Skip to main content
SpringerLink
Log in

The free-boundary problem for the die-swell of a viscous fluid

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

When a viscous fluid is extruded from a capillary or an annular die, the thickness of the fluid jet is in general unequal to the width of the die. This phenomenon is called “die-swell” and is studied in this paper for a die made up of two parallel plates. It is assumed that no slip will occur between the fluid and the plates, and that the pressure in the space into which the fluid is emitted is constant and uniform. The fluid surface is a free streamline. Its shape is calculated with the use of complex-function theory and conformal-mapping techniques. The predicted ratio of swell is found to be in full agreement with known finite-element results.

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. Chang, P.W., T.W. Patten and B.A. Finlayson, Collocation and Galerkin finite elements, methods for viscoelastic fluid flow; pt.2: die-swell problems with a free surface,Computers & Fluids 7 (1979) 285–293.

    Google Scholar 

  2. Crochet, M.J. and R. Keunings, Die-swell of a Maxwell fluid: numerical prediction,J. Non-Newt. Fluid Mech. 7 (1980) 199–212.

    Google Scholar 

  3. Crochet, M.J. and R. Keunings, On numerical die-swell calculation,J. Non-Newt. Fluid Mech. 10 (1982) 85–94.

    Google Scholar 

  4. England, A.H.,Complex variable methods in elasticity, London: Wiley-Interscience (1971).

    Google Scholar 

  5. Muskhelishvili, N.I.,Some basic problems of the mathematical theory of elasticity, Groningen: Noordhoff (1953).

    Google Scholar 

  6. Reddy, K.R. and R.I. Tanner, On the swelling of extruded plane sheets,J. Rheol. 22 (1978) 661–665.

    Google Scholar 

  7. Tanner, R.I.,Engineering rheology, Oxford: Clarendon Press (1985).

    Google Scholar 

  8. Vroonhoven, J. C. W. van and W. J. J. Kuijpers, A free boundary problem for viscous fluid flow in injection moulding,J. Engng. Math. 24 (1990) 151–165.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    J. C. W. Van Vroonhoven, A. J. M. Sipers & W. J. J. Kuijpers

Authors
  1. J. C. W. Van Vroonhoven
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. J. M. Sipers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. J. J. Kuijpers
    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 Vroonhoven, J.C.W., Sipers, A.J.M. & Kuijpers, W.J.J. The free-boundary problem for the die-swell of a viscous fluid. J Eng Math 24, 167–178 (1990). https://doi.org/10.1007/BF00129872

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00129872

Keywords

Search

Navigation