Comparison between classical Kelvin-Voigt and fractional derivative Kelvin-Voigt models in prediction of linear viscoelastic behaviour of waste activated sludge

Abstract

Appropriate sewage sludge rheological models are essential for computational fluid dynamic simulation of wastewater treatment processes, in particular aerobic and anaerobic digestions. The liquid-like behaviour of sludge is well documented but the solid-like behaviour remains poorly described despite its importance for dead-zone formation. In this study, classical Kelvin-Voigt model, commonly used for sludge in literature, were compared with fractional derivative Kelvin-Voigt model regarding their predictive ability for describing the solid-like behaviour. Results showed that the fractional Kelvin-Voigt model best fitted the experimental data obtained from creep and frequency sweep tests. Whereas, classical Kelvin-Voigt could not fit the frequency sweep data as this model is not a function of angular velocity. Also, the Kelvin-Voigt model was unable to predict the creep data at low stresses.

Keywords: Activated sludge; Fractional derivative Kelvin-Voigt; Kelvin-Voigt; Rheological modelling; Viscoelastic model.