Evaluation of Models for Temperature-Dependent Viscosity Changes in Dairy Protein Beverage Formulations During Thermal Processing

Abstract: 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 ^oC 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 ^oC 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.