Paulo Roberto Paraíso

Modelagem matemática e análise da hidratação de grãos de ervilha

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 Arrheniuss 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 Arrheniuss 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.

Application of the Hsu model to soybean grain hydration

Abstract 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, X eq , does not depend on temperature and is 21% higher than that found by Hsu, suggesting that soybean cultivar exerts great influence on X eq . 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.

Modeling of drying and adsorption isotherms of the fish feed

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.

AVALIAÇÃO DA CAPACIDADE DE ADSORÇÃO DE FLÚOR EM CARVÃO ATIVADO DE ORIGEM ANIMAL

Neste trabalho foi avaliado o potencial de adsorção do carvão ativado de osso bovino na remoção de íons fluoreto. Para tanto, inicialmente, determinou-se o ponto de carga zero do adsorvente (pHPCZ). Em seguida, avaliou-se a cinética de adsorção, os efeitos do pH da solução (2 – 12) e da temperatura do sistema (20, 30, 40 e 50°C) e, finalmente, o equilíbrio de adsorção. Todos os testes foram realizados em sistema fechado e batelada sob agitação constante (130 rpm). Os resultados obtidos mostram que o pHPCZ do adsorvente é igual a 6,63. A cinética de adsorção indica que o equilíbrio do sistema foi alcançado em, aproximadamente, 6 horas de operação. Os dois modelos cinéticos ajustados aos dados experimentais (pseudoprimeira e pseudossegunda ordens) descreveram de forma satisfatória a cinética de adsorção do flúor, com coeficiente de determinação superiores a 0,98. As avaliações dos efeitos do pH e temperatura apontam que as melhores condições de remoção de flúor foram obtidas em pH 2 e temperaturas de 40 e 50 °C para baixas concentrações e 30°C para concentrações acima de 4 mg L -1 . No estudo do equilíbrio, verificou-se que o modelo de Langmuir foi o que melhor se ajustou aos dados experimentais, apresentando capacidade máxima de adsorção de 2,03 mg g -1 em 30°C. Os resultados obtidos demonstraram que o adsorvente estudado apresenta grande potencial para a remoção de flúor, quando comparado a outros materiais adsorventes.