Mathematical modeling of vacuum freeze-drying for technology transfer from laboratory to industrial scale
https://doi.org/10.20914/2310-1202-2025-3-224-233
Abstract
The paper focuses on mathematical description of vacuum freeze-drying applied to dispersed and biologically active materials used in the production of finished dosage forms and composite polymer systems. The aim of the study was to develop a modeling approach supporting technology transfer of freeze-drying from laboratory to industrial scale while maintaining product uniformity and quality. The proposed method combines a one-dimensional drying kinetics model with computational fluid dynamics for simulation of water vapor distribution inside the lyophilizer chamber. The model describes the first and second drying periods, layer-by-layer movement of the sublimation front, coupled heat and mass transfer in frozen and dried regions, and diffusion-controlled moisture removal during secondary drying. Experimental investigations were carried out on a Labconco pilot freeze-dryer operated at 5–10 Pa with a condenser temperature of 188 K using a model peptide solution. Calculated temperature profiles showed good agreement with experimental data: the difference factor equaled 1.76 and the similarity factor reached 54.77, confirming model adequacy. Computational fluid dynamics simulations demonstrated nonuniform water vapor distribution within the chamber and increasing vapor concentration near the condenser during sublimation. The results indicate that integration of drying kinetics modeling with gas-dynamic simulations enables rational selection of operating regimes, reduction of drying time, and decrease in batch rejection risk. The developed approach is recommended for efficient scale-up and industrial implementation of vacuum freeze-drying technologies.
About the Authors
E. K. Mokhova
D. Mendeleev University of Chemical Technology of Russia
Cand. Sci. (Engin.), chemical and pharmaceutical engineering department, Miusskaya Sq. 9, Moscow, 125047, Russia
M. G. Gordienko
D. Mendeleev University of Chemical Technology of Russia
Dr. Sci. (Engin.), associate professor, chemical and pharmaceutical engineering department, Miusskaya Sq. 9, Moscow, 125047, Russia
N. V. Menshutina
D. Mendeleev University of Chemical Technology of Russia
Dr. Sci. (Engin.), professor, chemical and pharmaceutical engineering department, Miusskaya Sq. 9, Moscow, 125047, Russia
O. V. Karmanova
Voronezh State University of Engineering Technologies
Dr. Sci. (Engin.), professor, technology of organic compounds and polymer processing department, Revolution Av., 19 Voronezh, 394036, Russia
References
1. Maia F.R., Rui L.C., Reis R.L. et al. Natural origin materials for bone tissue engineering. Principles of Regenerative Medicine. 2019. pp. 535–558. doi: 10.1016/b978-0-12-809880-6.00032-1
2. Nie W., Dai X., Copus J.S. et al. Rapid mineralization of graphene-based 3D porous scaffolds by semi-dry electrodeposition for photothermal treatment of tumor-induced bone defects. Acta Biomaterialia. 2022. vol. 153. pp. 573–584. doi: 10.1016/j.actbio.2022.09.019
3. Chopra H., Kumar S., Singh I. Biopolymer-based scaffolds for tissue engineering applications. Current Drug Targets. 2021. vol. 22. no. 3. pp. 282–295. doi: 10.2174/1389450121999201102140408
4. Beltran-Vargas N.E., Del Prado-Audelo M.L., Leyva-Gómez G. et al. Sodium alginate/chitosan scaffolds for cardiac tissue engineering: The influence of its three-dimensional material preparation and the use of gold nanoparticles. Polymers. 2022. vol. 14. no. 16. p. 3233. doi: 10.3390/polym14163233
5. Osman M.A., Elbashir A.A., Elwassif M.M. et al. Development and characterization of functional polylactic acid/chitosan porous scaffolds for bone tissue engineering. Polymers. 2022. vol. 14. no. 23. p. 5079. doi: 10.3390/polym14235079
6. Gordienko M.G., Menshutina N.V., Lesnichaya M.V. et al. The alginate–chitosan composite sponges with biogenic Ag nanoparticles produced by combining of cryostructuration, ionotropic gelation and ion replacement methods. International Journal of Polymeric Materials and Polymeric Biomaterials. 2022. vol. 71. no. 1. pp. 34–44. doi: 10.1080/00914037.2020.1798439
7. Ramli R.H., Soon Fhong C., Rus Mohd A.Z. Synthesis of chitosan/alginate/silver nanoparticles hydrogel scaffold. MATEC Web of Conferences. 2016. vol. 78. p. 01031. doi: 10.1051/matecconf/20167801031
8. Keller T., Wolf M., Pröll T. Enhancing energy efficiency in pharmaceutical freeze drying: Adapting to EU legislation on fluorinated gases. International Journal of Thermofluids. 2025. vol. 21. p. 101304. doi: 10.1016/j.ijft.2025.101304
9. Garcia-Amezquita L.E., Welti-Chanes J., Vergara-Balderas F.T. et al. Freeze-drying: The basic process. Encyclopedia of Food and Health. Ed. by B. Caballero, P.M. Finglas, F. Toldrá. Oxford: Academic Press, 2016. pp. 104–109. doi: 10.1016/b978-0-12-384947-2.00328-7
10. Liao J., Guo Z., Yu G. Process intensification and kinetic studies of ultrasound-assisted extraction of flavonoids from peanut shells. Ultrasonics Sonochemistry. 2021. vol. 76. p. 105661. doi: 10.1016/j.ultsonch.2021.105661
11. Patel B.A., Pereira C.S. Process intensification at scale: an industrial perspective. Chemical Engineering and Processing – Process Intensification. 2022. vol. 181. p. 109098. doi: 10.1016/j.cep.2022.109098
12. Kurkin D.V., Makarov V.G., Chumakova N.V. et al. Methodological and regulatory aspects of pharmaceutical development of biologics. Pharmacy & Pharmacology. 2023. vol. 11. no. 5. pp. 384–398. (in Russian)
13. Gordeev L.S., Meshcheryakova S.A., Akhnazarova S.L. et al. Mathematical modeling of batch chemical engineering systems: methodological guidelines. Moscow: D.I. Mendeleev University of Chemical Technology of Russia, 1999. 68 p. (in Russian)
14. Akhnazarova S.L., Gordeev L.S., Glebov M.B. Modeling and optimization of chemical engineering processes with incomplete information about the mechanism: textbook. Moscow: D.I. Mendeleev University of Chemical Technology of Russia, 2010. 100 p. (in Russian)
15. Mokhova E., Gordienko M., Menshutina N. Mathematical model of freeze drying taking into account uneven heat and mass transfer over the volume of the working chamber. Drying Technology. 2022. vol. 40. no. 12. pp. 2470–2493. doi: 10.1080/07373937.2022.2058958
16. Nuytten G., Revatta S.R., Van Bockstal P.J. et al. Development and application of a mechanistic cooling and freezing model of the spin freezing step within the framework of continuous freeze-drying. Pharmaceutics. 2021. vol. 13. no. 12. p. 2076. doi: 10.3390/pharmaceutics13122076
17. Mokhova E.K., Gordienko M.G. Mathematical model of vacuum sublimation drying with uneven distribution of vapors over the chamber volume. Software & Systems. 2021. vol. 34. no. 3. pp. 10–22. (in Russian)
18. Tchessalov S., Dassu D., Latshaw II G. et al. Best practices and guidelines (2022) for scale-up and tech transfer in freeze-drying based on case studies. Part 1: challenges during scale up and transfer. AAPS PharmSciTech. 2022. vol. 24. no. 1. p. 11. doi: 10.1208/s12249-022-02463-x
19. Navrátil O., Kolář J., Zadražil A. et al. Model-based evaluation of drying kinetics and solvent diffusion in pharmaceutical thin film coatings. Pharmaceutical Research. 2022. vol. 39. no. 9. pp. 2017–2031. doi: 10.1007/s11095-022-03352-5
20. Kerkhoff J., Thomas A., Štěpánek F. et al. Drying kinetics of polymer-based pharmaceutical formulations. Fluid Phase Equilibria. 2025. vol. 594. p. 114390. doi: 10.1016/j.fluid.2025.114390
21. Uhlemann J., Diedam H., Hoheisel W. et al. Modeling and simulation of process technology for nanoparticulate drug formulations—a particle technology perspective. Pharmaceutics. 2020. vol. 13. no. 1. p. 22. doi: 10.3390/pharmaceutics13010022
Review
For citations:
Mokhova E.K., Gordienko M.G., Menshutina N.V., Karmanova O.V. Mathematical modeling of vacuum freeze-drying for technology transfer from laboratory to industrial scale. Proceedings of the Voronezh State University of Engineering Technologies. 2025;87(3):224-233. (In Russ.) https://doi.org/10.20914/2310-1202-2025-3-224-233
Views:
170
JATS XML
Email this article 
Post a Comment 
