Describing the firmness, springiness and rubberiness of food gels using fractional calculus. Part II: Measurements on semi-hard cheese

Abstract

We use the framework of fractional calculus to quantify the linear viscoelastic properties of full-fat, low-fat, and zero-fat, semi-hard cheeses over a range of temperatures and water / protein ratios. These fractional constitutive models correctly predict the time-dependence and interrelation of the firmness, springiness, and rubberiness of these emulsion-filled hydrocolloidal gels. Our equations for the firmness F, springiness S , and rubberiness R, also correctly predict the effect of changing the magnitude or time-scale of the stress loading on the material even in the case of irreversible flow events, when cheese progressively transitions from a solid to a liquid. Finally we show how our FSR-equations can be used in a texture engineering context; they provide rational guidance to product reformulation studies and allow for extrapolation of a firmness measurement to practical situations in which the gel is subjected to prolonged creep loading.

Quantifying the consistency and rheology of liquid foods using fractional calculus

“…In more quantitative terms, it appears that a c ≈ 4 wt % solution of TUC would also satisfy this viscosity criterion, yet its location on the phase space in Figure 8 is at nearly the opposite end of the ordinate axis, approaching the limit of of n → 0, where a truly 'elasto-plastic' or yield-stress-like response is recovered. More accurate phase boundaries demarcating textures such as 'pudding' must therefore correspond to more complex loci than the straight lines given by Equation (19).…”

“…In their studies of product aging, Quinchia et al have also modeled the linear viscoelastic response of a commercial strawberry pudding using power laws, although the direct connection to fractional calculus was not made at the time by these authors [17]. As a final example, Faber et al have recently applied fractional models towards the evaluation of the effect of fat and water content on technological measures such as the firmness, rubberiness, and springiness of cheese at different temperatures [18,19].…”

Fractional viscoelastic models for power-law materials

“…tissues, [29][30][31] single cells, 13,29,[32][33][34][35][36] intra and extra cellular components; 10,37,38 gels, 39,40 polymers, 9,41 concrete, 42,43 asphalt, [44][45][46] ice, 9 and food -e.g. cheese, 11,47 dough. 8,48 This behaviour represents a challenge to the commonly used viscoelastic models in obtaining a unique mathematical description of the constitutive relation with a limited number of parameters.…”

“…Fractional viscoelasticity has been applied to complex geological and construction materials such as bitumen (asphalt), 44,45 concrete, 42,43 rock mass, [54][55][56][57][58][59] waxy crude oil, 60,61 as well as polymers and gels, 41,[62][63][64][65] and food. 11 Numerous examples can also be found of fractional viscoelasticity applied to biological materials such as epithelial cells, 66 breast tissue cells, 67,68 lung parenchyma, 69 blood flow, 70,71 as well as red blood cell membranes. 72 Considering the microscale, some observations of anomalous diffusion in complex fluids have been interpreted based on fractional viscoelastic behaviours, [73][74][75] with applications to, for instance, transport movements in cell cytosol.…”

Effect of the stretching temperature on the texture and thermophysical properties of Mozzarella cheese

“…The stiffness (hardness) of cheese increases when the fat content of the cheese is decreased. According to Faber, Jaishankar, and McKinley (2017), the casein/fat ratio is important because it influences the texture. Standardization of the casein/milk fat ratio used in cheese processing decreased the fat content, which may explain the high TPA hardness obtained in the present study, especially at the beginning of storage.…”