Preprint Article Version 1 This version is not peer-reviewed

A diffusion model to describe water absorption by red rice during soaking: Variable mass diffusivity, variable volume, use of Boundary-Fitted Coordinates

Wilton Pereira da Silva
* ,
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
,
Eugênia Teles de Vilela Silva
,
Aluizio Freire da Silva Júnior
,
Leidjane Matos de Souto
Version 1 : Received: 3 July 2024 / Approved: 3 July 2024 / Online: 3 July 2024 (15:27:30 CEST)

How to cite: 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.; Silva, E. T. D. V.; Júnior, A. F. D. S.; Souto, L. M. D. A diffusion model to describe water absorption by red rice during soaking: Variable mass diffusivity, variable volume, use of Boundary-Fitted Coordinates. Preprints 2024, 2024070352. https://doi.org/10.20944/preprints202407.0352.v1 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.; Silva, E. T. D. V.; Júnior, A. F. D. S.; Souto, L. M. D. A diffusion model to describe water absorption by red rice during soaking: Variable mass diffusivity, variable volume, use of Boundary-Fitted Coordinates. Preprints 2024, 2024070352. https://doi.org/10.20944/preprints202407.0352.v1

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, as well as the analyses of water distribution and volumetric expansion of each grain, at a given instant, was done 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 (BFC). 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 variable volume and also variable mass diffusivity as a function of local moisture content. Optimizations based on 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 concluding that the model proposed was very satisfactory for all temperatures, making it possible to simulate 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.

Subject

Biology and Life Sciences, Food Science and Technology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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