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Volume 12
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10.3390/pr12081696
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates

by
Wilton Pereira da Silva
1,*,
Antonio Gilson Barbosa de Lima
2,
Joan Carlos Alves Pereira
1,
Josivanda Palmeira Gomes
1,
Alexandre José de Melo Queiroz
1,
Rossana Maria Feitosa de Figueirêdo
1,
Yaroslávia Ferreira Paiva
1,
Francislaine Suélia dos Santos
1,
Bruno Adelino de Melo
1,
Henrique Valentim Moura
1,
Eugênia Teles de Vilela Silva
1,
Aluizio Freire da Silva Júnior
3 and
Leidjane Matos de Souto
4
1
Department of Agricultural Engineering, Federal University of Campina Grande, Campina Grande 58429-900, Brazil
2
Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande 58429-900, Brazil
3
Physics and Mathematics Academic Unit, Federal University of Campina Grande, Campina Grande 58429-900, Brazil
4
Education and Health Center, Federal University of Campina Grande, Cuité 58175-000, Brazil
*
Author to whom correspondence should be addressed.
Processes 2024, 12(8), 1696; https://doi.org/10.3390/pr12081696
Submission received: 3 July 2024 / Revised: 9 August 2024 / Accepted: 12 August 2024 / Published: 13 August 2024
(This article belongs to the Section Food Process Engineering)
Versions Notes

Abstract

This article aims to carry out experiments on water absorption by husked red rice at constant temperatures of 28, 40, and 50 °C. The description of the absorption kinetics and the analyses of the water distribution and volumetric expansion of each grain, at a given instant, were carried out using a diffusion model. In order for the model to be as close as possible to the real physical situation, the mesh necessary to numerically solve the diffusion equation was generated from the photograph of a grain. Thus, the diffusion equation was written in Boundary-Fitted Coordinates (BFCs). The solution of the diffusion equation written in generalized coordinates was then discretized in space and time, using the Finite Volume method, with a fully implicit formulation, considering the variable volume and variable mass diffusivity as functions of the local moisture content. Optimizations based on the Levenberg–Marquardt algorithm make it possible to determine the parameters of an exponential function relating mass diffusivity and the local moisture content for each temperature. Statistical indicators (chi-square, determination coefficient, and Student’s t-test) allowed us to conclude that the proposed model was very satisfactory for all temperatures, making it possible to simulate the water absorption, water distribution, and volumetric expansion of the grain over time.
Keywords: generalized coordinates; real geometry; non-orthogonal structured mesh; water uptake; moisture distribution generalized coordinates; real geometry; non-orthogonal structured mesh; water uptake; moisture distribution

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MDPI and ACS Style

Silva, W.P.d.; Lima, A.G.B.d.; Pereira, J.C.A.; Gomes, J.P.; Queiroz, A.J.d.M.; Figueirêdo, R.M.F.d.; Paiva, Y.F.; Santos, F.S.d.; Melo, B.A.d.; Moura, H.V.; et al. A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates. Processes 2024, 12, 1696. https://doi.org/10.3390/pr12081696

AMA Style

Silva WPd, Lima AGBd, Pereira JCA, Gomes JP, Queiroz AJdM, Figueirêdo RMFd, Paiva YF, Santos FSd, Melo BAd, Moura HV, et al. A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates. Processes. 2024; 12(8):1696. https://doi.org/10.3390/pr12081696

Chicago/Turabian Style

Silva, Wilton Pereira da, Antonio Gilson Barbosa de Lima, Joan Carlos Alves Pereira, Josivanda Palmeira Gomes, Alexandre José de Melo Queiroz, Rossana Maria Feitosa de Figueirêdo, Yaroslávia Ferreira Paiva, Francislaine Suélia dos Santos, Bruno Adelino de Melo, Henrique Valentim Moura, and et al. 2024. "A Diffusion Model to Describe Water Absorption by Red Rice during Soaking: Variable Mass Diffusivity, Variable Volume, Use of Boundary-Fitted Coordinates" Processes 12, no. 8: 1696. https://doi.org/10.3390/pr12081696

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