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Energy Methods in Action: Equality, Inequality and Stability

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Fluid Mechanics of Viscoplasticity
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Abstract

This chapter is concerned with five types of problems in which energy principles play a significant role.

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References

  1. Mosolov PP, Miasnikov VP (1965) Variational methods in the theory of fluidity of a viscous-plastic medium. J Appl Math Mech (PMM) 31:545–577

    Article  Google Scholar 

  2. Mosolov PP, Miasnikov VP (1967) On qualitative singularities in the flow of a viscoplastic medium in pipes. J Appl Math Mech (PMM) 33:609–613

    Article  Google Scholar 

  3. Huilgol RR (2006) A systematic procedure to determine the minimum pressure gradient required for the flow of viscoplastic fluids in pipes of symmetric cross-section. J Non-Newton Fluid Mech 136:140–146

    Article  MATH  Google Scholar 

  4. Huilgol RR, You Z (2007) Determination of the minimum pressure gradient for the flow of viscoplastic fluids in the runner system. Report to Moldflow Pty. Ltd., School of Informatics and Engineering, Flinders University

    Google Scholar 

  5. Dubash N, Frigaard I (2004) Conditions for static bubbles in viscoplastic fluids. Phys Fluids 16:4319–4330

    Article  Google Scholar 

  6. Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    Google Scholar 

  7. Tsamopoulos J, Dimakopoulos Y, Chatzidai N, Karapetsas G, Pavlidis M (2008) Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment. J Fluid Mech 601:123–164

    Article  MATH  MathSciNet  Google Scholar 

  8. Dubash N, Frigaard IA (2007) Propagation and stopping of air bubbles in carbopol solutions. J Non-Newton Fluid Mech 142:123–134

    Article  MATH  Google Scholar 

  9. Mougin N, Magnin A, Piau J-M (2012) The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid. J Non-Newton Fluid Mech 171–172:42–55

    Article  Google Scholar 

  10. Beris AN, Tsamopoulos JA, Armstrong RC, Brown RA (1985) Creeping motion of a sphere through Bingham plastic. J Fluid Mech 158:219–244

    Article  MATH  MathSciNet  Google Scholar 

  11. Putz A, Frigaard IA (2010) Creeping flow around particles in a Bingham fluid. J Non-Newton Fluid Mech 165:263–280

    Article  MATH  Google Scholar 

  12. Duvaut G, Lions JL (1976) Inequalities in mechanics and physics. Springer, New York

    Book  MATH  Google Scholar 

  13. Courant R, Hilbert D (1953) Methods of mathematical physics, vol 1. Interscience, New York

    Google Scholar 

  14. Friedman B (1956) Principles and techniques of applied mathematics. Wiley, New York

    MATH  Google Scholar 

  15. Glowinski R, Lions J-L, Trèmoliéres R (1981) Numerical analysis of variational inequalities. North-Holland, Amsterdam

    MATH  Google Scholar 

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

    Google Scholar 

  17. Huilgol RR, Mena B (2000) On the time estimate for start-up of pipe flows in a Bingham fluid—a proof of the result due to Glowinski, Lions and Trèmoliéres. J Non-Newton Fluid Mech 94:113–118

    Article  MATH  Google Scholar 

  18. Huilgol RR (2002) Variational inequalities in the flows of yield stress fluids including inertia: theory and applications. Phys Fluids 14:1269–1283

    Article  MATH  MathSciNet  Google Scholar 

  19. Glowinski R (1974) Sur l’ecoulement d’un fluide de Bingham dans une conduite cylindrique. J de Mécanique 13:601–621

    MathSciNet  Google Scholar 

  20. Huilgol RR, Mena B, Piau JM (2002) Finite stopping times and rheometry of Bingham fluids. J Non-Newton Fluid Mech 102:97–107

    Article  MATH  Google Scholar 

  21. Damianou Y, Philippou M, Koullas G, Georgiou GC (2014) Cessation of viscoplastic flow with wall slip. J Non-Newton Fluid Mech 203:24–37

    Article  Google Scholar 

  22. Nouar C, Frigaard IA (2001) Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria. J Non-Newton Fluid Mech 100:127–149

    Google Scholar 

  23. Joseph DD (1976) Stability of fluid motions, vol 1. Springer, Berlin

    Google Scholar 

  24. Busse FH (1969) Bounds on transport of mass and momentum by turbulent flow between parallel plates. Z Angew Math Phys 20:1–14

    Article  MATH  Google Scholar 

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Correspondence to Raja R. Huilgol .

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Huilgol, R.R. (2015). Energy Methods in Action: Equality, Inequality and Stability. In: Fluid Mechanics of Viscoplasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45617-0_9

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  • DOI: https://doi.org/10.1007/978-3-662-45617-0_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45616-3

  • Online ISBN: 978-3-662-45617-0

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