Avaliação de modelos matemáticos no cálculo da viscosidade dinâmica de sucos de frutas

Abstract

The comsumption of fruit juices has grown due to co nvenience and practicality generated by the finished products. According to the Associação Brasileira das Indústrias de Refrigerantes, in 2012 the annual production was 987 million liter s of fruit juices in Brazil. However, to achieve greater efficiency and performance, it is n ecessary to know the rheological behavior of the raw materials. Among rheological properties, viscosity is widely used in industrial and academic applications such as: a parameter for the calculation of heat and mass transfer coefficients; equipment design; cost assessment; de sign processes; quality control of the product; and enable an understanding of the chemica l structure of raw materials. During industrial processing of fruit juices, the raw mate rials are submitted to temperatures and concentrations of solids variations that altering i ts viscosity. Therefore, the knowledge of the combined effect of temperature and concentration of solids on viscosity are essential for the juice processing. In this work, literature data fro m eleven clarified juices of fruit (mango, cherry, apple, peach, blackcurrant, pomegranate, pe ar, lemon, tangerine, lime and grape) at concentrations and temperatures from 15.0 to 74.0 º Brix and from 278.15 to 393.15 K, respectively, were modeled using empirical and semi -empirical correlations derived from the literature. Global and specific parameters for all studied models been obtained in function of temperature and total soluble solids (TSS) concentr ation. Four equations were evaluated to calculate the activation energy in each model (line ar equation, exponential, polynomial of 2nd and 3rd order) using activation energy as specific parameter, and three different modeling strategies were conducted: for all TSS concentratio ns and temperatures; two ranges concentrations of TSS; and, two ranges of temperatu res. The optimization strategy for the concentrations TSS range proved the most suitable. Two exponential mathematical relations based on correlation of Arrhenius have been success ful in predicting the dynamic viscosity of clarified fruit juices at concentrations from 17.0 to 50.1 °Brix for all temperatures studied. While Vogel's equation obtained good results for co ncentrations of 51.0 to 66.0 °Brix in predicting the dynamic viscosity of fruit juices. T he models were validated using experimental data to clarified orange juices at low (30.7 to 50.5 °Brix) and high concentrations (54.1 to 63.5 °Brix) of TSS, with ex cellent prediction of dynamic viscosity