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Multicritical phenomena in flow of viscoelastic liquids. 1. Zaremba-Fromm-De Witt liquid

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Abstract

It has been shown that multicritical phenomena caused by nonlinearity of viscosity and high elasticity, and forced anisotropy at finite shear rates take place during flow of viscoelastic polymer melts which are isotropic in the resting state. The sign of the low-frequency asymptotic values of the dynamic viscosity and elasticity measured during steady flow is a criterion of the appearance of instability. These arguments are illustrated by the solution and analysis of the complex reaction to low-amplitude, periodic shear of a steady-flowing, very simple viscoelastic liquid — ZFD liquid. It was shown that the instability of viscoelastic liquids for a given steady shear rate is due to the effect of perturbations lasting for no less than some limiting value and its manifestations are caused by superposition of different types of instability — multicritical phenomena.

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References

  1. A. Green and G. Adkins, Large Strains and Nonlinear Mechanics of a Continuous Medium [Russian translation], Mir, Moscow (1965).

    Google Scholar 

  2. A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  3. L. A. Faitel'son and É. É. Yakobson, “Components of the complex modulus in periodic shear of a flowing viscoelastic liquid,” Mekh. Kompozitn. Mater., No. 2, 277–286 (1981).

    Google Scholar 

  4. H. C. Booij, Effect of Superposed Steady Shear Flow on Dynamic Properties of Polymer Fluids, Dissertation, University of Leiden (1970).

  5. H. C. Booij, “Influence of the superposed steady shear flow on the dynamic properties of non-Newtonian fluids. II,” Rheol. Acta,5, No. 3, 222–227 (1966).

    Google Scholar 

  6. É. É. Jakobson and L. A. Faitel'son, “Stress-strain state of high-molecular-weight liquids in steady shear flow and accumulated energy,” Mekh. Kompozitn. Mater., No. 2, 328–336 (1985).

    Google Scholar 

  7. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymer Liquids. Vol. 1. Fluid Mechanics, Wiley, New York (1976).

    Google Scholar 

  8. S. Zaremba, Memorial de Sciences Mathematiques, No. 82, Paris (1937).

  9. H. Fromm, “Laminare Strömung Newtonscher und Maxwellscher Flüssigkeiten,” Z. Angew. Math. Mech.,25/27, No. 1, 146–150 (1947).

    Google Scholar 

  10. T. W. De Witt, “A Theological equation of state which predicts non-Newtonian viscosity, normal stresses and dynamic moduli,” J. Appl. Phys.,26, 889–894 (1955).

    Google Scholar 

  11. H. C. Booij, “Influence of the superposed steady shear flow on the dynamic properties of non-Newtonian fluids. I,” Rheol. Acta,5, No. 3, 215–227 (1966).

    Google Scholar 

  12. M. G. Tsiprin and L. A. Faitel'son, “Effect of steady flow of polyisobutylene solution on its dynamic characteristics measured in the direction of flow,” Mekh. Polim., No. 5, 913–919 (1970).

    Google Scholar 

  13. T. Kataoka and S. Ueda, “Influence of the superposed steady shear flow on the dynamic properties of polyethylene melts,” J. Polym. Sci.,A2, No. 7, 475–482 (1969).

    Google Scholar 

  14. Z. Laufer, H. L. Jalink, and A. J. Staverman, “Dynamic properties of some solutions subjected to a steady shear superposed on an oscillatory shear flow,” Rheol. Acta,14, 641–655 (1975).

    Google Scholar 

  15. L. A. Faitel'son and M. G. Tsiprin, “Possible mechanisms of flow of polymer solutions and melts,” Mekh. Polim., No. 3, 546–549 (1971).

    Google Scholar 

  16. J. M. Simons, “Dynamic modulus of polyisobutylene solutions in superposed steady shear flow,” Rheol. Acta,7, No. 2, 184–188 (1968).

    Google Scholar 

  17. R. I. Tanner and G. Williams, “On the orthogonal superposition of simple shearing and small-strain oscillatory motions,” Rheol. Acta,10, No. 4, 528–538 (1971).

    Google Scholar 

  18. J. Zeegers, D. van den Ende, G. Blom, E. G. Altena, G. J. Beukema, and J. Mellema, “An instrument for complex viscosity measurements in steady shear flow, based on the method of orthogonal superposition,” in: Progress and Trends in Rheology. IV, C. Gallegos (ed.), Proc. 4th Europ. Rheology Conf. Sevilla, September, 1994, Dietrich Steinkopf, Darmstadt (1994), pp. 540–542.

  19. H. Markovitz, “Small deformations superimposed on steady viscometric flows,” in: Proc. 5th Intern. Congr. on Rheology, Vol. 1, S. Onogi (ed.), University of Tokyo Press, Tokyo (1969), pp. 499–510.

    Google Scholar 

  20. Yo. Tokano, “Network theory for nonlinear viscoelasticity,” Polym. J.,6(1), No. 1, 61–71 (1974).

    Google Scholar 

  21. B. Bernstein, “On rheological relations,” Rheol. Acta,10, No. 2, 295–298 (1973).

    Google Scholar 

  22. R. I. Tanner, “Progress in experimental rheology,” in: Theoretical Rheology, London (1975), pp. 235–275.

  23. I. F. Macdonald, “On low frequency behavior in superposed flow,” Trans. Soc. Rheol.,18, No. 2, 313–322 (1974).

    Google Scholar 

  24. A. I. Leonov, “Nonequilibrium thermodynamics and rheology of viscoelastic polymer melts,” Rheol. Acta,15, 85–98 (1976).

    Google Scholar 

  25. C. M. Wong and A. I. Isayev, “Orthogonal superposition of small and large amplitude oscillations upon steady shear flow of polymer fluids,” Rheol. Acta,28, No. 2, 176–189 (1989).

    Google Scholar 

  26. K. A. Kline and S. I. Allen, Phys. Fluids,14, No. 9, 1863–1869 (1971).

    Google Scholar 

  27. K. A. Kline, “Polymers as structured continua: superposed oscillatory shear flows,” Trans. Soc. Rheol.,17, No. 3, 525–536 (1973).

    Google Scholar 

  28. J. M. Dealy, “Official nomenclature for material functions describing the response of a viscoelastic fluid to various shearing and extensional deformations,” J. Rheol.,37, No. 1, 136–148 (1993).

    Google Scholar 

  29. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids. Vol. 1. Fluid Mechanics, Wiley, New York (1987).

    Google Scholar 

  30. V. N. Burlii, Limits of Laminar Flow of Polymer Melts with Narrow Molecular-Weight Distribution, Candidate Dissertation, Riga (1989).

  31. S. Alam, “Network thermodynamics. An overview,” Biophys. J.,15, No. 7, 667–685 (1975).

    Google Scholar 

  32. H. K. Nason, “A high temperature-high pressure rheometer for plastics,” J. Appl. Phys.,16, 338–343 (1945).

    Google Scholar 

  33. R. S. Spenser and R. E. Dillon, J. Colloid Sci.,3, 163 (1948).

    Google Scholar 

  34. R. S. Spenser and R. E. Dillon, “The viscous flow of molten polystyrene,” J. Colloid Sci.,4, 241–255 (1949).

    Google Scholar 

  35. A. B. Metzner, “Fracture of non-Newtonian fluids at high shear stresses,” Ind. Eng. Chem.,50, 1577–1580 (1958).

    Google Scholar 

  36. E. B. Bagley and H. P. Schreiber, “Elasticity effects in polymer extrusion,” in: Rheology. Theory and Applications, F. R. Eirich (ed.), Vol. 5, Chapter 3, Academic Press, New York-London (1969), pp. 93–125.

    Google Scholar 

  37. G. V. Vinogradov, A. Ya. Malkin, and A. I. Leonov, “Conditions of unstable flow of viscoelastic polymer systems,” Kolloid. Z. Z. Polym.,191, 25–30 (1964).

    Google Scholar 

  38. W. Gleissle, “Stresses in polymer melts at the beginning of flow instabilities (melt fracture) in cylindrical capillaries,” Rheol. Acta,21, Nos. 4–5, 484–487 (1982).

    Google Scholar 

  39. J. P. Tordella, “Unstable flow of molten polymer,” in: Rheology. Theory and Applications, F. R. Eirich (ed.), Vol. 5, Academic Press, New York-London (1969), pp. 57–92.

    Google Scholar 

  40. A. Ya. Malkin and A. I. Leonov, “Unstable flow of polymers,” in: Advances in the Rheology of Polymers [in Russian], G. V. Vinogradov (ed.), Khimiya, Moscow (1970), pp. 98–117.

    Google Scholar 

  41. B. M. Khusid and Z. P. Shul'man, “Effects of elasticity in movement of hereditary liquids in channels,” Itogi Nauki Tekhn., Ser. Kompleks. Spets. Razdely Mekh.,2, 3–94 (1986).

    Google Scholar 

  42. J. R. A. Pearson and C. J. S. Petrie, “On melt flow instability of extruded polymers,” in: Polymer Systems. Deformation and Flow, R. E. Wetton and R. W. Whorlow (eds.), Macmillan, London (1968), pp. 163–187.

    Google Scholar 

  43. J. L. White, “Elastomer rheology and processing,” Rubber Chem. Technol.,42, No. 1, 257–338 (1969).

    Google Scholar 

  44. C. J. S. Petrie and M. M. Denn, “Instabilities in polymer processing,” Am. Inst. Chem. Eng. J.,22, 209–236 (1976).

    Google Scholar 

  45. E. Bandreaux and J. A. Cuculo, “Polymer flow instability: a review and analysis,” J. Macromol. Sci.,C16, No. 1, 39–77 (1977–1978).

    Google Scholar 

  46. M. M. Denn, “Issues in viscoelastic fluid mechanics,” Ann. Rev. Fluid Mech.,22, 13–34 (1990).

    Google Scholar 

  47. R. G. Larson, “Instabilities in viscoelastic flow,” Rheol. Acta,31, No. 3, 213–263 (1992).

    Google Scholar 

  48. V. I. Brizitskii, Polarization-optical Study of Polymers in a Wide Range of Stresses, Candidate Dissertation, Moscow (1977).

  49. J. L. White, “A continuum theory of nonlinear viscoelasticity in viscoelastic deformation with application to polymer processing,” J. Appl. Polym. Sci.,8, No. 3, 1129–1146 (1964).

    Google Scholar 

  50. N. M. Smirnova, I. V. Korepova, and Yu. Ya. Podol'skii, “Initial viscosity of rubber as a function of pressure,” in: Machines and Technologies for Processing Rubber, Polymers, and Rubber Blends [in Russian], Vol. 1, Yaroslavl' (1978), pp. 96–98.

    Google Scholar 

  51. A. A. Trapeznikov, G. N. Lesina, and T. I. Korotina, “Instability of paste and polymer deformation in passage through structural strength limits,” Zh. Fiz. Khim.,46, No. 6, 1380–1384 (1972).

    Google Scholar 

  52. W. M. Kulicke and R. Porter, “Irregularities in steady flow for non-Newtonian fluids between cone and plate,” J. Appl. Polym. Sci.,23, 953–965 (1979).

    Google Scholar 

  53. L. A. Faitel'son and I. P. Briedis, “Critical modes of deformation of polymer melts in rotary flowmeters with a cone-plate working unit,” Mekh. Polim., No. 4, 718–723 (1976).

    Google Scholar 

  54. L. V. McIntire, “On initiation of melt fracture,” J. Appl. Polymer Sci.,16, 2901–2908 (1972).

    Google Scholar 

  55. J. P. Tordella, “Unstable flow of molten polymers: a second site of melt fracture,” J. Appl. Polym. Sci.,7, No. 1, 215–229 (1963).

    Google Scholar 

  56. G. V. Vinogradov, M. L. Friedman, B. V. Yarlykov, and A. Ya. Malkin, “Unsteady flow of polymer melts: polypropylene,” Rheol. Acta,9, No. 3, 323–329 (1970).

    Google Scholar 

  57. N. I. Insarova [Insarowa], G. W. Vinogradov [Winogradow], and B. B. Boiko, “Uber kritische Zustände bei der Deformation linearer Polymerer,” Plaste Kautschuk,20, No. 4, 289–290 (1973).

    Google Scholar 

  58. G. V. Vinogradov, N. I. Insarova, B. B. Boiko, and E. K. Borisenkova, “Critical regimes of shear in linear polymers,” Polym. Eng. Sci.,12, No. 5, 323–334 (1972).

    Google Scholar 

  59. J. Molenaar and R. J. Koopmans, “Modeling polymer melt-flow instabilities,” J. Rheol.,38, No. 1, 99–109 (1994).

    Google Scholar 

  60. Yu. A. Buevich and A. I. Leonov, “Theory of dry friction of rubber-like materials,” Prikl. Mekh. Tekh. Fiz., No. 6, 77–83 (1965).

    Google Scholar 

  61. A. V. Karakin and A. I. Leonov, “Self-oscillations in flow of polymer melts from a capillary,” Prikl. Mekh. Tekh. Fiz., No. 3, 110–114 (1968).

    Google Scholar 

  62. A. M. Stolin and S. I. Khudyaev, “Formation of spatially inhomogeneous states of a structured liquid in superanomalous flow,” Dokl. Akad. Nauk SSSR,260, No. 5, 1180–1184 (1981).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Polymer Mechanics, Latvian Academy of Sciences, LV-1006, Riga, Latvia

    L. A. Faitel'son & É. É. Yakobson

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  1. L. A. Faitel'son
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  2. É. É. Yakobson
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 555–572, July–August, 1995.

The study was conducted based on Topic 93,177 of the Latvian Science Council.

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Faitel'son, L.A., Yakobson, É.É. Multicritical phenomena in flow of viscoelastic liquids. 1. Zaremba-Fromm-De Witt liquid. Mech Compos Mater 31, 408–421 (1996). https://doi.org/10.1007/BF00632632

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