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On the stability of plane poiseuille flow of viscoelastic fluids

Zur Stabilität der ebenen Poiseuille-Strömung viskoelastischer Flüssigkeiten

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Summary

We consider the stability of plane Poiseuille flow under plane infinitesimal disturbances of a finite linear viscoelastic fluid. The memory function is obtained on the basis of the bead-spring model in the molecular theory of dilute polymer solutions. The analysis shows the destabilizing influence of the viscoelastic character of the fluid; for small Weissenberg numbers, the number of relaxation times has little influence upon stability. The effect upon stability of the addition of a newtonian term in the stress constitutive relation of a finite linear viscoelastic fluid is also examined.

Zusammenfassung

Untersucht wird die Stabilität der ebenen Poiseuille-Strömung einer endlichen linear-viskoelastischen Flüssigkeit bei ebenen infinitesimalen Störungen. Die Gedächtnisfunktion wird auf der Grundlage des Kugel-Feder-Modells der Molekulartheorie verdünnter Polymerlösungen erhalten. Die Untersuchung zeigt den destabilisierenden Einfluß des viskoelastischen Charakters der Flüssigkeit; für kleine Weissenberg-Zahlen hat die Größe der Relaxationszeit geringen Einfluß auf die Stabilität. Ebenfalls untersucht wird der Einfluß eines zusätzlichen Newtonschen Gliedes in der Werkstoffbeziehung einer endlichen linear-viskoelastischen Flüssigkeit.

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Authors and Affiliations

  1. Unité de Mécanique Appliquée, Université Catholique de Louvain, Place du Levant, B-1348, Louvain-la-Neuve, Belgium

    M. J. Crochet & G. Tackels

Authors
  1. M. J. Crochet
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  2. G. Tackels
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Crochet, M.J., Tackels, G. On the stability of plane poiseuille flow of viscoelastic fluids. Acta Mechanica 24, 1–12 (1976). https://doi.org/10.1007/BF01175753

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