The Fractional derivative rheological model and the linear viscoelastic behavior of hydrocolloids

Abstract

This study was aimed at evaluating the possibility to use the Friedrich-Braun fractional derivative rheological model to assess the viscoelastic properties of xanthan gum with rice starch and sweet potato starch. The Friedrich-Braun fractional derivative rheological model allows to describe viscoelastic properties comprehensively, starting from the behaviour characteristic of purely viscous fluids to the behaviour corresponding to elastic solids. The Friedrich-Braun fractional derivative rheological model has one more virtue which distinguishes it from other models, it allows to determine the relationship between stress and strain and the impact of each of them on viscoelastic properties on the tested material. An analysis of the data described using the Friedrich-Braun fractional derivative rheological model allows to state that all the tested mixtures of starch with xanthan gum form macromolecular gels exhibiting behaviour typical of viscoelastic quasi-solid bodies. The Friedrich-Braun fractional derivative rheological model and 8 rheological parameters of this model allow to determine changes in the structure of the examined starch -xanthan gum mixtures. Similarly important is the possibility to find out the trend and changes going on in this structure as well as their causes.

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

“…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.…”

Thermomechanical Fractional Model of TEMHD Rotational Flow

“…The polymer fluid chosen for purposes of numerical evaluations is 0.2% Xanthan Gum (XG) [45, 46]. XG solution has been used extensively in the oil industry for different applications due to its unique rheological properties.…”

Viscoelastic Properties of Soft Materials on a Basis of Starch Mixtures

“…The Zener model—Eq. to —has 5 rheological parameters, that is G e , , τ 0 , α, and k , which represent the following properties of tested material (Pruska‐Kędzior ; Orczykowska and Dziubiński ).…”

“…The knowledge of these parameters allows us to get additional information on the tested material properties, namely to learn the value of dispersion modulus f , cross‐linking density of gel ω 0 , and gel stiffness S . Relations used to determine the values of 3 new parameters on the basis of the 5 parameters already existing in the Zener fractional model are described by the following equations (Mours and Winter ; Pruska‐Kędzior ; Orczykowska and Dziubiński ): ‐dispersion modulus f ‐cross‐linking density of gel ω 0 ‐gel stiffness S …”