Equivalence of Models of Freeze-Drying

Milena Veneva; William Lee

doi:10.1007/978-3-319-49544-6_19

Equivalence of Models of Freeze-Drying

Milena Veneva, William Lee

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Advanced Computing in Industrial Mathematics
Subtitle of host publication	Revised Selected Papers of the 10th Annual Meeting of the Bulgarian Section of SIAM December 21-22, 2015, Sofia, Bulgaria
Editors	Krassimir Georgiev, Michail Todorov, Ivan Georgiev
Publisher	Springer International Publishing AG
Pages	231-238
Number of pages	8
Volume	681
ISBN (Electronic)	9783319495446, 9783319841854
ISBN (Print)	9783319495439
DOIs	https://doi.org/10.1007/978-3-319-49544-6_19
Publication status	Published - 13 Feb 2017
Externally published	Yes
Event	10th Annual Meeting of the Bulgarian Section of SIAM - Sofia, Bulgaria Duration: 21 Dec 2015 → 22 Dec 2015 Conference number: 10 http://www.math.bas.bg/IMIdocs/BGSIAM/bgsiam15_announcement.htm (Link to Conference Website)

Publication series

Name	Studies in Computational Intelligence
Publisher	Springer
Volume	681
ISSN (Print)	1860-949X
ISSN (Electronic)	1860-9503

Conference

Conference	10th Annual Meeting of the Bulgarian Section of SIAM
Abbreviated title	BGSIAM 2015
Country/Territory	Bulgaria
City	Sofia
Period	21/12/15 → 22/12/15
Internet address	http://www.math.bas.bg/IMIdocs/BGSIAM/bgsiam15_announcement.htm (Link to Conference Website)

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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Milena_Veneva_and_William_LeeAccepted author manuscript, 91.9 KBLicence: Unspecified

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 International Publishing AG. 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 International Publishing AG, 2017. pp. 231-238 (Studies in Computational Intelligence).

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title = "Equivalence of Models of Freeze-Drying",

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.",

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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 International Publishing AG, 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 International Publishing AG, 2017. p. 231-238 (Studies in Computational Intelligence; Vol. 681).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Equivalence of Models of Freeze-Drying

AU - Veneva, Milena

AU - Lee, William

N1 - Conference code: 10

PY - 2017/2/13

Y1 - 2017/2/13

N2 - 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.

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.

KW - Water Vapor

KW - Hydraulic Conductivity

KW - Specific Heat Capacity

KW - Water Vapor Pressure

KW - Vapor Flow

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ER -

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 International Publishing AG. 2017. p. 231-238. (Studies in Computational Intelligence). Epub 2017 Feb 7. doi: 10.1007/978-3-319-49544-6_19

Equivalence of Models of Freeze-Drying

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