Abstract This work presents the mathematical modeling of clarification kinetics of the sugarcane juice by ozonation in batch reactor considering the reaction occurs homogeneously and ozone saturation in the juice is guaranteed. The sugarcane juice color was considered proportional to the light absorbance at wavelength λ = 420 ηm, according to the International Unit specified by ICUMSA - International Commission for Uniform Methods of Sugar Analysis. The model equation coefficients were obtained numerically, using the MATLAB® software, based on the experimental absorbance as a function of time, obtained for three different temperatures of the juice. The obtained results were so much satisfactory and led to the conclusion that mathematical model represents well the kinetics of clarification in the proposed conditions.

The aim of this work was to study the drying curves and equilibrium isotherms of extruded fish feed. The drying curves were determined at air temperatures of 50, 60, 70 and 80°C and airflow velocities of 1.5, 2.5 and 3.5 m/s). The equilibrium isotherms of relative humidity of air were obtained between 10 and 80% at 30, 40, 50, and 70°C. The experimental data were fitted for non-linear regression by using Statistica® to the models reported in the literature. The results showed that the drying curves and the equilibrium isotherms were significantly influenced by variations of the air temperature in a similar way to solid materials as described in the literature. The statistical results for models of Page and Peleg showed that the fitting of the experimental drying curve and isotherm data were satisfactory.

Desenvolveu-se uma análise comparativa do estudo teórico-experimental efetuado por Hsu sobre a hidratação de grãos de soja Amsoy 71 a partir da execução de diversos ensaios de hidratação de soja CD 202 nas temperaturas de 10, 20, 30, 40 e 50 °C, medindo-se a umidade ao longo do tempo. Os resultados revelam que o valor da umidade de equilíbrio, Xeq, da soja CD 202 independe da temperatura e é 21% superior àquele encontrado por Hsu, sugerindo que a variedade de soja exerce grande influência sobre Xeq. O modelo de Hsu foi resolvido numericamente e teve seus parâmetros ajustados pelo método dos mínimos quadrados, apresentando desvios máximos de +/-10% em relação aos valores experimentais. A etapa limitante do processo de transferência de massa na hidratação corresponde à difusão de água no interior do grão, conduzindo ao surgimento de gradientes radiais de umidade que diminuem com o aumento da temperatura e do tempo. Independentemente da variedade de soja utilizada, a difusividade aumenta com a elevação da temperatura e do teor de umidade, porém os valores desta propriedade de transporte para soja Amsoy 71 foram superiores aos da CD 202, sendo muito próximos no início da hidratação a 20 °C e quase três vezes maior ao final da hidratação a 50 °C.

A comparative analysis of the theoretical-experimental study, developed by Hsu on the hydration of Amsoy 71 soybean grain, was performed through several soaking experiments using CD 202 soybean at 10, 20, 30, 40, and 50 °C, measuring moisture content over time. The results showed that CD 202 soybean equilibrium moisture content, Xeq, does not depend on temperature and is 21% higher than that found by Hsu, suggesting that soybean cultivar exerts great influence on Xeq. The Hsu model was numerically solved and its parameters were adjusted by the least squares method, with maximum deviations of +/- 10% relative to the experimental values. The limiting step in the mass transfer process during hydration corresponds to water diffusion inside the grain, leading to radial moisture gradients that decrease over time and with an increase in temperature. Regardless of the soybean cultivar, diffusivity increases as temperature or moisture content increases. However, the values of this transport property for Amsoy 71 were superior to those of CD 202, very close at the beginning of hydration at 20 °C and almost three times higher at the end of hydration at 50 °C.

Desenvolveu-se um modelo matemático para estimar a concentração de água em grãos de ervilha durante sua hidratação, o qual foi obtido a partir de um balanço de massa em regime transiente, considerando-se volume constante e geometria esférica. Este modelo é representado por uma equação diferencial ordinária de primeira ordem e possui dois parâmetros: o coeficiente de transferência de massa (Ks) e a concentração de equilíbrio (ρAeq). Ambos foram ajustados numericamente tomando-se como critério a minimização da soma dos resíduos quadráticos, utilizando-se dados experimentais de hidratação de grãos de ervilha a 20, 30, 40, 50 e 60 ºC. Em todas as temperaturas, o modelo representou as principais tendências do processo de hidratação com desvios inferiores a 5%. Foi observado que Ks apresentou um comportamento segundo a equação de Arrhenius frente à temperatura, Ks = 182,8 exp (-3521/T), enquanto ρAeq permaneceu praticamente constante, obtendo-se um valor médio de 0,53 g.mL-1. Utilizando-se a correlação de Ks e assumindo-se o valor de ρAeq médio, obteve-se um modelo generalizado, o qual apresentou para todos os dados um desvio ligeiramente superior a 7%. Adicionalmente, constatou-se que a densidade dos grãos de ervilha permaneceu praticamente constante ao longo da hidratação independentemente da temperatura.

A mathematical model for estimating the water concentration in pea grains during hydration was developed from a transient water mass balance inside a grain of pea considering a constant volume and spherical geometry. This model is represented by an ordinary first order differential equation and has two parameters: the mass transfer coefficient (Ks) and the equilibrium concentration (ρAeq). Both parameters have been numerically fitted using the minimization of the sum-of-squared residuals criterion and the hydration experimental data for pea grains at 20, 30, 40, 50, and 60 ºC. At all temperatures, the model represented the major trends of the hydration process with standard deviations smaller than 5%. For the model fitted parameters, it was observed that the mass transfer coefficient behaved according to Arrhenius's equation in relation to the temperature variation, Ks = 182.8.exp(-3521/T) while the equilibrium concentration remained practically constant showing an average value of ρAeq = 0.533 g/cm³. Using the Ks Arrhenius's correlation and assuming the average value of ρAeq, a generalized model was obtained, which resulted in a standard deviation slightly greater than 7% for all the data values. Additionally, it was observed that the pea grains density remains practically constant along the hydration process and does not depend on the temperature.