Comparative Study on the Double Fractional Models for the Dynamic Analysis of Viscoelastic Fluids

Fractional calculus has become a powerful tool to describe viscoelastic mechanical behaviors. The key to its practical application lies in determining the number and combination form of fractional operators. In this paper, a systematic comparative study on the application effects of different forms of single and double fractional models has been conducted. To this end, various concentrations of polyacrylamide (PAAm) solutions were prepared as representatives, and the storage modulus and loss modulus were obtained through frequency sweep experiments. Subsequently, the single and double fractional models in Maxwell and Kelvin–Voigt types were used separately to describe the experimental data, and the goodness of fit was employed for the evaluation of the results. The results indicated that the double fractional models can provide more accurate results than the single fractional models, especially the double fractional Maxwell model, which demonstrated significant advantages in both the storage and loss moduli. Therefore, compared with the other three models, the double fractional Maxwell model is the optimal modeling tool for the dynamic mechanical analysis of viscoelastic fluids.