Exact solution for intrinsic nonlinearity in oscillatory shear from the corotational Maxwell fluid

Abstract

The ratio of the shear stress amplitudes of higher harmonics to the first, called relative intensities, is a widely established way of characterizing materials and of representing large-amplitude oscillatory shear flow (LAOS) measurements. If we divide these relative intensities by appropriate powers of strain amplitude, we define intrinsic nonlinearities. In their limits of vanishing strain amplitude, these relative intensities give relative intensity parameters, mQ0, where m is the number of the harmonic. Here, we arrive at the first exact analytical solution for the mth intrinsic nonlinearity for the shear stress of a corotational Maxwell fluid and, for example, evaluate it for the first three harmonics (third, fifth and seventh). We then use the Spriggs relations to generalize these relative intensities and corresponding intrinsic nonlinearities to multimode. For consistency, we check the expansion of our results against the well-known first term in the expansion in powers of the strain amplitude [Appl. Rheol., 26, 53809 (2016)]. We also introduce an expansion of the intrinsic nonlinearity in the shear rate amplitude. Finally, we compare our generalized results, third-to-first (I3/1) and fifth-to-first (I5/1) relative intensities, with measurement on molten 1,4-cis-polyisoprene.