The Mesoscopic Constitutive Equations for Polymeric Fluids and Some Examples of Viscometric Flows

ABSTRACT

Constitutive equations for melts and concentrated solutions of linear polymers are derived as consequences of dynamics of a separate macromolecule. The model is investigated for viscometric flows. It was shown that the model gives a good description of non-linear effects of simple shear polymer flows: viscosity anomalies, first and second normal stresses, non-steady shear stresses.

Constitutive equations for melts and concentrated solutions of linear polymers are derived as consequences of dynamics of a separate macromolecule. The model is investigated for viscometric flows. It was shown that the model gives a good description of non-linear effects of simple shear polymer flows: viscosity anomalies, first and second normal stresses, non-steady shear stresses.

Cite this paper

nullG. Pyshnograi, H. Joda and I. Pyshnograi, "The Mesoscopic Constitutive Equations for Polymeric Fluids and Some Examples of Viscometric Flows,"*World Journal of Mechanics*, Vol. 2 No. 1, 2012, pp. 19-27. doi: 10.4236/wjm.2012.21003.

nullG. Pyshnograi, H. Joda and I. Pyshnograi, "The Mesoscopic Constitutive Equations for Polymeric Fluids and Some Examples of Viscometric Flows,"

References

[1] W. W. Graessley, “The Constraint Release Concept in Polymer Rheology,” Advances in Polymer Science, Vol. 47, 1982, pp. 68-117.

[2] H. Watanabe, “Viscoelasticity and Dynamics of Entagled Polymers,” Progress in Polymer Science, Vol. 24, No. 9, 1999, pp. 1253-1403. doi:10.1016/S0079-6700(99)00029-5

[3] W. W. Graessley, “Polymeric Liquids & Networks: Dynamics and Rheology,” Garland Science, London, 2008.

[4] V. N. Pokrovskii, “The Mesoscopic Theory of Polymer Dynamics,” 2nd Edition, Springer, Berlin, 2010. doi:10.1007/978-90-481-2231-8

[5] J. D. Ferry, “Viscoelastic Properties of Polymars,” 3rd Edition, Wiley and Sons, London, 1980.

[6] A. Yu. Grosberg and A. R. Khokhlov, “Statistical Physics of Macromolecules,” Springer, Berlin, 1994.

[7] G. V. Pyshnograi, V. N. Pokrovskii, Yu. G. Yanovskii, Yu. N. Karnet and I. F. Obrazcov, “Equation of State for Nonlinear Viscoelastic (Polymer) Continua in Zero-App- roximations by Molecular Theory Parameters and Secu- entals for Shearing and Elongational Flows,” Doklady Russian Akademy Nauk, Vol. 335, No. 9, 1994, pp. 612- 615 (in Russian).

[8] M. Doi and S. F. Edwards, “The Theory of Polymer Dynamics,” Oxford University Press, Oxford, 1986.

[9] H. Ch. Ottinger, “Thermodynamically Admissible Reptation Models with Anisotropic Tube Cross Sections and Convective Constraint Release,” Journal of Non-New- tonian Fluid Mechanics, Vol. 89, No. 1-2, 2000, pp. 165- 185. doi:10.1016/S0377-0257(99)00025-7

[10] G. Astarita and G. Marucci, “Principles of Non-New- tonian Fluid Mechanics,” McGraw-Hill Inc., New York, 1974.

[11] A. I. Leonov, “A Brief Introduction to the Rheology of Polymeric Fluids,” Coxmoor Publishing Company, Oxford, 2008.

[12] A. Gusev, G. Afonin, I. Tretjakov and G. Pyshnogray, “The Mesoscopic Constitutive Equation for Polymeric Fluids and Some Examples of Flows,” In: N. P. Jennifer and M. L. Tyler, Eds., Viscoelasticity: Theories, Types and Models, Nova Publisher, New York, 2011, pp. 186-202.

[13] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi, “On the Difference between Weakly and Strongly Entangled Linear Polymer,” Journal of Non-Newtonian Fluid Mechanics, Vol. 121, No. 2-3, 2004, pp. 73-86. doi:10.1016/j.jnnfm.2004.05.001

[14] Y. G. Yanovsky, V. N. Pokrovskii, Y. A. Altukhov and G. V. Pyshnograi, “Properties of Constitutive Equations for Undilute Linear Polymers Based on the Molecular Theory,” International Journal of Polymeric Materials, Vol. 36, No. 1-2, 1997, pp. 75-117.

[15] A. S. Gusev, G. V. Pyshnograi and V. N. Pokrovskii, “Constitutive Equations for Weakly Entangled Linear Polymers,” Journal of Non-Newtonian Fluid Mechanics, Vol. 163, No. 1-3, 2009, pp. 17-28.

[16] Yu. A. Altukhov, G. V. Pyshnograi and I. G. Pyshnograi, “Slipping Phenomenon in Polymeric Fluids Flow between Parallel Planes,” World Journal of Mechanics, 2011, Vol. 1, No. 6, pp. 294-298. doi:10.1016/S0377-0257(97)00116-X

[17] W. W. Graessley, “Polymeric Liquids & Networks: Dynamics and Rheology,” Garland Science, London, 2008.

[1] W. W. Graessley, “The Constraint Release Concept in Polymer Rheology,” Advances in Polymer Science, Vol. 47, 1982, pp. 68-117.

[2] H. Watanabe, “Viscoelasticity and Dynamics of Entagled Polymers,” Progress in Polymer Science, Vol. 24, No. 9, 1999, pp. 1253-1403. doi:10.1016/S0079-6700(99)00029-5

[3] W. W. Graessley, “Polymeric Liquids & Networks: Dynamics and Rheology,” Garland Science, London, 2008.

[4] V. N. Pokrovskii, “The Mesoscopic Theory of Polymer Dynamics,” 2nd Edition, Springer, Berlin, 2010. doi:10.1007/978-90-481-2231-8

[5] J. D. Ferry, “Viscoelastic Properties of Polymars,” 3rd Edition, Wiley and Sons, London, 1980.

[6] A. Yu. Grosberg and A. R. Khokhlov, “Statistical Physics of Macromolecules,” Springer, Berlin, 1994.

[7] G. V. Pyshnograi, V. N. Pokrovskii, Yu. G. Yanovskii, Yu. N. Karnet and I. F. Obrazcov, “Equation of State for Nonlinear Viscoelastic (Polymer) Continua in Zero-App- roximations by Molecular Theory Parameters and Secu- entals for Shearing and Elongational Flows,” Doklady Russian Akademy Nauk, Vol. 335, No. 9, 1994, pp. 612- 615 (in Russian).

[8] M. Doi and S. F. Edwards, “The Theory of Polymer Dynamics,” Oxford University Press, Oxford, 1986.

[9] H. Ch. Ottinger, “Thermodynamically Admissible Reptation Models with Anisotropic Tube Cross Sections and Convective Constraint Release,” Journal of Non-New- tonian Fluid Mechanics, Vol. 89, No. 1-2, 2000, pp. 165- 185. doi:10.1016/S0377-0257(99)00025-7

[10] G. Astarita and G. Marucci, “Principles of Non-New- tonian Fluid Mechanics,” McGraw-Hill Inc., New York, 1974.

[11] A. I. Leonov, “A Brief Introduction to the Rheology of Polymeric Fluids,” Coxmoor Publishing Company, Oxford, 2008.

[12] A. Gusev, G. Afonin, I. Tretjakov and G. Pyshnogray, “The Mesoscopic Constitutive Equation for Polymeric Fluids and Some Examples of Flows,” In: N. P. Jennifer and M. L. Tyler, Eds., Viscoelasticity: Theories, Types and Models, Nova Publisher, New York, 2011, pp. 186-202.

[13] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi, “On the Difference between Weakly and Strongly Entangled Linear Polymer,” Journal of Non-Newtonian Fluid Mechanics, Vol. 121, No. 2-3, 2004, pp. 73-86. doi:10.1016/j.jnnfm.2004.05.001

[14] Y. G. Yanovsky, V. N. Pokrovskii, Y. A. Altukhov and G. V. Pyshnograi, “Properties of Constitutive Equations for Undilute Linear Polymers Based on the Molecular Theory,” International Journal of Polymeric Materials, Vol. 36, No. 1-2, 1997, pp. 75-117.

[15] A. S. Gusev, G. V. Pyshnograi and V. N. Pokrovskii, “Constitutive Equations for Weakly Entangled Linear Polymers,” Journal of Non-Newtonian Fluid Mechanics, Vol. 163, No. 1-3, 2009, pp. 17-28.

[16] Yu. A. Altukhov, G. V. Pyshnograi and I. G. Pyshnograi, “Slipping Phenomenon in Polymeric Fluids Flow between Parallel Planes,” World Journal of Mechanics, 2011, Vol. 1, No. 6, pp. 294-298. doi:10.1016/S0377-0257(97)00116-X

[17] W. W. Graessley, “Polymeric Liquids & Networks: Dynamics and Rheology,” Garland Science, London, 2008.