Fractional time-dependent apparent viscosity model for semisolid foodstuffs

Abstract

The difficulty in the description of thixotropic behaviors in semisolid foodstuffs is the time dependent nature of apparent viscosity under constant shear rate. In this study, we propose a novel theoretical model via fractional derivative to address the high demand by industries. The present model adopts the critical parameter of fractional derivative order $\alpha$ to describe the corresponding time-dependent thixotropic behavior. More interestingly, the parameter $\alpha$ provides a quantitative insight into discriminating foodstuffs. With the re-exploration of three groups of experimental data (tehineh, balangu, and natillas), the proposed methodology is validated in good applicability and efficiency. The results show that the present fractional apparent viscosity model performs successfully for tested foodstuffs in the shear rate range of $50\mbox{--}150~\mbox{s}^{ - 1}$. The fractional order $\alpha$ decreases with the increase of temperature at low temperature, below 50 °C, but increases with growing shear rate. While the ideal initial viscosity $k$ decreases with the increase of temperature, shear rate, and ingredient content. It is observed that the magnitude of $\alpha$ is capable of characterizing the thixotropy of semisolid foodstuffs.