Skip to main content
SpringerLink
Log in

Unsteady simple shear flow in a viscoplastic fluid: comparison between analytical and numerical solutions

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

Abstract

In this paper, an unsteady flow of a viscoplastic fluid for simple shear flow geometry is solved numerically using two regularizing functions to overcome the discontinuity for zero shear rate of the Bingham constitutive law. The adopted models are the well-known Papanastasiou relation and one based on the error function. The numerical results are compared with the analytical solution of the same problem obtained by Sekimoto (J Non-Newton Fluid Mech 39:107–113, 1991). The analysis of the results emphasizes that the errors are much smaller in the yielded than in the unyielded region. The models approximate closer the ideal Bingham model as the regularization parameters increase. The differences between the models tend to vanish as the regularization parameters are at least greater than 105.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Barnes HA (1999) The yield stress—a review or ‘παvτα ρει’—everything flows? J Non-Newton Fluid Mech 81:133–178

    Article  MATH  CAS  Google Scholar 

  • Daprà I, Scarpi G (2007) Unsteady axial Poiseuille flow of a Bingham fluid in an annulus. V Int Symp “Comp Civ Eng” Iasi

  • Dean EJ, Glowinski R, Guidoboni G (2007) On the numerical simulation of Bingham visco-plastic flow: old and new results. J Non-Newton Fluid Mech 142:36–62

    Article  MATH  CAS  Google Scholar 

  • Frigaard IA, Nouar C (2005) On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J Non-Newton Fluid Mech 127:1–26

    Article  CAS  Google Scholar 

  • Glowinski R (1984) Numerical methods for nonlinear variational problems. Springer, New York

    MATH  Google Scholar 

  • Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31(5):385–404

    Article  MATH  CAS  ADS  Google Scholar 

  • Sekimoto K (1991) An exact non-stationary solution of simple shear flow in a Bingham fluid. J Non-Newton Fluid Mech 39:107–113

    Article  MATH  CAS  Google Scholar 

Download references

Acknowledgements

The authors thank the reviewers for their constructive comments.

Author information

Authors and Affiliations

  1. DISTART—University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Irene Daprà & Giambattista Scarpi

Authors
  1. Irene Daprà
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giambattista Scarpi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irene Daprà.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Daprà, I., Scarpi, G. Unsteady simple shear flow in a viscoplastic fluid: comparison between analytical and numerical solutions. Rheol Acta 49, 15–22 (2010). https://doi.org/10.1007/s00397-009-0384-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-009-0384-6

Keywords

Search

Navigation