Frequency response analysis of the Bautista-Manero-Puig model with normal stress: analytical and numerical solution for large amplitudes

We derive explicit analytical expressions for the recurrence relations using the analytical matrix method for frequency response and the Bautista-Manero-Puig model for complex fluids. The BMP model is derived from the Extended Irreversible Thermodynamics formalism and has been shown to be useful in predicting the complex rheological behavior of self-associative systems. All harmonics of the alternating normal and shear stresses in oscillatory shear with various amplitude oscillatory regimes (AOS) can be calculated analytically, i.e., small amplitude oscillatory shear (SAOS), medium amplitude oscillatory shear (MAOS), and large amplitude oscillatory shear (LAOS). We show that incorporating the effects of the first and second normal stress differences for all AOS regimes leads to the emergence of higher harmonics. We establish the limits between the different AOS regimes based on criteria suggested by the analytical method. For some typical systems, such as CTAB-NaSal, we found a satisfactory quantitative agreement with the measured behavior of AOS.