidence: 99%