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Thermophoresis of a spherical particle : modelling through moment-based, macroscopic transport equations
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Padrino-Inciarte, Juan C., Sprittles, James E. and Lockerby, Duncan A. (2019) Thermophoresis of a spherical particle : modelling through moment-based, macroscopic transport equations. Journal of Fluid Mechanics, 862 . pp. 312-347. doi:10.1017/jfm.2018.907
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Official URL: https://doi.org/10.1017/jfm.2018.907
Abstract
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.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QC Physics | |||||||||||||||
| Divisions: | Faculty of Science > Engineering Faculty of Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Rarefied gas dynamics, Transport theory, Reynolds number | |||||||||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | |||||||||||||||
| Publisher: | Cambridge University Press | |||||||||||||||
| ISSN: | 0022-1120 | |||||||||||||||
| Official Date: | 10 March 2019 | |||||||||||||||
| Dates: |
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| Date of first compliant deposit: | 9 November 2018 | |||||||||||||||
| Volume: | 862 | |||||||||||||||
| Page Range: | pp. 312-347 | |||||||||||||||
| DOI: | 10.1017/jfm.2018.907 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Publisher Statement: | This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2018.907. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Copyright Holders: | 2019 Cambridge University Press | |||||||||||||||
| RIOXX Funder/Project Grant: |
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