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 ISSN 0022-1120.

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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
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics
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:	Date Event 10 March 2019 Published 10 January 2019 Available 25 October 2018 Accepted
Volume:	862
Page Range:	pp. 312-347
DOI:	10.1017/jfm.2018.907
Status:	Peer Reviewed
Publication Status:	Published
Re-use 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
Date of first compliant deposit:	9 November 2018
Date of first compliant Open Access:	25 January 2019
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/N016602/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/P020887/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EP/P031684/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 UNSPECIFIED Leverhulme Trust http://dx.doi.org/10.13039/501100000275
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