Skip to main content
SpringerLink
Log in

The effect of boundary absorption on longitudinal dispersion in steady laminar flows

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

The effect of absorbing or semi-absorbing boundary conditions on the dispersion of suspended particles in a flowing fluid are investigated. In the case of absorbing boundary conditions, the dispersion of absorption times gives rise to an increase in the longitudinal dispersion of the absorbed particles. The effect of sedimentation is discussed. For semi-absorbing boundary conditions, the longitudinal dispersion is increased by an amount proportional to the dispersion of the time spent by the particles in the semi-absorbing state. The relative importance of this dispersion versus Taylor diffusion is discussed.

Résumé

Nous étudions l'effet de conditions de bord absorbantes ou semi-absorbantes sur la dispersion de particules suspendues dans un fluide en écoulement. Dans le cas de conditions de bord absorbantes, la dispersion sur le temps d'absorption donne lieu à un accroissement de la dispersion longitudinale des particles absorbées. L'effet de la sédimentation est discutée. En cas de bords sémi-absorbant la dispersion longitudinale contient un terme proportional à la dispersion sur le temps de séjour des particules dans l'état sémi-absorbant. L'importance relative de cette dispersion et de la diffusion Taylor est discutée.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. I. Taylor, Proc. R. Soc. Lond.A219, 186 (1953).

    Google Scholar 

  2. R. Aris, Proc. R. Soc. Lond.A235, 67 (1956);A259, 370 (1960)

    Google Scholar 

  3. R. Dewey and J. P. Sullivan, Z. angew. Math. Phys.30, 601 (1979).

    Google Scholar 

  4. C. Van den Broeck, Physica112A, 343 (1982).

    Google Scholar 

  5. K. F. Bowden, J. Fluid Mech.21, 84 (1965).

    Google Scholar 

  6. P. C. Chatwin, J. Fluid Mech.71, 513 (1975).

    Google Scholar 

  7. E. R. Holley, D. R. F. Harleman and H. B. Fischer, J. Hydr. Div. A.S.C.E.96, 1691 (1970).

    Google Scholar 

  8. R. Smith, J. Fluid Mech.78, 677 (1976);105, 469 (1981);114, 379 (1982).

    Google Scholar 

  9. D. A. Farrell and W. E. Larson, Aust. J. Soil. Res.4, 1 (1966).

    Google Scholar 

  10. C. Van den Broeck and E. Dekempeneer,The effect of sedimentation on Taylor diffusion, Phys. Rev.27, No. 5, 2727 (1983).

    Google Scholar 

  11. B. M. Budak, A. A. Samarkskii and A. N. Tikhonov,A collection of problems on mathematical physics (Pergamon, Oxford, 1964).

    Google Scholar 

  12. J. C. Giddings and H. Eyring, J. Phys. Chem.59, 416 (1955).

    Google Scholar 

  13. T. S. Sörensen, J. Chrom.88, 197 (1974).

    Google Scholar 

  14. A. Papoulis,Probability, random variables and stochastic processes (McGraw-Hill, New York, 1965).

    Google Scholar 

  15. W. C. Thacker, J. Phys. Oceanog.6, 66 (1976).

    Google Scholar 

  16. K. Lindenberg, K. E. Shuler, J. Freeman and T. J. Lie, J. Stat. Phys.12, 217 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Natuurkunde, Vrije Universiteit Brussel, 1050, Brussels, Belgium

    C. Van den Broeck & E. Dekempeneer

  2. Aangesteld Navorser Nationaal Fonds Wetenschappelijk Onderzoek Belgium, Belgium

    C. Van den Broeck

Authors
  1. C. Van den Broeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Dekempeneer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van den Broeck, C., Dekempeneer, E. The effect of boundary absorption on longitudinal dispersion in steady laminar flows. Z. angew. Math. Phys. 34, 489–501 (1983). https://doi.org/10.1007/BF00944710

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00944710

Keywords

Search

Navigation