Simple flows of fluids with pressure-dependent viscosities

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 457, Issue 2011, 2001, Pages 1603-1622

  Hron, J ^a   Malek J ^a   Rajagopal, K R ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b Texas AandM University   (United States)

Author keywords

Incompressible fluid; Pressure dependent viscosity; Rheology

Indexed keywords

EID: 0001319402     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0723     Document Type: Article

References (31)

1. Amontons, G. 1699 De la résistance causée dans les machines. Mem. Acad. R. Sci. Paris A, 257-282.
2. Antman, S. S. 1981 Material constraints in continuum mechanics. Atti della Accademia Nazionale dei Lincei, Rendiconti, Classe di Scienza Fisiche, Matematiche e Naturali 70, 256-264.
3. Antman, S. S. & Marlow, R. S. 1991 Material constraints, Lagrange multipliers, and compatibility. Applications to rod and shell theories. Arch. Ration. Mech. Analysis 116, 257-299.
4. Bair, S. & Winer, W. O. 1992 The high pressure high shear stress rheology of liquid lubricants. J. Tribol. 114, 1-13.
5. Bair, S., Khonsari, M. & Winer, W. O. 1998 High pressure rheology of lubricants and limitations of the Reynolds equation. Tribol Int. 31, 573-586.
6. Bridgman, P. W. 1926 The effect of pressure on the viscosity of forty-three pure liquids. Proc. Am. Acad. 61, 57-99.
7. Bridgman, P. W. 1931 The physics of high pressure. New York: MacMillan.
8. Coulomb, C. A. 1785 Théorie des machines simples, en ayant égard au frottement de leurs parties, et à la roideur des cordages. Mémoires des Savantes étrangers.
9. Cutler, W. G., McMickle, R. H., Webb, W. &: Schiessler, R. W. 1958 Study of the compressions of several high molecular weight hydrocarbons. J. Chem. Phys. 29, 727-740.
10. Dugas, R. 1988 A history of mechanics. New York: Dover.
11. Gazzola, F. 1997 A note on the evolution of Navier-Stokes equations with a pressure-dependent viscosity. Z. Angew. Math. Phys. 48, 760-773.
12. Griest, E. M., Webb, W. & Schiessler, R. W. 1958 Effect of pressure on viscosity of higher hydrocarbons and their mixtures. J. Chem. Phys. 29, 711-720.
13. Gwynllyw, D. Rh., Davies, A. R. &; Phillips, T. N. 1996 On the effects of a piezoviscous lubricant on the dynamics of a journal bearing. J. Rheol. 40, 1239-1266.
14. Hron, J., Málek, J. & Turek, S. 2000 A numerical investigation of flows of shear-thinning fluids with applications to blood rheology. Int. J. Numer. Meth. Fluids 32, 863-879.
15. Johnson, K. L. & Cameron, R. 1967 Shear behaviour of elastohydrodynamic oil films at high rolling contact pressures. Proc. Inst. Mech. Engrs 182, 307-319.
16. Johnson, K. L. & Greenwood, J. A. 1980 Thermal analysis of an Eyring fluid in elastohydrodynamic traction. Wear 61, 355-374.
17. Johnson, K. L. & Tevaarwerk, J. L. 1977 Shear behaviour of elastohydrodynamic oil films. Proc. R. Soc. Lond. A 356, 215-236.
18. Málek, J., Nečas, J., Rokyta, M. & Růžička, M. 1996 Weak and measure-valued solutions to evolutionary PDEs. London: Chapman & Hall.
19. Malevsky, A. V. & Yuen, D. A. 1992 Strongly chaotic non-Newtonian mantle convection in the Earth's mantle. Geophys. Astrophys. Fluid Dyn. 65, 149-171.
20. Morgan, A. J. A. 1966 Some properties of media by constitutive equations in implicit form. Int. J. Engng Sci. 4, 155-162.
21. Navier, C. L. M. H. 1823 Mémoire sur les lois du mouvement des fluides. Mem. Acad. R. Sci. Paris 6, 389-416.
22. Newton, I. 1687 Philosophæ naturalis principia mathematica (transl. Andrew Motte 1995). New York: Prometheus Books.
23. Poisson, S. D. 1831 Mémoire sur les équations générales de l'équilibre et du mouvement des corps solides élastiques et des fluides. J. Ecole Polytech. 13, 1-174.
24. Rajagopal, K. R. 1995 Multiple natural configurations in continuum mechanics. Institute for Computational and Applied Mechanics, University of Pittsburgh, Technical Report 6.
25. Rajagopal, K. R. & Srinivasa, A. R. 2000 A thermodynamic framework for rate type fluid models. J. Non Newton. Fluid. Mech. 88, 207-227.
26. Rajagopal, K. R. & Wineman, A. 1980 On constitutive equations for branching of response with selectivity. Int. J. Nonlinear Mech. 15, 83-91.
27. Renardy, M. 1986 Some remarks on the Navier-Stokes equations with a pressure-dependent viscosity. Commun. PDEs 11, 779-793.
28. Schaeffer, D. G. 1987 Instability in the evolution equations describing incompressible granular flow. J. Diff. Eqns 66, 19-50.
29. Stokes, G. G. 1845 On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Camb. Phil. Soc. 8, 287-305.
30. Szeri, A. Z. 1998 Fluid film lubrication: theory and design. Cambridge University Press.
31. Turek, S. 1998 Efficient solvers for incompressible flow problems: an algorithmic and computational approach. Lecture Notes on Computational Science and Engineering, vol. 6. Springer.