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The dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by three-dimensional direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspension. A fictitious domain method is used to manage the particle motion. After the stress field is computed, the bulk properties are recovered by an averaging procedure. The numerical method is validated by comparing the computed linear viscoelastic response of Newtonian and non-Newtonian suspensions with previous theories and simulations. The numerical predictions are in very good quantitative agreement with experimental data for the Newtonian case, whereas deviations are found with respect to some sets of experiments for semidilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggregates in the bulk of the suspension is examined. The simulations show that the presence of structures significantly alters the loss modulus. Such an effect is more pronounced as the volume fraction increases. In this light, the above mentioned disagreement between simulations and data (and among experimental data themselves) can be rationalized, as its origin can be attributed to inhomogeneous particle configurations. For increasing strain amplitudes, both loss and storage moduli depart from the linear viscoelastic values. Although the deviations are qualitatively similar to the large amplitude response of the unfilled suspending matrix, our results for dilute and semidilute suspensions show that the decrease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, a higher concentration of solid particles reduces the value of strain amplitude such that the nonlinear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Finally, the effect of fluid elasticity on the particle motion is analyzed. The particles are found to move away from their starting positions and the average distance, computed at the beginning of each cycle with respect to the initial configuration, linearly increases with the number of cycles. The change in the microstructure is attributed to the long-range hydrodynamic interactions mediated by fluid viscoelasticity. [ABSTRACT FROM AUTHOR]

Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flow kinematics. The rheotens model of Doufas [J. Rheol. 50, 749-769 (2006)] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the Cox-Merz [J. Polym. Sci. 28, 619-621 (1958)] and Laun [J. Rheol. 30, 459-501 (1986)] rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of 20 000 s-1), problems that have been reported for other constitutive equations. [ABSTRACT FROM AUTHOR]