Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles

Large amplitude oscillatory shear (LAOS) is an increasingly popular nonlinear rheological test method, and the interpretation of the measurements is still an active area of research. Here, we demonstrate a new method whereby the nonlinear parameters of a popular constitutive equation used to model polymeric and other viscoelastic systems, the Giesekus model, may be determined directly from LAOS measurements without complicated, nonlinear model fitting. We define the stress response of the sample as an expansion in deformation strain and oscillation frequency. To leading order in strain, we derive the explicit analytic expressions for the first three harmonics of the stress response during LAOS for the Giesekus constitutive model. This allows for rapid determination of the Giesekus model parameters, including the nonlinear coupling parameter, directly from plots of the response obtained from modern rheological instruments. We demonstrate the validity, utility, and limits of this new method on a well-studied wormlike micelle (WLM) surfactant solution, cetyltrimethylammonium bromide (CTAB), and water. This robust and simple approach is especially advantageous for systems where steady shearing in the nonlinear regime is problematic and can provide rapid determination of parameters in rheological constitutive equations.