Fractional time-dependent apparent viscosity model for semisolid foodstuffs

Fractional calculus to control transport phenomena in food engineering: A systematic review of barriers and data agenda

“…All the works reached similar conclusions regarding the generalized models, Yang et al (2018), Yang et al (2017) and Dapčević Hadnadev et al (2013), found that the analyzed fluids presented characteristics that are beyond the ideality assumed by the models, such as non‐Newtonian characteristics, since the fractional order model adjusted well to the experimental data, in general the fractional order models better represented the studied rheological characteristics, being more thrifty. Fractional order adjustment also indicates anomalous memory effect and energy dissipation mechanism.…”

“…Other authors who also used fractional‐order models to study food viscosity were Yang et al (2018) applied a fractional‐order model to colloids to characterize the apparent viscosity of thixotropic materials, in which the order of the fractional derivative was designed to describe their historical dependence, that is, nonlocal properties, and Yang et al (2017) proposed a fractional derivative model for cellulose and milk viscosity, by generalizing the order of the Hooke's Law model for thixotropic fluids. As in the previous work, the authors generalize the order of the model by derivatives of Rieman–Liouville; Dapčević Hadnadev et al (2013) proposed a viscosity model, generalized the order of the model by Caputo derivatives, and adjusted the two models to study the influence of sodium starch octenyl succinate on the rheological behavior of wheat flour dough systems; Petrovic et al (2015) aimed to generalize the order of differentiation of Newton and Zener models and to adjust to the experimental data of three types of resin;(Orczykowska & Dziubinski, 2012) fitted a classic model and a fractional order model for the viscosity of colloids consisting of xanthan gum, rice starch and potato starch, and; (Lawal et al, 2011), adjusted a generalized order model based on Newton's law of viscosity to study rheological characteristics of fluids.…”

“…Petrovic et al (2015), Orczykowska and Dziubinski (2012), and Lawal et al (2011) obtained the same conclusions. Among these authors, the only ones who make suggestions for future research are Yang et al (2018), who suggests using their model in a transient regime with varying operating conditions, in addition to using the model in other materials.…”

“…Also, the model's order may indicate a change in viscosity or relaxation of tension over time. Yang et al (2018) attributed the success of fractional‐order models to the fact that first‐order models assume fluid ideality. Among the main barriers raised, it is possible to mention the difficulty of applying numerical methods due to mathematical formalism and the demand for greater computational power to solve the models, in addition to mathematical formalism in the deduction of equations.…”

“…Similarly, studies in rheology using fractional-order models to analyze fluid behavior shown to be more realistic then the classic integer-order descriptions (Mahiuddin et al, 2018;Petrovic et al, 2013). Therefore, if the model order is fractional, this may indicate that the fluid has a non-Newtonian behavior (Lawal et al, 2011) and such reasoning can also be applied to other types of fluids (Yang et al, 2018(Yang et al, , 2020.…”