Aluízio Freire da Silva Júnior

Osmotic dehydration kinetics of banana slices considering variable diffusivities and shrinkage

ABSTRACT This article studied the use of diffusion models to describe variation of water quantity and sucrose quantity during osmotic dehydration of bananas cut into cylindrical slices. Bananas with radius of 1.7 cm and 18 °Brix (on average) were cut into 1.0 cm of thickness. A solution was proposed for the diffusion equation in cylindrical coordinates using the finite volume method, with fully implicit formulation. The diffusion equation was discretized assuming diffusivities and dimensions with variable values for the banana slices. Boundary conditions of the third kind have also been considered. The osmotic dehydration experiments were conducted in binary solutions (water and sucrose) under conditions of 40 and 60 °Brix and temperatures of 40 and 70°C. Mathematical modeling was proposed to describe the processes presented good results for water quantity and sucrose quantity, with good statistical indicators for all fits.

Description of osmotic dehydration of apple using two-dimensional diffusion models considering shrinkage and variations in process parameters

ABSTRACT The main purpose of this paper is to study osmotic dehydration of apple in water and sucrose solutions. The kinetics of water quantity and solid gain are described by two mathematical models using numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with boundary condition of third kind. For the first model, both the process parameters and the product dimensions have been considered constant. For the second model these quantities have been taken as variable. The numerical solutions have been obtained via the finite volume method with fully implicit formulation. Process parameter estimation, using experimental data, was obtained by an optimizer based on the inverse method. The third-kind boundary condition was shown to be appropriate in view of the fact that the resistances to mass flows on the product surface are not at all negligible. The temperature and concentration of the osmotic solution used in the experiments influenced significantly the kinetics of solid uptake and water quantity as well as the values of estimated parameters. Mathematical model which considers the variations in the process parameters and the product shrinkage presents good physical consistency and well describes the mass migrations.

A Numerical Approach to Determine Some Properties of Cylindrical Pieces of Bananas During Drying

Abstract This article uses several liquid diffusion models to describe convective drying of bananas cut into cylindrical pieces. A two-dimensional numerical solution of the diffusion equation with boundary condition of the third kind, obtained through the finite volume method, was used to describe the process. The cylindrical pieces were cut into the following dimensions: length of about 21 mm and average radius of 15 mm. Drying air temperatures were 40°C, 50°C, 60°C and 70°C. In order to determine the process parameters, an optimizer was coupled with the numerical solution. A model that considers the shrinkage and variable effective moisture diffusivity well describes drying for all the experimental conditions, and enables to predict the moisture distributions at any given time. For this model, the determination coefficient has varied from 0.99937 (70°C) to 0.99995 (40°C), while the chi-square ranged from 3.41 × 10−4 (40°C) to 4.15 × 10−3 (70°C).

Guava Osmotic Dehydration: Description by Two-Dimensional Diffusion Models Considering Shrinkage and Variations in Process Parameters

Abstract This article describes the osmotic dehydration of guava dipped in sucrose solutions using two-dimensional numerical solutions of the diffusion equation with boundary condition of the first kind. Two models are used: model 1 disregards the shrinkage of the product and assumes that effective mass diffusivity does not vary during the process; model 2 takes into account shrinkage, considering effective mass diffusivity as variable. Process parameters estimation is obtained by means of an optimizer. Comparative analyzes indicate that the proposed models have similar statistical indicators. However, model 2 is recommended, for it presents much higher physical fitness when describing mass migrations. Comparison between two-dimensional numerical models presented in this research and one-dimensional models found in the literature reveals that one-dimensional models overestimate process parameters. In addition, one-dimensional models present limitations in predicting the distributions of water and sucrose on guava slices.

Apple osmotic dehydration described by three-dimensional numerical solution of the diffusion equation

ABSTRACT In the present study, experimental data of osmotic dehydration kinetics of apple, cut into slices with parallelepiped shape, were simulated using two types of diffusion models. Model 1 considers the constant values of mass diffusivities and volume of the slices. Model 2, on the other hand, considers variable mass diffusivities and also the shrinkage of the product. The numerical solution of the three-dimensional diffusion equation in Cartesian coordinates was obtained through the finite volume method, with a fully implicit formulation and boundary condition of the first kind. Process parameters were determined by optimization using the experimental data sets, through the minimization of an objective function, called χ2. The results of the osmotic dehydration kinetics were compatible with those of other studies found in the literature. Process temperature and osmotic solution concentration had influence on the phenomenon, but temperature was preponderant. A study was conducted on water and sucrose distribution during the osmotic dehydration. The results obtained through the mathematical model that considered the variable diffusivity and shrinkage showed greater adequacy to the experimental data.