Analytical solution of freeze-drying mathematical model based in Darcy's law: application to an orange juice-based cake

An analytical solution for moisture dynamic during freeze-drying based in non-ideal Darcy's law that resolves the singularity at zero time was deducted. The non-ideal Darcy's law is represented by a Darcy's pseudo permeability ( ) and a deviation index ( ). The analytical solution mus...

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Bibliographic Details
Published in:CYTA: journal of food 2021-01, Vol.19 (1), p.265-272
Main Authors: Uscanga-Ramos, Mariana Aziyadé, Lopez-Sanchez, Erik, Martínez-Navarrete, Nuria, García-Alvarado, Miguel Angel, Salgado-Cervantes, Marco Antonio
Format: Article
Language:English
Subjects:
analytical solutions
Cakes
Darcy's law
Deviation
Exact solutions
Food preservation
Fourier's law
Freeze drying
Fruit juices
Heat transfer
Ley de Darcy
Ley de Fourier
Mathematical analysis
mathematical model
Mathematical models
Modelos matemáticos
orange juice based cake
Permeability
Secado por congelación
Soluciones analíticas
Torta con base de jugo de naranja
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Summary:An analytical solution for moisture dynamic during freeze-drying based in non-ideal Darcy's law that resolves the singularity at zero time was deducted. The non-ideal Darcy's law is represented by a Darcy's pseudo permeability ( ) and a deviation index ( ). The analytical solution must be complemented with a numerical solution of Fourier's equations for heat transfer in the two product zones. The model was fitted to experimental freeze-drying dynamics of an orange juice-based cake. The Darcy's pseudo permeability obtained was 2.0X10 −12 m 2.5 with an ideal deviation index of 0.5. The proposed equations, solved with fitted Darcy pseudo permeability and ideal deviation index, reproduced other experimental freeze-drying dynamics of the same product at different temperatures.
ISSN:1947-6337
1947-6345
DOI:10.1080/19476337.2021.1892195