Skip to main content
Log in

On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

In this paper we solve the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. We use a non-linear slip model relating the shear stress to the velocity at the wall and exhibiting a maximum and a minimum. We assume that the material parameters in the slip equation are such that multiple steady-state solutions do not exist. The stability of the steady-state solutions is investigated by means of a one-dimensional linear stability analysis and by numerical calculations. The instability regimes are always within or coincide with the negative-slope regime of the slip equation. As expected, the numerical results show that the instability regimes are much broader than those predicted by the linear stability analysis. Under our assumptions for the slip equation, the Newtonian solutions are stable everywhere. The interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model. Perturbing an unstable steady-state solution leads to periodic solutions. The amplitude and the period of the oscillations increase with elasticity.

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

Access this article

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

  • Crochet MJ, Davies AR, Walters K (1984) Numerical simulation of non-Newtonian flow. Elsevier Science Publishers

  • El Kissi N, Piau JM (1989) Ecoulement de fluides polyméres enchevêtrés dans un capillaire. Modélisation du glissement macroscopique à la paroi. CR Acad Sci Paris t. 309, Série II:7–9

    Google Scholar 

  • Georgiou GC, Crochet MJ (1994) Compressible viscous flow in slits, with slip at the wall. J Rheology 38:639–654

    Google Scholar 

  • Hatzikiriakos SG, Dealy JM (1992a) Wall slip of molten high density polyethylenes. II. Capillary rheometer studies. J Rheol 36:703–741

    Google Scholar 

  • Hatzikiriakos SG, Dealy JM (1992b) Role of slip and fracture in the oscillating flow of HDPE in a capillary. J Rheol 36:845–884

    Google Scholar 

  • Hill DA, Hasegawa T, Denn MM (1990) On the apparent relation between adhesive failure and melt fracture. J Rheology 34:891–918

    Google Scholar 

  • Hunter JK, Slemrod M (1983) Viscoelastic fluid flow exhibiting hysteritic phase changes. Phys Fluids 26:2345–2351

    Google Scholar 

  • Kolkka RW, Malkus DS, Hansen MG, Ierley GR, Worthing RA (1988) Spurt phenomena of the Johnson-Segalman fluid and related models. J Non-Newtonian Fluid Mech 29:303–335

    Google Scholar 

  • Larson RG (1992) Instabilities in viscoelastic flows. Rheol Acta 31:213–263

    Google Scholar 

  • Leonov AI (1990) On the dependence of friction force on sliding velocity in the theory of adhesive friction of elastomer. Wear 141:137–145

    Google Scholar 

  • Lin Y-H (1985) Explanation for stick-slip melt fracture in terms of molecular dynamics in polymer melts. J Rheol 29:605–637

    Google Scholar 

  • McLeish TCB, Ball RC (1986) A molecular approach to the spurt effect in polymer melt flow. J Polym Sci B24:1735–1745

    Google Scholar 

  • Pearson JRA, Petrie CJS (1965) On the melt-flow instability of extruded polymers. Proc. 4th Int. Rheological Congress 3:265–282

    Google Scholar 

  • Pearson JRA, Petrie CJS (1968) On melt flow instability of extruded polymers. In: Wetton RE, Whorlow RW (eds) Polymer systems: deformation and flow. Macmillan, London 163–187

    Google Scholar 

  • Piau JM, El Kissi N, Tremblay B (1990) Influence of upstream instabilities and wall slip on melt fracture and sharkskin phenomena during silicones extrusion through orifice dies. J Non-Newtonian Fluid Mech 34:145–180

    Google Scholar 

  • Yerushalmi J, Katz S, Shinnar R (1970) The stability of steady shear flows of some viscoelastic fluids. Chem Eng Sci 25:1891–1902

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgiou, G.C. On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall. Rheol Acta 35, 39–47 (1996). https://doi.org/10.1007/BF00366551

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00366551

Key words

Navigation