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On exact solutions of the flow equations for Bingham visco-plastic fluids through an eccentric annular cross-section

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Abstract

We discuss properties of solutions of the Bingham flow equations for visco-plastic fluids through an eccentric annular cross-section. Particularly, we perform arguments which are not in favor of the well-known Szabo–Hassager’s conjecture that the rigid zone is confined by circles provided the eccentricity is small (J Non-Newtonian Fluid Mech 45:149-169, 1992).

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References

  • Basov IV, Shelukhin VV (1998) Generalized solutions to the equations of Bingham compressible flows. Z Angew Math Mech 78:185–192

    Google Scholar 

  • Basov IV, Shelukhin VV (2007) Nonhomogeneous incompressible Bingham viscoplastic as a limit of nonlinear fluids. J Non-Newton Fluid Mech 142:95–103

    Article  CAS  Google Scholar 

  • Bird RB, Dai GC, Yarusso BJ (1983) The rheology and flow of viscoplastic materials. Rev Chem Eng 1:1–70

    Google Scholar 

  • Chatzimina M, Xenophontos C, Georgiou GC, Argyropaidas I, Mitsoulis E (2007) Cessation of annular Poiselle flows of Bingham plastic. J Non-Newton Fluid Mech 142:135–142

    Article  CAS  Google Scholar 

  • Dent JD, Lang TE (1983) A biviscous modifed Bingham model of snow avalanche. Ann Glaciol 4:42–46

    Google Scholar 

  • Duvaut G, Lions JL (1976) Inequalities in Mechanics and Physics. Grun-dlehren der Mathematischen Wissenschaften, Springer, Berlin. p. 219

    Google Scholar 

  • Klimov DM, Petrov AG, Georgievskii DV (2005) Viscoplastic flows: dynamic chaos, stability, mixing. Nauka, Moscow

    Google Scholar 

  • Málek J, Ruz̆ic̆ka M, Shelukhin VV (2005) Herschel–Bulkley fluids: existence and regularity of steady flows. Math Model Meth Appl Sci 15(12):1845–1861

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Shelukhin VV (2002) Bingham viscoplastic as a limit of non-Newtonian fluid. J Math Fluid Mech 4:109–127

    Article  Google Scholar 

  • Szabo P, Hassager O (1992) Flow of viscoplastic fluids in eccentric annular geometries. J Non-Newton Fluid Mech 45:149–169

    Article  CAS  Google Scholar 

  • Wachs A (2007) Numerical simulation of steady Bingham flow through an eccentric annular cross-section by distributed Lagrange multiplier/fictitious domain and augmented Lagrangian methods. J Non-Newton Fluid Mech 142:183–198

    Article  CAS  Google Scholar 

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  1. Lavrentyev Institute of Hydrodynamics, Lavrentyev pr. 15, Novosibirsk, 630090, Russia

    Vladimir Shelukhin

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  1. Vladimir Shelukhin
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Correspondence to Vladimir Shelukhin.

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Shelukhin, V. On exact solutions of the flow equations for Bingham visco-plastic fluids through an eccentric annular cross-section. Rheol Acta 50, 335–342 (2011). https://doi.org/10.1007/s00397-010-0482-5

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  • DOI: https://doi.org/10.1007/s00397-010-0482-5

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