Rheological modeling as a function of temperature is a useful tool for describing products undergoing thermal processing. The rheological behavior of a range of dairy-based (4%, w/w) protein beverages was investigated for applicability to semi-empirical temperature-dependent viscosity equations. The viscosity at 16.8 rad/s of the beverages was measured during heating, holding, and cooling over a temperature range of 25 to 90 o C using a rheometer with starch pasting cell geometry. Five established fitting methods were applied based on the Arrhenius and Williams-Landel-Ferry (WLF) equations using nonlinear regression analysis. A two-parameter WLF (WLF2 ) model, using viscosity at a reference temperature of 25 o C resulted in high R2 values (0.974 to 0.988) and a statistically superior fit compared to the Arrhenius, Generalized Arrhenius, and exponential equations (P < 0.001). Deviation from the WLF2 modeled equation was used to describe and investigate the effect formulation had on the changes in viscosity during thermal heating. This study successfully applied the WLF equation to a liquid protein system, proving that a consistent and close fit can be achieved across a range of formulations. A rapid, quantitative method for viscosity-temperature profile evaluation is presented, which can ease product development and optimization of product processing stability.
Practical application: This study validated the use of the Williams-Landel-Ferry equation to describe the behavior of dairy beverages during thermal processing, providing a better fit to rheological data than the widely used Arrhenius-based equations. In conjunction with the WLF equation, a method was presented which reduced the complex rheological data to a single value, which can aid in the comparison of formulations for product development and optimization in both research and industry.
Keywords: Arrhenius; Williams-Landel-Ferry; dairy protein beverages; thermal processing viscosity.
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