Analysis of the normal stress differences of viscoelastic fluids under large amplitude oscillatory shear flow

The dynamic response of viscoelastic fluids under large amplitude oscillatory shear (LAOS) has been a subject of long history. In the LAOS flow, the analysis has been mostly focused on shear stress, possibly due to the lack of accurate measurement of normal stresses. However, as the instrumentation advances, it becomes possible to get more reliable data. The development of normal stresses under LAOS flow is a significant nonlinear effect that has been hardly obtainable in previous studies. Analyzing the normal stresses will be helpful in understanding and characterizing nonlinear viscoelastic behavior. In this work, we investigated the behavior of normal stress difference under LAOS flow using viscoelastic fluids including Boger fluid and polyethylene oxide aqueous solution. The first normal stress difference was measured and it was sinusoidal at a frequency twice that of the excitation frequency because of its dependence only on the magnitude of the strain, not on the direction of its operation. It showed a displacement that was equal to the elastic modulus multiplied by the square of the strain amplitude. It was also found that the shape of the first normal stress difference strongly depended on shear strain and frequency. At higher frequency, they showed asymmetric patterns in contrast to the shear stress, and the first normal stress difference became larger in magnitude than the shear stress. And higher harmonics of the first normal stress difference which are the sum of even functions were compared with that of shear stress in terms of Fourier spectra, which was also performed with the help of constitutive equations.