Korea-Australia Rheology Journal

The Korean Society of Rheology (한국유변학회)
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A phenomenological approach to suspensions with viscoelastic matrices

  • Tanner Roger I. (School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney) ;
  • Qi Fuzhong (School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney)
  • Published : 2005.12.01
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Abstract

A simple constitutive model for viscoelastic suspensions is discussed in this paper. The model can be used to predict the rheological properties (relative viscosity and all stresses) for viscoelastic suspensions in shear and elongational flow, and the constitutive equations combine a 'viscoelastic' behaviour component and a 'Newtonian' behaviour component. As expected, the model gives a prediction of positive first normal stress difference and negative second normal stress difference; the dimensionless first normal stress difference strongly depends on the shear rate and decreases with the volume fraction of solid phase, but the dimensionless second normal stress difference (in magnitude) is nearly independent of the shear rate and increases with the volume fraction. The relative viscosities and all the stresses have been tested against available experimental measurements.

Keywords

References

  1. Barnes, H.A., 2003, A review of the rheology of filled viscoelastic systems, Rheology Reviews 1, 1-36
  2. Frankel, N.A. and A. Acrivos, 1967, On the viscosity of a concentrated suspensions of solid sphere, Chem. Eng. Sci. 22, 847- 853 https://doi.org/10.1016/0009-2509(67)80149-0
  3. Gadala-Maria, F. and A. Acrivos, 1980, Shear-induced structure in a concentrated suspension of solid spheres, J. Rheol. 24, 799-814 https://doi.org/10.1122/1.549584
  4. Jenkins, T.J. and D.F. McTigue, 1992, Viscous fluctuations and the rheology of concentrated suspensions (unpublished manuscript)
  5. Krieger, I.M., 1972, Rheology of monodispersed Lattices, Adv. Colloid Interface Sci. 3, 111-136 https://doi.org/10.1016/0001-8686(72)80001-0
  6. Le Meins J-F., P. Moldenaers and J. Mewis, 2003, Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow, Rheol. Acta 42, 184-190 https://doi.org/10.1007/s00397-002-0270-y
  7. Leighton, D. and A. Acrivos, 1987, The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech. 181, 415-439 https://doi.org/10.1017/S0022112087002155
  8. Mall-Gleissle, S.E., W. Gleissle, G.H. McKinley and H. Buggisch, 2002, The normal stress behaviour of suspensions with viscoelastic matrix fluids, Rheol. Acta 41, 61-76 https://doi.org/10.1007/s003970200006
  9. Metzner, A.B., 1985, Rheology of suspensions in polymeric liquids, J. Rheology 29, 739-775 https://doi.org/10.1122/1.549808
  10. Nam, J.G., K. Hyun, K.H. Ahn and S.J. Lee, 2004, Rheological behaviour of hard sphere suspensions in a large shear flow, Proc. XIV Conf. Rheol. Seoul, SU65, 1-3
  11. Nott, P.R. and J.F. Brady, 1994, Pressure-driven flow of suspensions: simulation and theory, J. Fluid Mech. 275, 157-199 https://doi.org/10.1017/S0022112094002326
  12. Ohl, N. and W. Gleissle, 1993, The characterization of the steadshear and normal stress functions of highly concentrated suspensions formulated with viscoelastic fluids, J. Rheol. 37, 381- 406 https://doi.org/10.1122/1.550449
  13. Phan-Thien, N., 1995, Constitutive equation for concentrated suspensions in Newtonian liquids, J. Rheol. 39(4), 679-695 https://doi.org/10.1122/1.550651
  14. Phan-Thien, N., X.J. Fan and B.C. Khoo, 1999, A new constitutive model for monodispersed suspensions of spheres at high concentrations, Rheol. Acta 38, 297-304 https://doi.org/10.1007/s003970050181
  15. Philips, R.J., R.C. Armstrong, R.A. Brown, A.L. Graham and J.R. Abbott, 1992, A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration, Phys. Fluid A4(1), 30-40
  16. Tanner, R.I., 2000, Engineering Rheology, Oxford U. Press, 273
  17. Tanner, R.I., 2002, A suspension model for low shear rate polymer solidification, J. Non-Newtonian Fluid Mech. 102, 397-408 https://doi.org/10.1016/S0377-0257(01)00189-6
  18. Tanner, R.I. and F. Qi, 2005, A comparison of some models for describing polymer crystallization at low deformation rates, J. Non-Newtonian Fluid Mech. 127, 131-141 https://doi.org/10.1016/j.jnnfm.2005.02.005
  19. Zarraga, I.E., D.A. Hill and D.T. Leighton, 1999, The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids, J. Rheol. 44, 185-120 https://doi.org/10.1122/1.551083
  20. Zarraga, I.E., D.A. Hill and D.T. Leighton, 2001, Normal stress and free surface deformation in concentrated suspensions of noncolloidal spheres in a viscoelastic fluid, J. Rheol. 45, 1065- 1084 https://doi.org/10.1122/1.1396356