Rheology Study on Low-Sugar Apple Jam by a New Nonlinear Regression Method of Herschel-Bulkley Model

Abstract

Structure break was found in shearing process of static prepared low‐sugar apple jam, which is a thixotropic and shear‐thinning fluid. In order to investigated this jam, a new nonlinear regression method of Herschel–Bulkley (H‐B) model without measuring yield stress was set up using R2 as optimizing criterion, and compared with Casson model. Dynamic yield stress was calculated using the regression of downward curve. Casson model was found fit in high shear rate (in one case, R2 0.9986, still lower than H‐B model, 0.9997). Break stress (from 113 to 497 Pa) could be largely increased by soluble solid concentration rising, and dynamic yield stress of H‐B model changed from 0.004 to 20.75 Pa, mainly depending on sugar and soluble solid concentration. Consistency index (24.50–102.3 Pa·sn) was increased with adding soluble solid and decreased with adding sugar. Flow behavior index (0.229–0.363) was increased evidently with adding pectin and sugar. Practical Applications The low‐sugar jams are more nutrition‐reasonable since they generally provide fewer calories, now short of deep research. Rheological properties are of great significance for processed food fluids. Traditional steady‐state test was applied widely in rheologic study of food fluids. However, information under flow curves could not be explored in detail because definition of yield stress was confused for a long time and the most common model of fluid, Herschel–Bulkley model, lacked suitable regression method. Additionally, upward curve was often ignored. In this work, a new simple nonlinear regression of Herschel–Bulkley model was set up without measuring yield stress investigated. Then the influences of ingredients on rheologic properties of low‐sugar apple jam could be investigated in detail. It is expected that the new method and observation would be applied by other rheologic researchers, and it is useful for finding relationships between mouth feel and indexes of Herschel–Bulkley model.

Optimization of physicochemical, textural, and rheological properties of sour cherry jam containing stevioside by using response surface methodology

“…The flow index is a parameter that expresses the internal structure of food fluids (Guo et al., 2017). n indicates fluid deviation from Newtonian behavior.…”

“…Also, according to the flow curves, it was found that the samples with higher sucrose concentration and TSS value have higher viscosity. Shear-thinning behavior was also observed in the jam of other fruits such as mango (Basu & Shivhare, 2010), apple (Guo et al, 2017), and gabiroba (Barbieri et al, 2018), which is determined by the flow curve. Herschel-Bulkley model was appropriate for the rheological behavior described by the flow curves, and the value of R 2 for it was 0.996, which is similar to the results of mango jam (Basu & Shivhare, 2010), with R 2 values between 0.818 and 0.996 and apple jam (Guo et al, 2017), with R 2 values from 0.891 to 0.998.…”

“…Figure 5C,D shows the interaction of sucrose and pectin with sucrose and stevia on the consistency index of sour cherry jam. Guo et al (2017) and Basu et al (2011) also reported that the increase in soluble solids is the main factor in increasing the consistency index of low-calorie jam.…”

A GPU-Based δ-Plus-SPH Model for Non-Newtonian Multiphase Flows

“…The Herschel-Bulkley model is adopted in the present work to study multiphase flow. This model is widely used in different fields [35][36][37][38] and can be expressed as:…”

Development of explicit and constitutive lattice-Boltzmann models for food product rheology

“…Both equations (2.12) and (2.14) are shown to represent shear thinning behaviour of food products very well [32]. A plot of the above non-Newtonian models is visible in Fig.…”