Abstract
We present mathematical results that are needed to analyse novel phenomena occurring in dynamic shearing flows of highly elastic and viscous non-Newtonian fluids. The key property of solutions to the time-dependent, quasilinear partial differential equations that are used to model such flows is a non-monotonic relation between the steady shear stress and strain rate. The phenomena discussed may lead to material instabilities that could disrupt polymer processing.
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References
M. Denn, “Issues in Viscoelastic Fluid Dynamics,” Annual Reviews of Fluid Mechanics 22 (1990), pp. 22–34.
W. Hrusa, J. Nohel, and M. Renardy, “Initial Value Problems in Viscoelasticity,” Appl. Mech. Rev. 41 (1988), pp. 371–378.
J. Hunter and M. Slemrod, “Viscoelastic Fluid Flow Exhibiting Hysteretic Phase Changes,” Phys. Fluids 26 (1983), pp. 2345–2351.
M. Johnson and D. Segalman, “A Model for Viscoelastic Fluid Behavior which Allows Non-Affine Deformation,” J. Non-Newtonian Fluid Mech. 2 (1977), pp. 255–270.
R. Kolkka and G. Ierley, “Spurt Phenomena for the Giesekus Viscoleastic Liquid Model,” J. Non-Newtonian Fluid Mech., 1989. To appear.
R. Kolkka, D. Malkus, M. Hansen, G. Ierley, and R. Worthing, “Spurt Phenomena of the Johnson-Segalman Fluid and Related Models,” J. Non-Newtonian Fluid Mech. 29 (1988), pp. 303–325.
D. Malkus, J. Nohel, and B. Plohr, “Time-Dependent Shear Flow Of A Non-Newtonian Fluid,” pp. 91-109 in Conference on Current Problems in Hyberbolic Problems: Riemann Problems and Computations, ed. B. Lindquist, Contemporary Mathematics. Amer. Math. Soc., Providence, R. I., 1989.
D. Malkus, J. Nohel, and B. Plohr, “Dynamics of Shear Flow of a Non-Newtonian Fluid,” J. Comput. Phys., 1989. To appear; also CMS Tech. Summary Rep. #89-14.
D. Malkus, J. Nohel, and B. Plohr, “Analysis of New Phenomena in Shear Flow of Non-Newtonian Fluids,” SIAM J. Appl. Math., 1989. Submitted; also CMS Technical Summary Report #90-6.
J. Nohel, R. Pego, and A. Tzavaras, “Stability of Discontinuous Shearing Motions of Non-Newtonian Fluids,” Proc. Royal Soc. Edinburgh, 1989. To appear..
J. Oldroyd, “Non-Newtonian Effects in Steady Motion of Some Idealized Elastico- Viscous Liquids,” Proc. Roy. Soc. London A 245 (1958), pp. 278–297.
J. Pearson, Mechanics of Polymer Processing, Elsevier Applied Science, London, 1985.
M. Renardy, W. Hrusa, and J. Nohel, Mathematical Problems in Viscoelasticity, Pitman Monographs and Surveys in Pure and Applied Mathematics V. 35, Longman Scientific & Technical, Essex, 1987.
G. Vinogradov, A. Malkin, Yu. Yanovskii, E. Borisenkova, B. Yarlykov, and G. Berezhnaya, “Viscoelastic Properties and Flow of Narrow Distribution Polybutadienes and Polyisoprenes,” J. Polymer Sci., Part A-2 10 (1972), pp. 1061–1084.
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© 1991 Kluwer Academic Publishers
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Nohel, J.A. (1991). Non-Newtonian Phenomena in Shear Flow. In: Spigler, R. (eds) Applied and Industrial Mathematics. Mathematics and Its Applications, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1908-2_16
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DOI: https://doi.org/10.1007/978-94-009-1908-2_16
Publisher Name: Springer, Dordrecht
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