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Using the Euler–Lagrange variational principle to obtain flow relations for generalized Newtonian fluids

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Abstract

The Euler–Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in theflow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models, which include power law, Bingham, Herschel–Bulkley, Carreau, and Cross, are used for demonstration.

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References

  • Carreau P, Kee DD, Chhabra R (1997) Rheology of polymeric systems. Hanser Publishers, New York

    Google Scholar 

  • Owens R, Phillips T (2002) Computational rheology. Imperial College Press, London

    Book  Google Scholar 

  • Skelland A (1967) Non-Newtonian flow and heat transfer. Wiley, New York

    Google Scholar 

  • Sochi T (2007) Pore-scale modeling of non-Newtonian flow in porous media. Ph.D. thesis. Imperial College London

  • Sochi T (2009) Pore-scale modeling of viscoelastic flow in porous media using a Bautista-Manero fluid. Int J Heat Fluid Flow 30(6):1202–1217

    Article  Google Scholar 

  • Sochi T (2010a) Computational techniques for modeling non-Newtonian flow in porous media. Int J Model Simul Sci Comput 1(2):239–256

    Article  Google Scholar 

  • Sochi T (2010b) Flow of non-Newtonian fluids in porous media. J Polym Sci Part B 48(23):2437–2467

    Article  Google Scholar 

  • Sochi T (2010c) Modelling the flow of yield-stress fluids in porous media. Transp Porous Media 85(2):489–503

    Article  Google Scholar 

  • Sochi T (2010d) Non-Newtonian flow in porous media. Polymer 51(22):5007–5023

    Article  Google Scholar 

  • Sochi T (2011a) Slip at fluid-solid interface. Polym Rev 51:1–33

    Article  Google Scholar 

  • Sochi T (2011b) The flow of power-law fluids in axisymmetric corrugated tubes. J Pet Sci Eng 78(3–4):582–585

    Article  Google Scholar 

  • Sochi T (2013) Newtonian flow in converging-diverging capillaries. Int J Model Simul Sci Comput 04(03):1350011

    Article  Google Scholar 

  • Sochi T, Blunt M (2008) Pore-scale network modeling of Ellis and Herschel-Bulkley fluids. J Pet Sci Eng 60(2):105–124

    Article  Google Scholar 

  • Sorbie K (1991) Polymer-improved oil recovery. CRC Press, Inc., Boca Raton

    Book  Google Scholar 

  • Tanner R (2000) Engineering rheology, 2nd edn. Oxford University Press, London

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

    Taha Sochi

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  1. Taha Sochi
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Correspondence to Taha Sochi.

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Sochi, T. Using the Euler–Lagrange variational principle to obtain flow relations for generalized Newtonian fluids. Rheol Acta 53, 15–22 (2014). https://doi.org/10.1007/s00397-013-0741-3

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  • DOI: https://doi.org/10.1007/s00397-013-0741-3

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