Heat and Mass Transfer Modeling in Freeze Drying

Calculates the primary drying time of a frozen slab during lyophilization under heat-transfer and mass-transfer limited regimes, identifying the controlling bottleneck.

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1. Define Input Parameters

Slab thickness (Z)[m]

Bulk density of frozen product (rho)[kg/m³]

Initial ice mass fraction (w_i)[dimensionless]

Final ice mass fraction (w_f)[dimensionless]

Latent heat of sublimation (lambda_s)[J/kg]

Effective thermal conductivity of the dry layer (k)[W/(m·K)]

Temperature at the slab surface (T_0)[K]

Temperature at the sublimation front (T_i)[K]

Vapor permeability of the dry layer (Pi)[kg/(m·s·Pa)]

Saturation vapor pressure at sublimation front (p_i)[Pa]

Partial pressure of water vapor at the condenser (p_0)[Pa]

2. Engineering Output

Temperature difference (dT)
- K

Pressure difference (dp)
- Pa

Heat-transfer limited drying time (t_heat)
- s

Mass-transfer limited drying time (t_mass)
- s

Final drying time (t_final)
- s

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Context & Assumptions

The freeze drying (lyophilization) of a slab is a critical unit operation in pharmaceutical and food engineering, used to remove moisture from heat-sensitive products while maintaining structural integrity. This calculation models the primary drying phase, where a sublimation front moves through a frozen material. Understanding the drying time is essential for process scale-up, optimizing cycle times, and ensuring that the product does not exceed its collapse temperature.

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Heat and Mass Transfer Modeling in Freeze Drying

1. Define Input Parameters

2. Engineering Output

Context & Assumptions

Understand the Engineering Principles

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