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

Juarez Everton de Farias Aires; Wilton Pereira da Silva; Kalina Lígia Cavalcante de Almeida Farias Aires; Aluízio Freire da Silva Júnior; Deise Souza de Castro; Cleide Maria Diniz Pereira da Silva e Silva

doi:10.1515/ijfe-2016-0056

Article

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

Juarez Everton de Farias Aires , Wilton Pereira da Silva , Kalina Lígia Cavalcante de Almeida Farias Aires , Aluízio Freire da Silva Júnior , Deise Souza de Castro and Cleide Maria Diniz Pereira da Silva e Silva

Published/Copyright: July 5, 2016

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From the journal International Journal of Food Engineering Volume 12 Issue 6

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.

Keywords: numerical simulation; two-dimensional model; osmotic dehydration; optimization; diffusivity

Funding statement: Conselho Nacional de Desenvolvimento Científico e Tecnológico, (Grant / Award Number: ‘302480/2015-3’).

Acknowledgment

The second author would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the support given to this research and for his research grant (Processes Number 302480/2015-3 and 444053/2014-0).

Nomenclature

A: area of the guava slices (m²)
Aij: area of control volumes “i, j” (m²)
D_S: effective mass diffusivity of sucrose (m² s⁻¹)
D_W: effective mass diffusivity of water (m² s⁻¹)
L_x, L_y: dimensions of the guava slices (m)
Lx∗,Ly∗: dimensionless values of slice dimensions
Lx0,Ly0: initial values of slab dimensions (m)
mW(t): water mass at time t (kg)
mW(0): water mass at the initial time (kg)
mS(t): sucrose mass at time t (kg)
md0: initial dry matter (kg)
P, E, N, W and S: nodal points
S: local value of the sucrose gain (g of sucrose/100 g of initial dry matter)
S₀: initial value of the sucrose gain (g of sucrose/100 g of initial dry matter)
S‾: average value of sucrose gain (g of sucrose/100 g of initial dry matter)
t: time (s)
W: local value of water quantity (g of water/100 g of initial water mass)
W₀: initial value of water quantity (g of water/100 g of initial water mass)
W‾: average value of water quantity (g of water/100 g of initial water mass)
x, y: position variables (m)
Φ: transport variable in the diffusion equation
Φ‾: average value of the transport variable
Φ‾tiexp: average experimental value of the transport variable
Φ‾tisim: average simulated value of the transport variable.
1/σi2: statistical weight
χ2: chi-square function
ΓΦ: transport coefficient
ΓfrΦ: value of ΓΦ on interface of neighbors control volumes
Δxe, Δxw_,Δyn and Δys: distances between nodal points (m)

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Published Online: 2016-7-5

Published in Print: 2016-8-1

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Articles in the same Issue

https://doi.org/10.1515/ijfe-2016-0056

Keywords for this article

numerical simulation; two-dimensional model; osmotic dehydration; optimization; diffusivity