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Brownian motion in a medium with inhomogeneous temperature

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  • Widder, M.E.
  • Titulaer, U.M.

Abstract

We consider the motion of a Brownian particle in a medium with inhomogeneous temperature in the presence of an external potential. We start from the Klein-Kramers equation; in this equation a thermophoretic force, proportional to the temperature gradient, should in general be included to obtain a correct description of thermodiffusion effects in the hydrodynamic stage of the evolution. With the Chapman-Enskog method we derive the correct form for the Smoluchowski equation, which reduces to van Kampen's recent result in the absence of thermophoretic forces. We also give the first correction to this equation caused by deviations from local thermal equilibrium. For the system considered, such deviations persist even in the steady state.

Suggested Citation

  • Widder, M.E. & Titulaer, U.M., 1989. "Brownian motion in a medium with inhomogeneous temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(3), pages 452-466.
    • Handle: RePEc:eee:phsmap:v:154:y:1989:i:3:p:452-466
    DOI: 10.1016/0378-4371(89)90259-8
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    References listed on IDEAS

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    1. Van Kampen, N.G., 1988. "Ten theorems about quantum mechanical measurements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 97-113.
    2. Landauer, Carl, 1972. "Die amerikanische Wirtschaftslage und die Präsidentenwahl," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 52(5), pages 259-262.
    3. Van Kampen, N.G., 1987. "A set of oscillators in a common bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 165-183.
    4. Skinner, James L. & Wolynes, Peter G., 1979. "Derivation of Smoluchowski equations with corrections for Fokker-Planck and BGK collision models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 96(3), pages 561-572.
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    Cited by:

    1. Pflügl, W & Titulaer, U.M, 1993. "The size distribution of liquid droplets during their growth from a vapor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 410-422.
    2. Bringuier, E., 2011. "Gauge-invariant approach to thermodiffusion in a liquid binary mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1861-1875.
    3. Pflügl, W. & Titulaer, U.M., 1995. "The droplet size distribution in the late stage of phase separation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(1), pages 52-67.
    4. Kosztołowicz, Tadeusz, 1998. "Continuous versus discrete description of the transport in a membrane system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 44-56.
    5. Hui-Yun, Pan & Hai Jun, Wang, 1996. "A two-species surface reaction model of the mixing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(3), pages 234-238.
    6. Belan, S., 2016. "Concentration of diffusional particles in viscous boundary sublayer of turbulent flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 128-136.
    7. Zhong, Yuheng & Zhong, Weirong, 2024. "Inverse thermodiffusion of active matter in temperature gradient systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    8. Albano, Ezequiel V., 1995. "Irreversible phase transitions into non-unique absorbing states in a multicomponent reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(3), pages 426-434.

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