A novel representation of time-varying viscosity with power-law and comparative study

Time-varying viscosity of viscoelastic materials has been found to induce complex rheology behaviors, which cannot be well characterized by the classical viscoelastic models. In this paper, different types of time-varying viscosity, namely, linearly varying viscosity, exponentially varying viscosity, and the proposed power-law viscosity are introduced with the applications to describing experimental data. Subsequently, these time-varying viscosities are embedded into the classical viscoelastic models. The relaxation and creep responses of the modified viscoelastic models are analytically derived and compared with the performance of the corresponding fractional models. The results indicate that the proposed power-law viscosity and the exponentially varying viscosity are capable of characterizing both thixotropy and rheopexy. The modified Maxwell model with power-law viscosity agrees well with the creep and relaxation responses of time-varying materials. It is also found that viscoelastic materials exhibiting thixotropy show faster rheological responses than the materials exhibiting rheopexy.