A Fixed Grid Finite Volume Analysis of Multi-Dimensional Freeze Drying Process under Vacuum Condition

고정격자계에서 유한체적법을 이용한 진공동결건조 과정의 열 및 물질전달에 대한 연구

  • Published : 2004.09.01


Freeze drying under vacuum condition is a complex process that involves simultaneous heat and mass transfer, sublimation of ice, and motion of sublimation front. Proper treatment of the motion of sublimation interface is crucial for an accurate prediction of the freeze drying process. Based on the enthalpy formulation that has been successfully used in liquid/solid phase change problems. a fixed grid method. streamlined for the freeze drying analysis. was developed in this study. The accuracy of the fixed grid method was checked by solving a one-dimensional tray freeze drying and a two-dimensional vial freeze drying problem and then comparing the results with those by the moving grid method. Finally. the freeze drying characteristics of two-dimensional slab and axis-symmetric cylinder was investigated using the fixed grid method.



  1. Millman, M.J., Liapis, A.I. and Marchello, J.M., 1985, An Analysis of the Lyophilization Process using a Sorption-Sublimation Model and Various Operation Policies, AIChE Journal 31, 1594-1604
  2. Liapis, A.I.. 1987. Freeze Drying. pp. 295-326. in A.S. Mujumdar (Ed.) Handbook of Industrial Drying. Marcel Dekker. Inc., New York
  3. Ratti. C., 2001. Hot Air and Freeze-Drying of High-Value Foods: a Review, Journal of Food Engineering 49. 311-319
  4. Lin. S., 1981. An Exact Solution of the Sublimation Problem in a Porous Medium. Journal of Heat Transfer 103. 165-168
  5. Fey. Y.C. and Boles. M.A., 1988, Analytic Study of Vacuum Sublimation in an initially partially filled Frozen Porous Medium with Recondensation. International Journal of Heat and Mass Transfer 31, 1645-1653
  6. Peng, S.-W. and Chen. G.-Q., 1994. Coupled Heat and Mass Transfer with One Discrete Sublimation Moving Interface and One Desorption Mushy Zone. Journal of Heat Transfer 116. 215-220
  7. Liapis. A.I. and Litchfield. R.J., 1979. Optimal Control of a Freeze Dryer. Chemical Engineering Science 34, 975-981 https://doi.org/10.1016/0009-2509(79)85009-5
  8. Liapis. A.I. and Bruttini. R., 1994. A Theory for the Primary and Secondary Drying Stages of the Freeze-Drying of Pharmaceutical Crystalline and Amorphous Solutes: Comparison between Experimental Data and Theory. Separations Technology 4. 144-155
  9. Sadikoglu, H. and Liapis. A.I., 1997. Mathematical Modeling of the Primary and Secondary Drying Stages of Bulk Solution Freeze Drying in Trays: Parameter Estimation and Model Discrimination by Comparison of Theoretical Results with Experimental Data. Drying Technology 15. 791-810
  10. Sheehan. P. and Liapis, A.I., 1998. Modeling of the Primary and Secondary Drying Stages of the Freeze Drying of Pharmaceutical Products in Vials: Numerical Results obtained from the Solution of a Dynamic and Spatially MultiDimensional Lyophilization Model for Different Operation Policies. Biotechnology and Bioengineering 60. 712-728
  11. Ang, T.K.. Ford. J.D. and Pei. D.C.T.. 1977. Microwave FreezeDrying of Food: A Theoretical Investigation. International Journal of Heat and Mass Transfer 20. 517-526
  12. Lombrana. J.I.. Elvira. C.D. and Villaran. M.C., 1997. Analysis of Operation Strategies in the Production of Special Foods in Vials by Freeze Drying. International Journal of Food and Technology 32. 107-115
  13. Wang. Z.H. and Shi. M.H., 1998. Numerical Study on SublimationCondensation Phenomena during Microwave Freeze Drying. Chemical Engineering Science 53. 3189-3197
  14. Wang. Z.H. and Shi. M.H., 1998. The Effect of Sublimation-Condensation Region on Heat and Mass Transfer during Microwave Freeze Drying. Journal of Heat Transfer 120
  15. Ferguson. W.J. and Lewis. R.W., 1993. A Finite Element Analysis of Freeze-Drying of a Coffee Sample. Computer Methods in Applied Mechanics and Engineering 108. 341-352
  16. Mascarenhas. W.J., Akay. H.U. and Pikal. M.J., 1998. A Computational Model for Finite Element Analysis of the Freeze-Drying Process. Computer Methods in Applied Mechanics and Engineering 148. 105-124
  17. Evans. R.B., Watson. G.M. and Mason. E.A., 1962. Gaseous Diffusion in Porous Media. Journal of Chemical Physics 36. 1894-1902
  18. Song. C.S., Nam, J.H.. Kim. C.-J. and Eo. S.T.. 2002. A Finite Volume Analysis of Vacuum Freeze Drying Processes of Skim Milk Solution in Trays and Vials. Drying Technology 20. 283-305