Equivalence of Models of Freeze-Drying

Milena Veneva, William Lee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Freeze-drying is a preservation process, consisting of two main stages: during the primary drying water is removed by sublimation; during the secondary drying chemically bound water is removed by desorption. Two different models of secondary drying are built. The first one consists of coupled heat and mass balances equations, the second one uses a modified Richards equation. Using scale transformations derived from the PDEs and the BCs, the first model is nondimensionalized. The model is further simplified by asymptotic reduction. It is proven that the reduced model is equivalent to the model that uses the modified Richards equation if the partial pressure of air is negligible compared to that of water vapor in the vials and in the chamber of the freeze-drier. This result shows that there is an opportunity for technology transfer, since solvers developed for modelling groundwater flows using Richards equations can also be used to model the economically important problem of freeze-drying.

LanguageEnglish
Title of host publicationAdvanced Computing in Industrial Mathematics
Subtitle of host publicationRevised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria
EditorsKrassimir Georgiev, Michail Todorov, Ivan Georgiev
PublisherSpringer Verlag
Pages231-238
Number of pages8
Volume681
ISBN (Electronic)9783319495446
ISBN (Print)9783319495439
DOIs
Publication statusPublished - 7 Feb 2017
Externally publishedYes
Event10th Annual Meeting of the Bulgarian Section of SIAM - Sofia, Bulgaria
Duration: 21 Dec 201522 Dec 2015
Conference number: 10
http://www.math.bas.bg/IMIdocs/BGSIAM/bgsiam15_announcement.htm (Link to Conference Website)

Publication series

NameStudies in Computational Intelligence
PublisherSpringer
Volume681
ISSN (Print)1860-949X

Conference

Conference10th Annual Meeting of the Bulgarian Section of SIAM
Abbreviated titleBGSIAM 2015
CountryBulgaria
CitySofia
Period21/12/1522/12/15
Internet address

Fingerprint

Drying
Groundwater flow
Technology transfer
Sublimation
Partial pressure
Water vapor
Water
Desorption
Air

Cite this

Veneva, M., & Lee, W. (2017). Equivalence of Models of Freeze-Drying. In K. Georgiev, M. Todorov, & I. Georgiev (Eds.), Advanced Computing in Industrial Mathematics: Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria (Vol. 681, pp. 231-238). (Studies in Computational Intelligence; Vol. 681). Springer Verlag. Journal of Mathematics in Industry https://doi.org/10.1007/978-3-319-49544-6_19
Veneva, Milena ; Lee, William. / Equivalence of Models of Freeze-Drying. Advanced Computing in Industrial Mathematics: Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria. editor / Krassimir Georgiev ; Michail Todorov ; Ivan Georgiev. Vol. 681 Springer Verlag, 2017. pp. 231-238 (Studies in Computational Intelligence). (Journal of Mathematics in Industry).
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Veneva, M & Lee, W 2017, Equivalence of Models of Freeze-Drying. in K Georgiev, M Todorov & I Georgiev (eds), Advanced Computing in Industrial Mathematics: Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria. vol. 681, Studies in Computational Intelligence, vol. 681, Springer Verlag, Journal of Mathematics in Industry, pp. 231-238, 10th Annual Meeting of the Bulgarian Section of SIAM, Sofia, Bulgaria, 21/12/15. https://doi.org/10.1007/978-3-319-49544-6_19

Equivalence of Models of Freeze-Drying. / Veneva, Milena; Lee, William.

Advanced Computing in Industrial Mathematics: Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria. ed. / Krassimir Georgiev; Michail Todorov; Ivan Georgiev. Vol. 681 Springer Verlag, 2017. p. 231-238 (Studies in Computational Intelligence; Vol. 681).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - Freeze-drying is a preservation process, consisting of two main stages: during the primary drying water is removed by sublimation; during the secondary drying chemically bound water is removed by desorption. Two different models of secondary drying are built. The first one consists of coupled heat and mass balances equations, the second one uses a modified Richards equation. Using scale transformations derived from the PDEs and the BCs, the first model is nondimensionalized. The model is further simplified by asymptotic reduction. It is proven that the reduced model is equivalent to the model that uses the modified Richards equation if the partial pressure of air is negligible compared to that of water vapor in the vials and in the chamber of the freeze-drier. This result shows that there is an opportunity for technology transfer, since solvers developed for modelling groundwater flows using Richards equations can also be used to model the economically important problem of freeze-drying.

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Veneva M, Lee W. Equivalence of Models of Freeze-Drying. In Georgiev K, Todorov M, Georgiev I, editors, Advanced Computing in Industrial Mathematics: Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria. Vol. 681. Springer Verlag. 2017. p. 231-238. (Studies in Computational Intelligence). (Journal of Mathematics in Industry). https://doi.org/10.1007/978-3-319-49544-6_19