Time-dependent viscoelastic properties of Oldroyd-B fluid studied by advection-diffusion lattice Boltzmann method

Young Ki Lee; Kyung Hyun Ahn; Seung Jong Lee

Korea-Australia Rheology Journal, Vol.29, No.2, 137-146, May, 2017

DOI10.1007/s13367-017-0015-1 Export Citation

Time-dependent viscoelastic properties of Oldroyd-B fluid studied by advection-diffusion lattice Boltzmann method

Young Ki Lee, Kyung Hyun Ahn^†, and Seung Jong Lee

Institute of Chemical Processes, School of Chemical and Biological Engineering, Seoul National University, Seoul 08826, Republic of Korea

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Time-dependent viscoelastic properties of Oldroyd-B fluid were investigated by lattice Boltzmann method(LBM) coupled with advection-diffusion model. To investigate the viscoelastic properties of Oldroyd-B fluid, realistic rheometries including step shear and oscillatory shear tests were implemented in wide ranges of Weissenberg number (Wi) and Deborah number (De). First, transient behavior of Oldroyd-B fluid was studied in both start up shear and cessation of shear. Stress relaxation was correctly captured, and calculated shear and normal stresses agreed well with analytical solutions. Second, the oscillatory shear test was implemented. Dynamic moduli were obtained for various De regime, and they showed a good agreement with analytical solutions. Complex viscosity derived from dynamic moduli showed two plateau regions at both low and high De limits, and it was confirmed that the polymer contribution becomes weakened as De increases. Finally, the viscoelastic properties related to the first normal stress difference were carefully investigated, and their validity was confirmed by comparison with the analytical solutions. From this study, we conclude that the LBM with advection-diffusion model can accurately predict time-dependent viscoelastic properties of Oldroyd-B fluid.

Keywords:rheology;viscoelastic fluid;Oldroyd-B;lattice Boltzmann method;advection-diffusion model

[References]

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[1] Aidun CK, Clausen JR, Annu. Rev. Fluid Mech., 42, 439 (2010)

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

[3] Boger DV, J. Non-Newton. Fluid Mech., 3, 87 (1977)

[4] Denniston C, Orlandini E, Yeomans JM, Phys. Rev. E, 63, 056702 (2001)

[5] Ferry JD, 1980, Viscoelastic Properties of Polymers, 3rd ed., Wiley, New York.

[6] Ginzburg I, Silva G, Talon L, Phys. Rev. E, 91, 023307 (2015)

[7] Giraud L, d’Humieres D, Lallemand P, Europhys. Lett., 42, 625 (1998)

[8] Gross M, Kruger T, Varnik F, Soft Matter, 10, 4360 (2014)

[9] Guo Z, Zheng C, Shi B, Phys. Rev. E, 65, 046308 (2002)

[10] He X, Luo LS, J. Stat. Phys., 88, 927 (1997)

[11] Hyun K, Wilhelm M, Klein CO, Cho KS, Nam JG, Ahn KH, Lee SJ, Ewoldt RH, McKinley GH, Prog. Polym. Sci, 36, 1697 (2011)

[12] Ispolatov I, Grant M, Phys. Rev. E, 65, 056704 (2002)

[13] James DF, Annu. Rev. Fluid Mech., 41, 129 (2009)

[14] Kromkamp J, van den Ende D, Kandhai D, van der Sman R, Boom R, Chem. Eng. Sci., 61(2), 858 (2006)

[15] Kruger T, Varnik F, Raabe D, Phys. Rev. E, 79, 046704 (2009)

[16] Kulkarni PM, Morris JF, Phys. Fluids, 20, 040602 (2008)

[17] Ladd AJC, J. Fluid Mech., 271, 285 (1994)

[18] Lallemand P, d’Humieres D, Luo LS, Rubinstein R, Phys. Rev. E, 67, 021203 (2003)

[19] Lee YK, Nam J, Hyun K, Ahn KH, Lee SJ, Soft Matter, 11, 4061 (2015)

[20] Love PJ, Nekovee M, Coveney PV, Chin J, Gonzalez- Segredo N, Martin JMR, Comput. Phys. Commun., 153, 340 (2003)

[21] Malaspinas O, Fietier N, Deville M, J. Non-Newton. Fluid Mech., 165(23-24), 1637 (2010)

[22] Marenduzzo D, Orlandini E, Cates ME, Yeomans JM, Phys. Rev. E, 76, 031921 (2007)

[23] Molaeimanesh GR, Akbari MH, Korean J. Chem. Eng., 32(3), 397 (2015)

[24] Nam JG, Hyun K, Ahn KH, Lee SJ, J. Non-Newton. Fluid Mech., 150(1), 1 (2008)

[25] Nam JG, Hyun K, Ahn KH, Lee SJ, Korea-Aust. Rheol. J., 22(4), 247 (2010)

[26] Nguyen NQ, Ladd AJC, Phys. Rev. E, 66, 046708 (2002)

[27] Onishi J, Chen Y, Ohashi H, Prog. Comput. Fluid Dyn., 5, 75 (2005)

[28] Qian YH, D’Humieres D, Lallemand P, Europhys. Lett., 17, 479 (1992)

[29] Qian YH, Deng YF, Phys. Rev. Lett., 79, 2742 (1997)

[30] Saksena RS, Coveney PV, Soft Matter, 5, 4446 (2009)

[31] Succi S, 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York.