A mathematical model of multi-dimensional freeze-drying for food products

摘要

A simple mathematical model was developed to predict the kinetics of freeze-drying where sublimation progresses multi-dimensionally in a product, and the model was adopted to the freeze-drying of peeled apple cubes. This model consists of classical heat and mass transfer equations, which are solved by assuming a quasi-steady-state energy balance at the sublimation interface. The radiative heat coefficient and mass transfer coefficient between the chamber and the condenser are included in the model, and were experimentally obtained by carrying out the ice sublimation tests with the freeze-dryer employed. The mass transfer property is a specification of a given freeze-dryer. This work suggested that it strongly influenced the drying kinetics and it would be an important parameter to meet scaling-up issue. When the sublimation progresses multi-dimensionally, the surface areas of the product exterior, the product bottom and the sublimation interface varied as a function of the extent of drying. These relationships were obtained from experiments with freeze-drying of peeled apple cubes and employed for estimating the mean thickness of the dried and frozen layers with a hollow spherical model proposed in the study. The model equations were solved using commercial spreadsheet software, and the weight loss during drying was predicted as a function of time. The calculation results were in good agreement with the experimental data. This approach allows to set a heating program and/or localized variances of microstructural parameters by manual input, and easily simulate drying kinetics and temperature history. This makes big advantage for planning a desired drying operation. (C) 2015 Elsevier Ltd. All rights reserved.