Influence of shear banding of polymeric fluids on the shape of rheological curves
DOI:
https://doi.org/10.7242/1999-6691/2018.11.4.33Keywords:
polymer fluids, shear banding, modified Vinogradov-Pokrovsky model, non-monotonic flow curve, plateau and hysteresis loop, numerical simulationAbstract
The recently discovered effect of shear banding in polymer fluids has provoked great interest in studying basic physics underlying this effect, which can also be considered as the main mechanism responsible for the appearance of specific features of polymer liquids in rheometric flows. In this paper, we study the influence of shear banding in polymeric fluids on the shape of the torque-angular velocity curve obtained using a coaxial cylinder sensor system during the experiments on a rotational rheometer. A modified Vinogradov-Pokrovsky model with parameters ensuring а non-monotonic flow curve was used to simulate shear banding. Analytical relations for determination of velocity and stress fields at a given torque are found. A numerical method for establishing stationary solutions from the state of rest is proposed. It was found that the torque-angular velocity curve, which was plotted on the basis of the modified Vinogradov-Pokrovsky model for the controlled velocity of rotation of the cylinder, qualitatively changes its shape under different loading conditions. In addition, the influence of the time of acceleration up to the prescribed velocity of rotation of the inner cylinder (characteristic of any experimental device) on the shape of these curves is investigated. It is shown that the modified Vinogradov-Pokrovsky model with a non-monotonic flow curve predicts the formation of a horizontal section, so-called “plateau”, on the torque-angular velocity curve in the case of the controlled velocity of rotation of the cylinder and the formation of a hysteresis loop at controlled torque. Such a behavior of the obtained curves is in qualitative agreement with the experimental data.
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References
Tapadia P., Wang S.-Q. Direct visualization of continuous simple shear in non-Newtonian polymeric fluids. Rev. Lett., 2006, vol. 96, 016001. DOI
Boukany P.E., Wang S.-Q. Shear banding or not in entangled DNA solutions depending on the level of entanglement. Rheol., 2009, vol. 53, pp. 73-84. DOI
Vinogradov G.V., Malkin A.Ya., Yanovskii Yu.G., Borisenkova E.K., Yarlykov B.V., Berezhnaya G.V. Viscoelastic properties and flow of narrow polybutadienes and polyisoprenes. Polymer Sci. B Polymer Phys., 1972, vol. 10, no. 6, pp. 1061-1084. DOI
Sui Ch., McKenna G.B. Instability of entangled polymers in cone and plate rheometry. Acta, 2007, vol. 46, pp. 877‑888. DOI
Ravindranath S., Wang S.-Q. Steady state measurements in stress plateau region of entangled polymer solutions: Controlled-rate and controlled-stress modes. Rheol., 2008, vol. 52, pp. 957-980. DOI
Robert L., Demay Y., Vergnes B. Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry. Acta, 2004, vol. 43, pp. 89-98. DOI
Bird R.B., Wiest J.M. Constitutive equations for polymeric liquids. Rev. Fluid Mech., 1995, vol. 27, pp. 169-193. DOI
Remmelgas J., Harrison G., Leal L.G. A differential constitutive equation for entangled polymer solutions. Journal of Non-Newtonian Fluid Mechanics, 1999, vol. 80, pp. 115-134. DOI
Likhtman A.E., Graham R.S. Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. Journal of Non-Newtonian Fluid Mechanics, 2003, vol. 114, pp. 1-12. DOI
Altukhov Yu.A., Gusev A.S., Pyshnogray G.V. Vvedeniye v mezoskopicheskuyu teoriyu tekuchikh polimernykh sistem [Introduction to the mesoscopic theory of fluid polymer systems]. Barnaul, AltGPA, 2012. 121 p.
Bambaeva N.V., Blokhin A.M. Stationary solutions of equations of incompressible viscoelastic polymer liquid. Math. Math. Phys., 2014, vol. 54, no. 5, pp. 874-899. DOI
Blokhin A.M., Yegitov A.V., Tkachev D.L. Linear instability of solutions in a mathematical model describing polymer flows in an infinite channel. Math. Math. Phys., 2015, vol. 55, no. 5, pp. 848-873. DOI
Kuznetsova Ju.L., Skul’skiy O.I., Pyshnograi G.V. Presure driven flow of a nonlinear viscoelastic fluid in a plane channel. mekh. splosh. sred – Computational Continuum Mechanics, 2010, vol. 3, no. 2, pp. 55-69. DOI
Kuznetsova Ju.L., Skul’skiy O.I. Shear flow of the nonlinear elastic viscous fluid. Vestnik Permskogo universiteta. Matematika. Mekhanika. Informatika – Bulletin of Perm University. Mathematics. Mechanics. Computer science, 2011, vol. 8, no. 4, pp. 18-26.
Wilson H.J., Fielding S.M. Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson–Segalman fluids. Journal of Non-Newtonian Fluid Mechanics, 2006, vol. 138, pp. 181-196. DOI
Germann N., Gurnon A.K., Zhou L., Cook L.P., Beris A.N., Wagner N.J. Validation of constitutive modeling of shear banding, threadlike wormlike micellar fluids. Rheol., 2016, vol. 60, pp. 983-999. DOI
Boltenhagen P., Hu Y., Matthys E.F., Pine D.J. Observation of bulk phase separation and coexistence in a sheared micellar solution. Rev. Lett., 1997, vol. 79, pp. 2359-2362. DOI