Simple Scalar Model and Analysis for Large Amplitude Oscillatory Shear

Abstract

This work presents a simple, scalar model for predicting a nonlinear shear stress response of a viscoelastic fluid in Large Amplitude Oscillatory Shear (LAOS) experiments. The model is constructed by replacing the viscosity in the well-known Maxwell model by a shear rate dependent viscosity function. By assuming the empirical Cox-Merz rule to be valid, this shear rate dependent viscosity function is specified based on the Maxwell expression for the complex viscosity. We thus construct a particular case of the White-Metzner constitutive equation. Numerical solutions as well as an asymptotic analytical solution of the model are presented. The results, analyzed for higher harmonic content by Fourier transform, are compared to experimental data of a viscoelastic solution of wormlike micelles based on cetyltrimethylammonium bromide. Good agreement is found for low frequencies, where viscous properties dominate.

Keywords

• large amplitude oscillatory shear (laos)
• constitutive modeling
• cox-merz rule
• maxwell model
• non-linear rheology
• wormlike micelles