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Couette flows of fluids with pressure dependent viscosity

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Języki publikacji
EN
Abstrakty
EN
For liquids such as water, for a range of pressures for which the density remains nearly constant, the viscosity could change by several orders of magnitude. Thus, such liquids could be approximated as incompressible liquids whose viscosity depends on the pressure. Stokes (1945) recognized this possibility and the fact that the viscosity could be considered to be independent of the pressure in only special flows. That this is indeed so has been verified in the case of numerous liquids (Bridgman, 1931). In this short study, we allow the viscosity of the fluid to be dependent on the pressure and investigate the consequence of the effect of gravity in simple flows such as Couette flows between parallel plates. We find that gravity can have a profound effect on the structure of the flow. Its presence leads to the concentration of vorticity adjacent to one of the plates.
Rocznik
Strony
573--585
Opis fizyczny
Bibliogr. 20 poz., wykr.
Twórcy
  • Department of Mechanical Engineering Texas A&M University, College Station, TX 77843-3123, USA
Bibliografia
  • [1] Andrade C. (1930): Viscosity of liąuids. - Naturę, vol,125, pp.309-310.
  • [2] Bair S. and Winer W.O. (1992): The high pressure high shear stress rheology of liquid lubricants. - J. Tribology, vol.ll4, pp.1-13.
  • [3] Bridgman P.W. (1931): The Physics of High Pressure. - New York: The MacMillan Company.
  • [4] Cutler W.G., McMicke R.H., Webb W. and Scheissler R.W. (1958): Study of the compressions of several high molecular weight hydrocarbons. - J. Chem. Phys., vol.29, pp.727-740.
  • [5] Franta M., Malek J. and Rajagopal K.R.: On steady flows of fluids with pressure and shear dependant yiscosities, - Submitted for publication.
  • [6] Gazzola F. (1997): A notę on the solution of Navier-Stokes equations with a pressure-dependent yiscosity. - Z. Angew. Math. Phys., vol.48, pp.760-773.
  • [7] Griest E.M., Webb W. and Schiessler R.W. (1958): Effect of pressure on viscosity of high hydrocarbons and their mixture. - J. Chem. Phys., vol.29, pp.711-720.
  • [8] Hron J., Małek J., Necas J. and Rajagopal K.R. (2003): Numerical simulations and global existence of Solutions of two dimensional flows fluids with pressure and shear dependent viscosities. - Mathematics and Computers in Simulation, vol.61, pp.297-315.
  • [9] Hron J., Małek J. and Rajagopal K.R. (2001): Simple flows of fluids with pressure dependent viscosities. - Proc. Roy. Soc., London, Ser.A, Mathematical Physical and Engineering Sciences, vol.457, pp.1603-1622.
  • [10] Johnson K.L. and Cameron R. (1967): Shear behavior of elastohydrodynamic oil films at high rolling contact pressures. - Proc. Instn. Mech. Engrs., vol.l82, pp.307-319.
  • [11] Johnson K.L. and Greenwood J.A. (1980): Thermal analysis of an Eyring fluid in elastohydrodynamic traction. - Wear, vol.61, pp.355-371.
  • [12] Johnson K.L. and Tevaarwerk J.L. (1977): Shear behayior of elastohydrodynamic oil films. - Proc. Roy. Soc., London, Ser.A, vol.356, pp.215-236.
  • [13] Malek J., Necas J. and Rajagopal K.R. (2002a): Global analysis of flows of fluids with pressure dependant yiscosities. - Archive for Rational Mechanics and Analysis, yol.165, pp.243-269.
  • [14] Malek J., Necas J. and Rajagopal K.R. (2002b): Global existence of Solutions for flows of fluids with pressure and shear dependent viscosities. - Applied Mathematics Letters, vol.l5, pp.961-967.
  • [15] Rajagopal K.R. and Kannan K. (2004): Flows of fluid with pressure dependent viscosities between rotating parallel plates. - In press.
  • [16] Rajagopal K.R. and Szeri A.Z. (2003): On an inconsistency in the derivation of the equations of elastohydrodynamic lubrication. - Proc. Roy. Soc., London, Ser.A, yol.459, pp.2771-2786.
  • [17] Renardy M. (1986): Some remarks on the Navier-Stokes equations with pressure-dependent viscosity. - Comm. PDEs, vol.ll, pp.779-793.
  • [18] Stokes G.G. (1945): On the theories of internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. - Trans. Cambridge Philosophical Soc., vol.8, pp.287-305.
  • [19] Szeri A.Z. (1998): Fluid Film Lubrication: Theory and Design. - Cambridge: Cambridge University Press.
  • [20] Vasudevaiah M. and Rajagopal K.R. (2004): On fully developed flows of fluids with a pressure dependent viscosity in a pipe. - In press, Application of Mathematics, Czech Academy of Sciences.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0007-0037
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