Verification of mesoscopic models of viscoelastic fluids with a non-monotonic flow curve

Julia L. Kuznetsova; Oleg I. Skul’skiy

Korea-Australia Rheology Journal, Vol.28, No.1, 33-40, February, 2016

DOI10.1007/s13367-016-0003-x Export Citation

Verification of mesoscopic models of viscoelastic fluids with a non-monotonic flow curve

Julia L. Kuznetsova, and Oleg I. Skul’skiy^†

Institute of Continuous Media Mechanics, UB RAS, Perm 614013, Russia, Russian Federation

E-mail:

The non-monotonic flow curve of a 1 wt.% polyacrylonitrile solution in dimethyl sulfoxide is described by two mesoscopic models: the modified Vinogradov-Pokrovsky model and the model proposed by Remmelgas, Harrison and Leal. To obtain an adequate description of the experimental curve, we have selected suitable internal parameters for these models. Analytical solutions for the Couette-Poiseuille flow problems are determined in parametric form, which allows us to plot the distribution of stress components and anisotropy tensor as well as the velocity profiles containing closed loops and weak tangential discontinuities. It is shown that both models predict a similar qualitative picture of structure evolution, but exhibit a significant discrepancy in the quantitative description of the magnitude of molecular chain stretching.

Keywords:non-monotonic flow curve;mesoscopic rheological models;channel flow;analytical solution;model parameter determination

[References]

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Malkin A, Ilyin S, Roumyantseva T, Kulichikhin V, Macromolecules, 46(1), 257 (2013)
Marrucci G, Grizzuti N, Gaz. Chim. Ital, 118, 1988
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[1] Aristov SN, Skul'skiy OI, J. Appl. Mech. Tech. Phys., 76, 88 (2003)

[2] Bird RB, Curtiss CF, Armstrong RC, Hassager O, 1987, Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory, 2nd ed., Wiley, New York.

[3] Bird RB, Dotson PJ, Johnson NL, J. Non-Newton. Fluid Mech., 7, 213 (1980)

[4] de Gennes PG, J. Chem. Phys., 66, 5825 (1977)

[5] de Gennes PG, 1979, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca.

[6] Doi M, Edwards SF, J. Chem. Soc.-Faraday Trans., 74, 1789 (1978)

[7] Doi M, Edwards SF, 1986, The Theory of Polymer Dynamics, Oxford University Press, Oxford.

[8] Gusev AS, Pyshnograi GV, Pokrovskii VN, J. Non-Newton. Fluid Mech., 163, 17 (2009)

[9] Gusev AS, Makarova MA, Pyshnograi GV, J. Eng. Phys. Thermophys., 78, 892 (2005)

[10] Harrison GM, Remmelgas J, Leal LG, J. Rheol., 43(1), 197 (1999)

[11] Ilyin SO, Kulichikhin VG, Malkin AY, Polym. Sci. Ser. A, 55, 503 (2013)

[12] Kuznetsova JL, Skul’skiy OI, Pyshnograi GV, Comput. Continuum Mech., 3, 55 (2010)

[13] Kuznetsova YL, Skul’skiy OI, Comput. Continuum Mech., 6, 224 (2013)

[14] Malkin A, Ilyin S, Roumyantseva T, Kulichikhin V, Macromolecules, 46(1), 257 (2013)

[15] Marrucci G, Grizzuti N, Gaz. Chim. Ital, 118, 1988

[16] Olbricht WL, Rallison JM, Leal LG, J. Non-Newton. Fluid Mech., 10, 291 (1982)

[17] Pokrovskii VN, Sov. Phys. Usp., 35, 384 (1992)

[18] Pokrovskii VN, 1978, Statistical Mechanics of Dilute Suspensions, Nauka, Moskow.

[19] Pokrovskii VN, Altukhov YA, Pyshnograi GV, J. Non-Newton. Fluid Mech., 76(1-3), 153 (1998)

[20] Altukhov YA, Pokrovskii VN, Pyshnograi GV, J. Non-Newton. Fluid Mech., 121(2-3), 73 (2004)

[21] Remmelgas J, Harrison G, Leal LG, J. Non-Newton. Fluid Mech., 80(2-3), 115 (1999)

[22] Remmelgas J, Leal LG, J. Non-Newton. Fluid Mech., 90(2-3), 187 (2000)

[23] Skul'skiy OI, Slavnov YV, Shakirov NV, J. Non-Newton. Fluid Mech., 81(1-2), 17 (1999)

[24] Volkov VS, Vinogradov GV, J. Non-Newton. Fluid Mech., 15, 29 (1984)

[25] Volkov VS, Vinogradov GV, J. Non-Newton. Fluid Mech., 18, 163 (1985)

[26] Yesilata B, Clasen C, McKinley GH, J. Non-Newton. Fluid Mech., 133(2-3), 73 (2006)