Slipping Phenomenon in Polymeric Fluids Flow between Parallel Planes

ABSTRACT

At this article studies of nonlinear viscoelastic fluid with one internal tensor parameter flow between parallel planes under a constant pressure gradient, taking into account the slipping phenomenon on the boundary. Numerically depending found on the components of the stress tensor and the flow velocity of the pressure gradient and the distance to the wall, enabled us to explain the emergence of non-parabolic profile of the flow velocity of the polymeric melt.

At this article studies of nonlinear viscoelastic fluid with one internal tensor parameter flow between parallel planes under a constant pressure gradient, taking into account the slipping phenomenon on the boundary. Numerically depending found on the components of the stress tensor and the flow velocity of the pressure gradient and the distance to the wall, enabled us to explain the emergence of non-parabolic profile of the flow velocity of the polymeric melt.

Cite this paper

nullY. Altukhov, G. Pyshnograi and I. Pyshnograi, "Slipping Phenomenon in Polymeric Fluids Flow between Parallel Planes,"*World Journal of Mechanics*, Vol. 1 No. 6, 2011, pp. 294-298. doi: 10.4236/wjm.2011.16037.

nullY. Altukhov, G. Pyshnograi and I. Pyshnograi, "Slipping Phenomenon in Polymeric Fluids Flow between Parallel Planes,"

References

[1] A. I. Leonov, “A Brief Introduction to the Rheology of Polymeric Fluids,” Coxmoor Publishing Company, Ox- ford, 2008, p. 257.

[2] V. N. Pokrovskii, “The Mesoscopic Theory of Polymer Dy- namics,” 2nd Edition, Springer, New York, 2010, p. 256. doi:10.1007/978-90-481-2231-8

[3] 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-Appro- ximations by Molecular Theory Parameters and Secuentals for Shearing and Elongational Flows,” Doklady Rus- sian Akademy Nauk, Vol. 335, No. 9, 1994, pp. 612-615.

[4] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi, “The Mesoscopic Approach to the Dynamics of Polymer Melts: Consequences for the Constitutive Equation,” Jour- nal of Non-Newtonian Fluid Mechanics, Vol. 76, No. 1-3, 1998, pp. 153-181. doi:10.1016/S0377-0257(97)00116-X

[5] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi “On the Difference between Weakly and Strongly Entan- gled 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

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

[7] А. S. Gusev, М. А. Makarova and G. V. Pyshnograi, “Me- soscopic Equation of State of Polymer Systems and De- scription of the Dynamic Characteristics Based on It,” Jour- nal of Engineering Physics and Thermophysics, Vol. 78; No. 5, 2005, pp. 892-898. doi:10.1007/s10891-006-0009-1

[8] A. Gusev, G. Afonin, I. Tretjakov amd G. Pyshnogray, “The Mesoscopic Constitutive Equation for Polymeric Fluids and Some Examples of Flows,” In: J. N. Perkins and T. M. Lach, Eds., Viscoelasticity: Theories, Types and Models, Nova publisher, 2011, in print.

[9] H. Munstedt, M. Schmidt and E. Wassner, “Stick and Slip Phenomena during Extrusion of Polyethylene Melts as Investigated by Laser-Doppler Velocimetry,” Journal of Rheology, Vol. 44, No. 2, 2000, pp. 413-427. doi:10.1122/1.551092

[10] E. Wassner, M. Schmidt and H. Munstedt, “Entry Flow of a Low-Density-Polyethylene Melt into a Slit Die: An Experimental Study by Laser-Doppler Velocimetry,” Jour- nal of Rheology, Vol. 43, No. 6, 1999, pp. 1339-1353. doi:10.1122/1.551050

[1] A. I. Leonov, “A Brief Introduction to the Rheology of Polymeric Fluids,” Coxmoor Publishing Company, Ox- ford, 2008, p. 257.

[2] V. N. Pokrovskii, “The Mesoscopic Theory of Polymer Dy- namics,” 2nd Edition, Springer, New York, 2010, p. 256. doi:10.1007/978-90-481-2231-8

[3] 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-Appro- ximations by Molecular Theory Parameters and Secuentals for Shearing and Elongational Flows,” Doklady Rus- sian Akademy Nauk, Vol. 335, No. 9, 1994, pp. 612-615.

[4] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi, “The Mesoscopic Approach to the Dynamics of Polymer Melts: Consequences for the Constitutive Equation,” Jour- nal of Non-Newtonian Fluid Mechanics, Vol. 76, No. 1-3, 1998, pp. 153-181. doi:10.1016/S0377-0257(97)00116-X

[5] V. N. Pokrovskii, Yu. A. Altukhov and G. V. Pyshnograi “On the Difference between Weakly and Strongly Entan- gled 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

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

[7] А. S. Gusev, М. А. Makarova and G. V. Pyshnograi, “Me- soscopic Equation of State of Polymer Systems and De- scription of the Dynamic Characteristics Based on It,” Jour- nal of Engineering Physics and Thermophysics, Vol. 78; No. 5, 2005, pp. 892-898. doi:10.1007/s10891-006-0009-1

[8] A. Gusev, G. Afonin, I. Tretjakov amd G. Pyshnogray, “The Mesoscopic Constitutive Equation for Polymeric Fluids and Some Examples of Flows,” In: J. N. Perkins and T. M. Lach, Eds., Viscoelasticity: Theories, Types and Models, Nova publisher, 2011, in print.

[9] H. Munstedt, M. Schmidt and E. Wassner, “Stick and Slip Phenomena during Extrusion of Polyethylene Melts as Investigated by Laser-Doppler Velocimetry,” Journal of Rheology, Vol. 44, No. 2, 2000, pp. 413-427. doi:10.1122/1.551092

[10] E. Wassner, M. Schmidt and H. Munstedt, “Entry Flow of a Low-Density-Polyethylene Melt into a Slit Die: An Experimental Study by Laser-Doppler Velocimetry,” Jour- nal of Rheology, Vol. 43, No. 6, 1999, pp. 1339-1353. doi:10.1122/1.551050