A non-Newtonian fluid model with an objective vorticity

• We provide a non-Newtonian fluid model with an objective vorticity tensor.
• Two different time scales are used for strain relaxation and rotation recovery.
• The objective vorticity tensor introduces a strain softening effect.
• The model simultaneously predicts shear thinning and extensional thickening.

Closed-form constitutive equations that explicitly correlate kinematic variables such as the strain rate tensor to the stress tensor are highly desired in modeling of polymeric flow of practical relevance. However, conventional fluid models of the Reiner–Rivlin type encounter a difficulty in differentiating flow types and predicting realistic elastic effects. In this paper, a constitutive model of type τ=τ(L‾) where L‾ is an objective velocity gradient is presented to treat the objective rotation of a fluid-like material containing a conformational structure. Specifically, this model contains two different relaxation processes to separately tackle rotation and straining. The base model with three parameters is able to simultaneously model shear thinning and extensional thickening as well as normal stress differences in simple shear. Additional model accuracy is achieved by incorporating finite stretch and disentanglement effects.