Temperature–viscosity models reassessed

Abstract

ABSTRACTThe temperature effect on viscosity of liquid and semi-liquid foods has been traditionally described by the Arrhenius equation, a few other mathematical models, and more recently by the WLF and VTF (or VFT) equations. The essence of the Arrhenius equation is that the viscosity is proportional to the absolute temperature's reciprocal and governed by a single parameter, namely, the energy of activation. However, if the absolute temperature in K in the Arrhenius equation is replaced by T + b where both T and the adjustable b are in °C, the result is a two-parameter model, which has superior fit to experimental viscosity–temperature data. This modified version of the Arrhenius equation is also mathematically equal to the WLF and VTF equations, which are known to be equal to each other. Thus, despite their dissimilar appearances all three equations are essentially the same model, and when used to fit experimental temperature–viscosity data render exactly the same very high regression coefficient. It is shown that three new hybrid two-parameter mathematical models, whose formulation bears little resemblance to any of the conventional models, can also have excellent fit with r2 ∼ 1. This is demonstrated by comparing the various models' regression coefficients to published viscosity–temperature relationships of 40% sucrose solution, soybean oil, and 70°Bx pear juice concentrate at different temperature ranges. Also compared are reconstructed temperature–viscosity curves using parameters calculated directly from 2 or 3 data points and fitted curves obtained by nonlinear regression using a larger number of experimental viscosity measurements.