Macromolecular Origins of Harmonics Higher than the Third in Large-Amplitude Oscillatory Shear Flow

In 1935, Andrew Gemant conceived of the complex viscosity, a~rheological material function measured~by "jiggling" an~elastic liquid in oscillatory shear [\textit{Rheol. Acta},~\textbf{51}, 481 (2012)].~~This test reveals information about both~the viscous and elastic properties of the liquid, and about~how these~properties depend on frequency. ~The test gained popularity with~chemists when John Ferry perfected instruments for measuring~both the real~and imaginary parts of the complex viscosity [\textit{Mem. Trib., NAE},~\textbf{17}, 96 (2013)]. ~In 1958,~Cox and Merz~discovered that the steady shear viscosity curve was easily~deduced from the magnitude of the complex viscosity, and today~ oscillatory shear is the single most popular rheological property measurement. With oscillatory shear, we can control two things: the frequency~(Deborah number) and the shear rate~amplitude (Weissenberg number).~~When the Weissenberg number is large, the elastic liquids respond~with~a shear stress over a series of odd-multiples of the test frequency.~~In this lecture we will explore recent attempts to deepen our understand of the physics of these higher harmonics, including especially harmonics higher than the third. ~