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Comparison of quasi-steady-state and unsteady-state formulations in a freeze dryer modeling

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Abstract

An unsteady-state model is developed for primary and secondary stages of freeze drying process of skim milk. The results are compared with those obtained from a quasi-steady-state (QSS) formulation. The QSS formulation is not valid where the applied heat load is high. The applied heat load affects on the drying time the most compared to other parameters like chamber pressure and the radiation surface temperature.

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Abbreviations

C p :

Heat capacities

C :

Concentration (kg/m3)

c :

Weight fraction of internal water

h :

Sample thickness (m)

H :

Position of interface (m)

k 2, k 4 :

Self diffusivity constant (m2/s)

k 1, k 3 :

Bulk diffusivity constant (m2/s)

k :

Thermal conductivity (kW/m K)

f (T z ):

Water vapor pressure–temperature functional form (N/m2)

ΔH sub :

Heat of sublimation of ice (kJ/kg)

ρ :

Density (kg/m3)

K g :

Internal mass transfer coefficient (s)

M :

Molecular weight

m s :

Weight of dry solid

N :

Mass flux (kg/m2 s)

N t :

Total flux (Nt = Nw + Nin)

P :

Partial pressure (N/m2)

P° :

Partial pressure of water vapor at z = 0 (N/m2)

q :

Heat flux at the bottom of the vial (kW/m2)

R :

Universal gas constant

S :

Vial surface area (m2)

t :

Time (s)

T :

Temperature (K)

V :

Velocity of interface (m/s)

V tot :

Volume of the sample

X :

Weight fraction of total moisture (dry basis)

z :

Sample length coordinate

α :

Thermal diffusivity

ε :

Porosity

σ :

Stefan-Boltzmann constant

ρ :

Density (kg/m3)

e :

Effective value

eq :

Equilibrium value

f :

Frozen layer

d :

Dried layer

in :

Inert gas

up :

Irradiation surface

w :

Water vapor

wh :

Interface

o :

Initial value at time zero

t :

Value at time t

QSS:

Quasi-steady-state

USS:

Unsteady-state

References

  1. Liapis AI, Pim ML, Bruttini R (1996) Research and development needs and opportunities in freeze drying. Dry Technol 14:1265–1300. doi:10.1080/07373939608917146

    Article  Google Scholar 

  2. Ratti C (2001) Hot air and freeze-drying of high-value foods: a review. J Food Eng 49:311–319. doi:10.1016/S0260-8774(00)00228-4

    Article  Google Scholar 

  3. Dolan JP (1998) Use of volumetric heating to improve heat transfer during Vial Freeze-Drying Virginia Polytechnic Institute and State University

  4. Chakraborty R, Saha AK, Bhattacharya P (2006) Modeling and simulation of parametric sensitivity in primary freeze-drying of foodstuffs. Sep Purif Technol 49:258–263. doi:10.1016/j.seppur.2005.10.008

    Article  Google Scholar 

  5. Sandall OC, King CJ, Wilke CR (1967) The relationship between transport properties and rates of freeze-drying of poultry meat. AIChE J 13:428–438. doi:10.1002/aic.690130309

    Article  Google Scholar 

  6. Sheng TYR, Peck RE (1977) Rates for freeze-drying. Water Removal Process American Institute of Chemical Engineers, New York

    Google Scholar 

  7. Hill JE, Sunderland JE (1971) Sublimation-dehydration in the continuum, transition and free-molecule flow regimes. Int J Heat Mass Transf 14:625–638. doi:10.1016/0017-9310(71)90011-1

    Article  Google Scholar 

  8. Liapis AI, Litchfield RJ (1979) Optimal control of a freeze dryer-I theoretical development and quasi steady state analysis. Chem Eng Sci 34:975–981. doi:10.1016/0009-2509(79)85009-5

    Article  Google Scholar 

  9. Litchfield RJ, Liapis AI (1982) Optimal control of a freeze dryer-II: dynamic analysis. Chem Eng Sci 37:45–55. doi:10.1016/0009-2509(82)80066-3

    Article  Google Scholar 

  10. George JP, Datta AK (2002) Development and validation of heat and mass transfer models for freeze-drying of vegetable slices. J Food Eng 52:89–93. doi:10.1016/S0260-8774(01)00091-7

    Article  Google Scholar 

  11. Hottot A, Peczalski R, Vessot S, Andrieu J (2006) Freeze-drying of pharmaceutical proteins in vials: modeling of freezing and sublimation steps. Dry Technol 24:561–570. doi:10.1080/07373930600626388

    Article  Google Scholar 

  12. Zhai S, Su H, Taylor R, Slater NKH (2005) Pure ice sublimation within vials in a laboratory lyophiliser; comparison of theory with experiment. Chem Eng Sci 60:1167–1176. doi:10.1016/j.ces.2004.09.078

    Article  Google Scholar 

  13. Velardi SA, Barresi AA (2008) Development of simplified models for the freeze-drying process and investigation of the optimal operating conditions. Chem Eng Res Des 86:9–22. doi:10.1016/j.cherd.2007.10.007

    Article  Google Scholar 

  14. Evans RB, Waston GM, Mason EA (1962) Gaseous diffusion in porous media. II. Effect of pressure gradients. J Chem Phys 36:1894–1902

    Google Scholar 

  15. Song CS, Nam JH, Kim CJ, Ro ST (2005) Temperature distribution in a vial during freeze-drying of skim milk. J Food Eng 67:467–475. doi:10.1016/j.jfoodeng.2004.04.041

    Article  Google Scholar 

  16. Murray WD, Landis F (1959) Numerical and machine solutions of transient heat conduction problems involving phase change. J Heat Transf 81:106–112

    Google Scholar 

  17. Millman MJ, Liapis AI, Marchello JM (1985) An analysis of the lyophilization process using a sorption-sublimation model and various operational policies. AIChE J 31:1594–1604. doi:10.1002/aic.690311003

    Article  Google Scholar 

  18. Liapis AI, 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. Sep Technol 4:144–155. doi:10.1016/0956-9618(94)80017-0

    Article  Google Scholar 

  19. Tsinontides SC, Rajniak P, Pham D, Hunke WA, Placek J, Reynolds SD (2004) Freeze drying-principles and practice for successful scale-up to manufacturing. Int J Pharm 280:1–16. doi:10.1016/j.ijpharm.2004.04.018

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Isfahan, P.O. Box 81746–73441, Esfahān, Iran

    Shekoufe Adhami, Amir Rahimi & Mohammad S. Hatamipour

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  1. Shekoufe Adhami
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  2. Amir Rahimi
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  3. Mohammad S. Hatamipour
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Correspondence to Amir Rahimi.

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Adhami, S., Rahimi, A. & Hatamipour, M.S. Comparison of quasi-steady-state and unsteady-state formulations in a freeze dryer modeling. Heat Mass Transfer 50, 1291–1300 (2014). https://doi.org/10.1007/s00231-014-1337-x

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  • DOI: https://doi.org/10.1007/s00231-014-1337-x

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