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Diffusion of macromolecular solutions in the boundary layer

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Summary

This paper concerns the study of a diffusion layer of macromolecular solutions annularly injected in a cylindric pipe in turbulent flow. The study includes firstly the analysis of the longitudinal and transversal projections of the concentration gradient, secondly the study of the state of turbulence in the diffusion layer.

The concentrations are determined by the measurement of the concentration salt (salt was added to the injected solution). A mathematical model of the development of concentration is proposed.

The turbulent state of diffusion layer has been studied with Laser-Doppler-Anemometry. An analysis of Eulerian autocorrelation and the power spectral density has been done.

Zusammenfassung

Es werden Ergebnisse über die turbulente Diffusionsschicht von nicht-newtonschen Flüssigkeiten (PÄO) mitgeteilt, die an der Wand eines kreiszylindrischen Rohrs injiziert werden. Diese Untersuchungen betreffen die Analyse der Längs- und Querkomponenten des Konzentrationsgradienten in der Diffusionsschicht und im Turbulenzfeld.

Die Konzentrationen werden mit Hilfe von Salz (NaCl) gemessen, das der injizierten Polymerlösung beigefügt worden ist. Ein mathematisches Modell für die Konzentrationsverteilung wird vorgeschlagen.

Der Turbulenzzustand der Diffusionsschicht wird mit Hilfe der Laser-Doppler-Anemometrie untersucht. Die Eulersche Autokorrelation und das Intensitätsspektrum werden analysiert.

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Abbreviations

c :

polymer concentration (wppm)

c 0 :

wall value ofc

c i :

value ofc at the slot

D :

diameter of the pipe

e :

slot thickness

L 0 :

distance from the slot at which the wall concentration drops toe −1of its original value

m :

distance in meter from the slot

U :

means freestream velocity

u i :

injection velocity

x :

distance from the slot

y :

normal distance from the surface

ϑ :

boundary layer thickness

λ :

characteristic height of the diffusion, i. e. the value ofy at whichc/c 0 = 0.5

References

  1. Poreh, M., K. S. Hsu, J. Hydronautics6 (1972).

  2. Collins, D. J., A turbulent boundary layer with slot injection of drag reducing polymer; Thesis Georgia Institute of Technology (July 1973).

  3. Latto, B., O. K. F. El Riedy, J. Hydronautics10, (1976).

  4. Bhowmick, S. K., C. Gebel, H. Reitzer Rheol. Acta14, 1026 (1975).

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Authors and Affiliations

  1. Institut de Mécanique des Fluides, Université Louis Pasteur, E. R. A. C. N. R. S. 0594 2, rue Boussingault, F-67083, Strasbourg Cedex, France

    C. Gebel & H. Reitzer

  2. École Nationale Supérieure des Arts et Industries de Strasbourg, F-67083, Strasbourg Cedex, France

    M. Bues

Authors
  1. C. Gebel
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  2. H. Reitzer
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  3. M. Bues
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Gebel, C., Reitzer, H. & Bues, M. Diffusion of macromolecular solutions in the boundary layer. Rheol Acta 17, 172–175 (1978). https://doi.org/10.1007/BF01517708

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  • DOI: https://doi.org/10.1007/BF01517708

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