A Thermal Force Drifting Particles Along a Temperature Gradient

<- Back to II. Mechanical Engineering & Physics Vol. 5

Cite the paper

Amelia Carolina Sparavigna (2016). A Thermal Force Drifting Particles Along a Temperature Gradient. Mechanics, Materials Science & Engineering, Vol 5. doi:10.13140/RG.2.1.2347.7365

Authors: Amelia Carolina Sparavigna

ABSTRACT. In 1972, V. Gallina and M. Omini of the Polytechnic of Turin proposed a phenomenological model for the thermal diffusion in liquid metals, explaining the isotope separation as provoked by a thermal force which is arising when a temperature gradient is established in the material. Here, we discuss this thermal force and its statistical origin from the bulk. We will see that it can be considered as a force of the form F = − S grad T, that is as a thermal/entropic force obtained from the derivative of the Helmholtz free energy with respect to the volume.

Keywords: thermal gradient, thermal transport, thermal forces, entropic forces

DOI 10.13140/RG.2.1.2347.7365


[1] Cercignani, C. (1975). Theory and application of the Boltzmann equation. Scottish Academic Press. ISBN: 978-1-4612-6995-3.

[2] Succi, S. (2001). The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford University Press. DOI: 10.1016/S0997-7546(02)00005-5

[3] Omini, M., & Sparavigna, A. (1995). An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Physica B: Condensed Matter, 212(2), 101-112. DOI: 10.1016/0921-4526(95)00016-3

[4] Omini, M., & Sparavigna, A. (1996). Beyond the isotropic-model approximation in the theory of thermal conductivity. Physical Review B, 53(14), 9064. DOI: 10.1103/physrevb.53.9064

[5] Sparavigna, A. C. (2016). The Boltzmann equation of phonon thermal transport solved in the relaxation time approximation – I – Theory. Mechanics, Materials Science & Engineering Journal, 3, 1-13. DOI: 10.13140/RG.2.1.1001.1923

[6] Müller, I. (2007). A History of thermodynamics: The doctrine of Energy and Entropy, Springer Science & Business Media. ISBN 978-3-540-46226-2

[7] Neumann,  R. M. (1980). Entropic approach to Brownian movement. American Journal of Physics, 48(5):354. DOI: 10.1119/1.12095.

[8] Neumann, R. M. (1977). The entropy of a single Gaussian macromolecule in a noninteracting solvent. The Journal of Chemical Physics 66(2):870. DOI: 10.1063/1.433923

[9] Roos, N. (2014). Entropic forces in Brownian motion. American Journal of Physics, 82(12), 1161-1166.

[10] Huebner, R. P. (1979). Magnetic flux structures in superconductors, Springer Verlag.  DOI:  10.1007/978-3-662-02305-1

[11] Pengcheng  Li  (2007).   Novel   transport   properties  of  electron – doped  superconductors Pr2-xCexCuO4-δ, UMD Theses and Dissertations.

[12] Gallina, V., & Omini, M. (1972). On thermal diffusion in liquid metals. Il Nuovo Cimento,  8B(1):65-89. DOI:  10.1007/bf02743508

[13] Ott, A. (1969). Isotope separation by thermal diffusion in liquid metal. Science,  164(3877):297. DOI: 10.1126/science.164.3877.297

[14] Platten, J. K. (2006). The Soret effect: a review of recent experimental results. Journal of applied mechanics, 73(1):5-15. DOI:  10.1115/1.1992517

[15] Huang, F., Chakraborty, P., Lundstrom, C. C., Holmden, C., Glessner, J. J. G., Kieffer, S. W., &  Lesher, C. E. (2010). Isotope fractionation in silicate melts by thermal diffusion. Nature, 464(7287):396-400. DOI: 10.1038/nature08840

[16] Richter, F.M. (2011).  Isotope fractionation in silicate melts by thermal diffusion.  Nature, 472(7341):E1. DOI: 10.1038/nature09954

[17] Goel, G., Zhang, L., Lacks, D. J., & Van Orman, J. A. (2012). Isotope fractionation by diffusion in silicate melts: Insights from molecular dynamics simulations. Geochimica et Cosmochimica Acta,  93:205-213. DOI:  10.1016/j.gca.2012.07.008

[18] Bindeman, I. N., Lundstrom, C. C., Bopp, C., &  Huang, F. (2013). Stable isotope fractionation by thermal diffusion through partially molten wet and dry silicate rocks. Earth and Planetary Science Letters, 365:51-62. DOI:  10.1016/j.epsl.2012.12.037

[19] Sparavigna, A. C. (2015). Dimensional equations of entropy. International Journal of Sciences, 4(8):1-7. DOI:  10.18483/ijsci.811

[20] Omini, M. (1999). Thermoelasticity and thermodynamics of irreversible processes. Physica B, 270:131-139. DOI: 10.1016/s0921-4526(99)00172-6

[21] Peter Atkins, P., & De Paula, J. (2014).  Atkins’ Physical Chemistry, OUP Oxford. ISBN 9780199543373


Creative Commons Licence
Mechanics, Materials Science & Engineering Journal by Magnolithe GmbH is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at www.mmse.xyz.