First-harmonic nonlinearities can predict unseen third-harmonics in medium-amplitude oscillatory shear (MAOS)

We use first-harmonic MAOS nonlinearities from G₁′ and G₁″ to test a predictive structure-rheology model for a transient polymer network. Using experiments with PVA-Borax (polyvinyl alcohol cross-linked by sodium tetraborate (borax)) at 11 different compositions, the model is calibrated to first-harmonic MAOS data on a torque-controlled rheometer at a fixed frequency, and used to predict third-harmonic MAOS on a displacement controlled rheometer at a different frequency three times larger. The prediction matches experiments for decomposed MAOS measures [e₃] and [v₃] with median disagreement of 13% and 25%, respectively, across all 11 compositions tested. This supports the validity of this model, and demonstrates the value of using all four MAOS signatures to understand and test structure-rheology relations for complex fluids.