Abstract
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.
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References
Aidun, C.K. and J.R. Clausen, 2010, Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. 42, 439–472.
Bird, R.B., C.F. Curtiss, R.C. Armstrong, and O. Hassager, 1987, Dynamics of Polymeric Liquids, Vol.2: Kinetic Theory, 2nd ed., Wiley, New York.
Boger, D.V., 1977, A highly elastic constant-viscosity fluid, J. Non-Newton. Fluid Mech. 3, 87–91.
Denniston, C., E. Orlandini, and J.M. Yeomans, 2001, Lattice Boltzmann simulations of liquid crystal hydrodynamics, Phys. Rev. E 63, 056702.
Ferry, J.D., 1980, Viscoelastic Properties of Polymers, 3rd ed., Wiley, New York.
Ginzburg, I., G. Silva, and L. Talon, 2015, Analysis and improvement of Brinkman lattice Boltzmann schemes: Bulk, boundary, interface. Similarity and distinctness with finite elements in heterogeneous porous media, Phys. Rev. E 91, 023307.
Giraud, L., D. d’Humières, and P. Lallemand, 1998, A lattice Boltzmann model for Jeffreys viscoelastic fluid, Europhys. Lett. 42, 625–630.
Gross, M., T. Krüger, and F. Varnik, 2014, Rheology of dense suspensions of elastic capsules: Normal stresses, yield stress, jamming and confinement effects, Soft Matter 10, 4360–4372.
Guo, Z., C. Zheng, and B. Shi, 2002, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65, 046308.
He, X. and L.S. Luo, 1997, Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys. 88, 927–944.
Hyun, K., M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, and G.H. McKinley, 2011, A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS), Prog. Polym. Sci. 36, 1697–1753.
Ispolatov, I. and M. Grant, 2002, Lattice Boltzmann method for viscoelastic fluids, Phys. Rev. E 65, 056704.
James, D.F., 2009, Boger fluids, Annu. Rev. Fluid Mech. 41, 129–142.
Kromkamp, J., D. van den Ende, D. Kandhai, R. van der Sman, and R. Boom, 2006, Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow, Chem. Eng. Sci. 61, 858–873.
Krüger, T., F. Varnik, and D. Raabe, 2009, Shear stress in lattice Boltzmann simulations, Phys. Rev. E 79, 046704.
Kulkarni, P.M. and J.F. Morris, 2008, Suspension properties at finite Reynolds number from simulated shear flow, Phys. Fluids 20, 040602.
Ladd, A.J.C., 1994, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part I. Theoretical foundation, J. Fluid Mech. 271, 285–309.
Lallemand, P., D. d’Humières, L.S. Luo, and R. Rubinstein, 2003, Theory of the lattice Boltzmann method: Three-dimensional model for linear viscoelastic fluids, Phys. Rev. E 67, 021203.
Lee, Y.K., J. Nam, K. Hyun, K.H. Ahn, and S.J. Lee, 2015, Rheology and microstructure of non-Brownian suspensions in the liquid and crystal coexistence region: Strain stiffening in large amplitude oscillatory shear, Soft Matter 11, 4061–4074.
Love, P.J., M. Nekovee, P.V. Coveney, J. Chin, N. González-Segredo, and J.M.R. Martin, 2003, Simulations of amphiphilic fluids using mesoscale lattice-Boltzmann and lattice-gas methods, Comput. Phys. Commun. 153, 340–358.
Malaspinas, O., N. Fiétier, and M. Deville, 2010, Lattice Boltzmann method for the simulation of viscoelastic fluid flows, J. Non-Newton. Fluid Mech. 165, 1637–1653.
Marenduzzo, D., E. Orlandini, M.E. Cates, and J.M. Yeomans, 2007, Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations, Phys. Rev. E 76, 031921.
Molaeimanesh, G.R. and M.H. Akbari, 2015, A pore-scale model for the cathode electrode of a proton exchange membrane fuel cell by lattice Boltzmann method, Korean J. Chem. Eng. 32, 397–405.
Nam, J.G., K. Hyun, K.H. Ahn, and S.J. Lee, 2008, Prediction of normal stresses under large amplitude oscillatory shear flow, J. Non-Newton. Fluid Mech. 150, 1–10.
Nam, J.G., K. Hyun, K.H. Ahn, and S.J. Lee, 2010, Phase angle of the first normal stress difference in oscillatory shear flow, Korea-Aust. Rheol. J. 22, 247–257.
Nguyen, N.Q. and A.J.C. Ladd, 2002, Lubrication corrections for lattice-Boltzmann simulations of particle suspensions, Phys. Rev. E 66, 046708.
Onishi, J., Y. Chen, and H. Ohashi, 2005, A lattice Boltzmann model for polymeric liquids, Prog. Comput. Fluid Dyn. 5, 75–84.
Qian, Y.H., D. D’Humières, and P. Lallemand, 1992, Lattice BGK models for Navier-Stokes equation, Europhys. Lett. 17, 479–484.
Qian, Y.H. and Y.F. Deng, 1997, A lattice BGK Model for viscoelastic media, Phys. Rev. Lett. 79, 2742–2745.
Saksena, R.S. and P.V. Coveney, 2009, Shear rheology of amphiphilic cubic liquid crystals from large-scale kinetic lattice-Boltzmann simulations, Soft Matter 5, 4446–4463.
Succi, S., 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York.
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Lee, Y.K., Ahn, K.H. & Lee, S.J. Time-dependent viscoelastic properties of Oldroyd-B fluid studied by advection-diffusion lattice Boltzmann method. Korea-Aust. Rheol. J. 29, 137–146 (2017). https://doi.org/10.1007/s13367-017-0015-1
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DOI: https://doi.org/10.1007/s13367-017-0015-1