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

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.