IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v112y1982i1p315-330.html
   My bibliography  Save this article

The kinetic boundary layer for the Fokker-Planck equation: A Brownian particle in a uniform field

Author

Listed:
  • Burschka, M.A.
  • Titulaer, U.M.

Abstract

We study stationary solutions of the Fokker-Planck equation for velocity and position of a Brownian particle in the presence of a constant external field and a completely or selectively absorbing plane wall. Adapting a procedure used earlier for the field-free case, we determine analytically a set of boundary layer solutions and combine them numerically with the Chapman-Enskog solutions to satisfy various boundary conditions at the wall, albeit approximately. Various aspects of the solutions so obtained are presented, in particular the profiles of the density and the kinetic energy density in the boundary layer. The most important quantity that can be extracted from them is the effective absorption rate at the wall corresponding to complete or partial absorption of particles hitting the wall. This quantity is noticeably increased by the presence of the external field; as in the field-free case it also depends on the reflection mechanism adopted for the non-absorbed particles. The trends in the absorption rate, and even their numerical values, are predicted remarkably well by a simple analytical approximation, a self-consistent modification of the usual transition state theory for chemical reactions.

Suggested Citation

  • Burschka, M.A. & Titulaer, U.M., 1982. "The kinetic boundary layer for the Fokker-Planck equation: A Brownian particle in a uniform field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(1), pages 315-330.
    • Handle: RePEc:eee:phsmap:v:112:y:1982:i:1:p:315-330
    DOI: 10.1016/0378-4371(82)90222-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437182902229
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(82)90222-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Krüger, Jens, 1992. "Effective-medium theory of diffusion and chemical reactions in the presence of stationary overlapping sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 9-22.
    2. Kauerauf, A. & Felderhof, B.U., 1996. "Transient survival probability of a particle diffusing in a disordered system of perfectly absorbing spherical sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(1), pages 1-33.
    3. Felderhof, B.U & Kauerauf, A, 1995. "Electron spectral density in a disordered system of hard sphere scatterers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 376-389.
    4. Krüger, Jens, 1990. "Effective medium theory of diffusion-controlled reactions among stationary perfect sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 166(2), pages 206-219.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:112:y:1982:i:1:p:315-330. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.