(230af) Nonlinear Relaxation Modulus Via Dual-Frequency Medium Amplitude Oscillatory Shear (MAOS): General Framework and a Case Study for a Dilute Suspension of Brownian Spheroids

We present a framework for determining the viscoelastic relaxation moduli of a complex fluid from an oscillatory shear deformation. Knowledge of these moduli allows one to predict the stress response under an arbitrary transient deformation via a memory integral expansion. Our framework is demonstrated by determining the first nonlinear relaxation modulus, referred to here as the medium amplitude oscillatory shear (MAOS) relaxation modulus, for a dilute suspension of Brownian spheroids subject to a dual-frequency oscillatory simple shear flow. Specifically, we first determine the second normal stress difference for such a deformation from a co-rotational memory integral expansion. Second, the microstructural stress response of the model system of Brownian spheroids is determined via a regular perturbation expansion of the orientation distribution function at small dimensionless strain-rate amplitude, or Weissenberg number. An analytical expression for the MAOS relaxation modulus is resolved by comparing the second normal stress difference results of the memory integral expansion and microstructural stress response. Finally, using the MAOS relaxation modulus, we reconstruct the stress response of our model system for the start-up and cessation of steady shear and steady uniaxial extension. In summary, our work offers a route to utilizing medium (and large) amplitude oscillatory shear data to predict stress dynamics in other transient, nonlinear flows.