Modification of the Weibull Distribution for Modeling Atmospheric Freeze-Drying of Food

An empirical physical model was derived from the Weibull distribution and investigated for its ability to describe the moisture content for common atmospheric (or convective) freeze-drying processes (AFD). A set of experiments was performed for different products: peas, apple, pineapple, cod, and zooplankton. The effect of drying temperatures (-6 degrees C, -3 degrees C, 0 degrees C, 10 degrees C and 20 degrees C), approach velocities (1 m sec(-1), 1.8 m sec(-1), 2.6 m sec(-1), 3.1 m sec(-1), and 4.7 m sec(-1)), and particle sizes (8.7 mm, 15.7 mm, and 28.8 mm) was investigated using the selected products. Non-linear regression analyses showed good agreement between the model and experimental data. The coefficient of determination was at least 99.9% (R(2) > 0.999) and the chi-square lower than 0.0001 (chi(2) < 0.0001) for all investigations. The shape parameter beta in the modified Weibull model varied in a narrow range from 0.661 to 0.937, which indicates that AFD is controlled by internal mass transfer (=diffusivity). The diffusivity (D(calc)) ranged from 1.554 to 8.681 10(-9) m(2) sec(-1), depending on the product and drying conditions. The modification of the Weibull distribution can be used to describe AFD processes based on a simple empirical but highly accurate model and for the determination of the effective diffusion (Fick's law).