The effects of gas and particle properties on thermophoresis

Li, Wanguang; Davis, E. James

doi:10.1016/0021-8502(95)00048-h

Cited by 58 publications

(15 citation statements)

References 26 publications

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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%

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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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Section: Solutions Of the Original Bgk Equationmentioning

confidence: 99%

“…Davis (1995b) studied DOP droplets in He and carbon dioxide (CO 2 ) ( = 0.8 and 12) and PSL and glass spheres in CO 2 ( = 10 and 75). Figure 9e shows that the dataset for DOP droplets in CO 2 displays a similar trend to that of dataset 0510d and is more representative of a value of about unity.…”

Section: Comparison Of the Thermophoretic Force Data With Theorymentioning

confidence: 99%

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

Young

2011

Aerosol Science and Technology

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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%

Effects of gas species on pressure dependence of thermophoretic velocity

Razali

Mori

Suzuki

et al. 2012

Journal of Aerosol Science

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“…Waldmann's solution was later reproduced by Mason and co-workers [21,22] using a dustygas model that considers both specular and diffuse scattering. Experimental [23][24][25][26] and numerical studies [27,28] have shown that for large Knudsen numbers the thermophoretic force and velocity approach the Waldmann solution.…”

Section: Introductionmentioning

confidence: 99%

Thermophoretic force and velocity of nanoparticles in the free molecule regime

Wang

2004

Phys. Rev. E

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We extend our previous gas-kinetic theory analysis of drag force in a uniform temperature field [Li and Wang, Phys. Rev. E. 68, 061206 (2003); 68, 061207 (2003)] to particle transport in fluids with nonuniform temperature. Formulations for drag and thermophoretic forces are proposed for nanoparticle transport in lowdensity gases. We specifically consider the influence of nonrigid body collision due to van der Waals or other forces between the particle and gas molecules and find that these forces play a notable role for particles a few nanometers in size. It is shown that the present formulations can be easily reduced to the classical result of Waldmann [Z. Naturforsch. A 14a, 589 (1959)] by assuming rigid body collision. From the force formulations we also obtain the equation governing the thermophoretic velocity. This velocity is found to be highly sensitive to the potential energy of interactions between gas molecules and particle, and as such Waldmann's thermophoretic velocity is not expected to be accurate for nanosized particles.

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The effects of gas and particle properties on thermophoresis

Cited by 58 publications

References 26 publications

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

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

Effects of gas species on pressure dependence of thermophoretic velocity

Thermophoretic force and velocity of nanoparticles in the free molecule regime

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