Advertisement

Tribology Letters

, 68:7 | Cite as

Viscous Heating in Compressed Liquid Films

  • Scott BairEmail author
Original Paper
  • 51 Downloads

Abstract

The greatest challenge in high-shear viscometry is the recognition of the difference between constitutive behavior and thermal feedback. The failure to realize this distinction was the cause of a serious mistake which has had a profound effect upon the EHL field for four decades. A traction curve is not a rheological flow curve. The classical approach to EHL has ignored the measurement of viscosity in viscometers at elevated pressures. As a consequence, the field has not benefitted from the understanding gained from directly observing the thermal softening effects of viscous heating. The Eyring sinh-law appears in high-shear viscometry when viscous heating causes thermal softening. The thermal limit of pressurized thin film Couette viscometers with high thermal conductivity cylinders is well-defined by the Nahme–Griffith number. The Spikes and Jie equation overcorrects at low values of the Nahme–Griffith number and undercorrects at high values. The viscous heating in a shear-thinning liquid may cause an apparent transition from power-law to sinh-law above some viscous power. Surprisingly, the sinh-law in this instance extrapolates back to the correct low-shear viscosity. The same response has been observed in one set of NEMD simulations.

Keywords

Quantitative EHL Rheology Thermal EHL 

List of Symbols

a

Yasuda parameter

c

Heat capacity of the solid (J/kg K)

d

Divisor

F

Heat flux (W/m2)

G

Effective shear modulus or critical shear stress for shear-thinning (Pa)

h

Film thickness (m)

k

Thermal conductivity of liquid (W/m K)

ks

Thermal conductivity of the solid (W/m K)

p

Pressure (Pa)

Na

Nahme–Griffith number

n

Power-law exponent

T

Temperature (K or  °C)

t

Time (s)

w

Half of the width of the shear zone (m)

X

Dimensionless coordinate in the flow direction of a contact

x

Coordinate in the axial direction of a cylinder pair (m)

\(\dot{\beta }\)

Temperature-viscosity coefficient (K−1)

\(\dot{\gamma }\)

Shear rate (s−1)

\(\eta\)

Generalized (non-Newtonian) viscosity (Pa s)

\(\mu\)

Low-shear viscosity (Pa s)

\(\rho\)

Mass density of the solid (kg/m3)

\(\tau\)

Shear stress (Pa)

\(\tau_{E}\)

Eyring stress (Pa)

Notes

References

  1. 1.
    Houpert, L.: New results of traction force calculations in elastohydrodynamic contacts. J. Tribol. 107(2), 241–245 (1985)CrossRefGoogle Scholar
  2. 2.
    Roelands CJA (1966) Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils. Doctoral dissertation, Delft University of TechnologyGoogle Scholar
  3. 3.
    Bair, S.S.: High pressure rheology for quantitative elastohydrodynamics, 2nd edn. Elsevier, Amsterdam (2019)Google Scholar
  4. 4.
    Johnson, K.L., Tevaarwerk, J.L.: Shear behaviour of elastohydrodynamic oil films. Proc. R. Soc. Lond. A 356(1685), 215–236 (1977)CrossRefGoogle Scholar
  5. 5.
    Bair, S.: The variation of viscosity with temperature and pressure for various real lubricants. J. Tribol. 123(2), 433–436 (2001)CrossRefGoogle Scholar
  6. 6.
    Bair, S.: Rheology and high-pressure models for quantitative elastohydrodynamics. Proc. Inst. Mech. Eng. 223(4), 617–628 (2009)CrossRefGoogle Scholar
  7. 7.
    Bair, S., Mary, C., Bouscharain, N., Vergne, P.: An improved Yasutomi correlation for viscosity at high pressure. Proc. Inst. Mech. Eng. 227(9), 1056–1060 (2013)CrossRefGoogle Scholar
  8. 8.
    Casalini, R., Roland, C.M.: Why liquids are fragile. Phys. Rev. E 72(3), 031503 (2005)CrossRefGoogle Scholar
  9. 9.
    Habchi, W., Eyheramendy, D., Bair, S., Vergne, P., Morales-Espejel, G.: Thermal elastohydrodynamic lubrication of point contacts using a Newtonian/generalized Newtonian lubricant. Tribol. Lett. 30(1), 41–52 (2008)CrossRefGoogle Scholar
  10. 10.
    Habchi, W., Bair, S., Vergne, P.: On friction regimes in quantitative elastohydrodynamics. Tribol. Int. 58, 107–117 (2013)CrossRefGoogle Scholar
  11. 11.
    Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.: Friction reduction in elastohydrodynamic contacts by thin-layer thermal insulation. Tribol. Lett. 53(2), 477–486 (2014)CrossRefGoogle Scholar
  12. 12.
    Gruntfest, I.J.: Apparent departures from Newtonian behavior in liquids caused by viscous heating. Trans. Soc. Rheol. 9(1), 425–441 (1965)CrossRefGoogle Scholar
  13. 13.
    Hahn, S.J., Eyring, H., Higuchi, I., Ree, T.: Flow properties of lubricating oils under pressure. NLGI Spokesm. 21(3), 123–128 (1958)Google Scholar
  14. 14.
    Hahn, S.J., Ree, T., Eyring, H.: Flow mechanism of thixotropic substances. Ind. Eng. Chem. 51(7), 856–857 (1959)CrossRefGoogle Scholar
  15. 15.
    Lower, G.W., Walker, W.C., Zettlemoyer, A.C.: The rheology of printing inks. II. temperature control studies in the rotational viscometer. J. Colloid Sci. 8(1), 116–129 (1953)CrossRefGoogle Scholar
  16. 16.
    Gerrard, J.E., Steidler, F.E., Appledoorn, J.K.: Viscous heating in capillaries. adiabatic case. Indus. Eng. Chem. Fundam. 4(3), 332–339 (1965)CrossRefGoogle Scholar
  17. 17.
    Yasuda, K.Y., Armstrong, R.C., Cohen, R.E.: Shear flow properties of concentrated solutions of linear and star branched polystyrenes. Rheol. Acta 20(2), 163–178 (1981)CrossRefGoogle Scholar
  18. 18.
    Jakobsen J (1973) Lubricant rheology at high shear stress. Doctoral dissertation, Georgia Institute of TechnologyGoogle Scholar
  19. 19.
    Norton, A.E., Knott, M.J., Muenger, J.R.: Flow properties of lubricants under high pressure. ASME Trans 63(7), 631–643 (1941)Google Scholar
  20. 20.
    Hirst, W., Moore, A.J.: The effect of temperature on traction in elastohydrodynamic lubrication. Phil. Trans. R. Soc. Lond. A 298(1438), 183–208 (1980)CrossRefGoogle Scholar
  21. 21.
    Ockendon, H., Ockendon, J.R.: Variable-viscosity flows in heated and cooled channels. J. Fluid Mech. 83(1), 177–190 (1977)CrossRefGoogle Scholar
  22. 22.
    Wakeham, W.A., Assael, M.J., Avelino, H.M., Bair, S., Baled, H.O., Bamgbade, B.A., Bazile, J.P., Caetano, F.J., Comunas, M.J., Daridon, J.L., Diogo, J.C.: In pursuit of a high-temperature, high-pressure, high-viscosity standard: the case of tris (2-ethylhexyl) trimellitate. J. Chem. Eng. Data 62(9), 2884–2895 (2017)CrossRefGoogle Scholar
  23. 23.
    Vinogradov, G.V., Malkin, A.Y.: Temperature-independent viscosity characteristics of polymer systems. J. Polym. Sci. Part A 2(5), 2357–2372 (1964)Google Scholar
  24. 24.
    Poehlein, G.: Note: temperature effects in couette viscometers. Trans. Soc. Rheol. 12(2), 351–353 (1968)CrossRefGoogle Scholar
  25. 25.
    Wright, B., Mather, J.: Use of a couette high-shear-rate viscometer for measuring the viscosity of engine lubricants. The relationship between engine oil viscosity and engine performance—Part V and Part VI. ASTM International, Pennsylvania (1980)Google Scholar
  26. 26.
    Manrique, L.A., Porter, R.S.: An improved Couette high shear viscometer. Rheol. Acta 14(10), 926–930 (1975)CrossRefGoogle Scholar
  27. 27.
    Spikes, H., Jie, Z.: History, origins and prediction of elastohydrodynamic friction. Tribol. Lett. 56(1), 1–25 (2014)CrossRefGoogle Scholar
  28. 28.
    Archard, J.F.: The temperature of rubbing surfaces. Wear 2(6), 438–455 (1959)CrossRefGoogle Scholar
  29. 29.
    Bair, S.: The temperature and pressure dependence of viscosity and volume for two reference liquids. Lubr. Sci. 28(2), 81–95 (2016)CrossRefGoogle Scholar
  30. 30.
    Bair, S.: Density scaling of the thermal conductivity of a jet oil. Tribol. Trans. 57(4), 647–652 (2014)CrossRefGoogle Scholar
  31. 31.
    Harris, K.R., Bair, S.: Temperature and pressure dependence of the viscosity of diisodecyl phthalate at temperatures between (0 and 100) °C and at pressures to 1 GPa. J. Chem. Eng. Data 52(1), 272–278 (2007)CrossRefGoogle Scholar
  32. 32.
    Jaeger, J.C., Carslaw, H.S.: Conduction of heat in solids, 2nd edn. Clarendon Press, Oxford (1959)Google Scholar
  33. 33.
    Habchi, W., Bair, S.: Effect of lubricant rheology on friction in coated elastohydrodynamic lubricated contacts. Proc. Inst. Mech. Eng. 231(8), 975–985 (2017)CrossRefGoogle Scholar
  34. 34.
    Winter, H.H.: Viscous dissipation in shear flows of molten polymers. Adv. Heat Transf. 13, 205–267 (1977)CrossRefGoogle Scholar
  35. 35.
    Yang, P., Kaneta, M., Masuda, S.: Quantitative comparisons between measured and solved EHL dimples in point contacts. J. Tribol. 125(1), 210–214 (2003)CrossRefGoogle Scholar
  36. 36.
    Jadhao, V., Robbins, M.O.: Probing large viscosities in glass-formers with nonequilibrium simulations. Proc. Natl. Acad. Sci. USA 114(30), 7952–7957 (2017)CrossRefGoogle Scholar
  37. 37.
    Jadhao, V., Robbins, M.O.: Rheological properties of liquids under conditions of elastohydrodynamic lubrication. Tribol. Lett. 67(3), 66 (2019)CrossRefGoogle Scholar
  38. 38.
    Bair, S.: Reference liquids for quantitative elastohydrodynamics: selection and rheological characterization. Tribol. Lett. 22(2), 197–206 (2006)CrossRefGoogle Scholar
  39. 39.
    Bair, S., Winer, W.O.: The high shear stress rheology of liquid lubricants at pressures of 2 to 200 MPa. J. Tribol. 112(2), 246–252 (1990)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Regents’ Researcher, Georgia Institute of Technology, Center for High-Pressure RheologyGeorge W. Woodruff School of Mechanical EngineeringAtlantaUSA

Personalised recommendations