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Investigation of heat and mass transfer behavior of mannitol during vial freeze-drying

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The vial design feature, such as the base curvature, acts as the primary heat transfer barrier in the lyophilization process. In this study, heat and mass transport characteristics of mannitol (5%) during vial freeze-drying are numerically investigated by including the vial base curvature effects. The influence of the product fill height, chamber pressure, and the vial base curvature on the product temperature, drying time, and mass transfer resistance is analyzed in detail. The diameter of the vial is taken as 15 mm, while the fill height of the product is varied from 3 to 5 mm. The chamber pressure is maintained between 5 and 50 Pa. The results revealed that the product with a 3 mm fill height experienced a 2.5 °C lower temperature than the product with a 5 mm fill height. As opposed to the flat vial predictions, if the vial base curvature effects are considered, the drying time is increased by 1.96 and 3.8 h for the 3 mm and 5 mm fill heights, respectively. The increased drying time is attributed to the reduced direct contact area between the vial and shelf and the vapor entrainment in the gap. The results showed that the dry layer mass transfer resistance contributes to 95% of the total mass transfer resistance; however, the contribution of semi-stoppered vial resistance is 1–2% only.

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A c :

Contact area between vial and shelf (m2)

C p :

Heat capacity (J kg1 K1)

C 1 :

Direct contact heat transfer model coefficient (W m4 K1)

C 2 :

Gas heat transfer model coefficient (W m2 K1 Pa1)

F :

Visualization factor

h :

Heat transfer coefficient (W m2 K1)


Sublimation interface position

k :

Thermal conductivity (W m1 K1)

k c :

Direct conduction heat transfer coefficient (W m2 K1)

k g :

Gas conduction heat transfer coefficient (W m2 K1)

k r :

Radiative heat transfer coefficient (W m2 K1)

k v :

Total heat transfer coefficient (W m2 K1)

l :

Effective curvature depth (mm)

L :

Product height (mm)

m :

Sublimation rate (kg s1)

N :

Mass flux (kg m2 s1)

p c :

Chamber pressure (Pa)

p eq :

Equilibrium vapor pressure of ice (Pa)

p v :

Total pressure in the vial (Pa)

q :

Heat flux (W m2)

R d :

Dry layer resistance (kPa s m2 kg1)

R s :

Semi-stoppered vial resistance (kPa s m2 kg1)

T :

Temperature (K)

t :

Time (s)

v n :

Normal velocity of sublimation interface (m s1)

z :

Spatial coordinate

ΔH s :

Sublimation enthalpy of ice (J kg1)

ρ :

Density (kg m3)

σ :

Stefan Boltzmann constant (W m2 K4)

α c :

Accommodation coefficient

λ amb :

Heat conductivity of water vapor at ambient pressure (W m1 K1)

Λ 0 :

Free molecular heat conductivity of water vapor at 0 °C (W Pa1 K1 m2)


Sublimation interface/front



tp :

Top heating plate


Dry layer


Frozen layer


Water vapor


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The authors would like to thank the Department of Science and Technology (DST-SERC), India (Ref no: SR/S3/MMER/0005/2014) and Ministry of Science and Technology, Taiwan (Contract Nos: 108-2622-E-009-004-CC2 and 108-2622-E-009-027-CC2) for their financial aid to carry out the work.

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Correspondence to Chi-Chuan Wang.

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Muneeshwaran, M., Srinivasan, G., Raja, B. et al. Investigation of heat and mass transfer behavior of mannitol during vial freeze-drying. J Therm Anal Calorim 147, 2393–2404 (2022).

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