Numerical analysis of atmospheric freeze-drying based on lamellar mannitol

Atmospheric freeze drying (AFD) has removed the vacuum-creating equipment to reduce energy consumption while maintaining the product quality, compared with traditional vacuum freeze drying. However, the increasing pressure can lead to a significant increase in the drying time. Water vapor diffusion can then be obstructed to limit the practical implementation. Therefore, it is essential to understand the controlling variables in the heat and mass transfer of the AFD process. The purpose of this study was to quantitatively investigate the effects of drying conditions on the drying time, drying rate, and heat/mass transfer resistances. Among them, the thermal/mass transfer resistances were analyzed to explore the drying mechanism during atmospheric freeze drying. The mathematical model of the lamellar product during AFD was proposed to consider the external flow. The Navier–Stokes equations were introduced for the external pressure field into the adsorption-sublimation model. The model was solved and validated using COMSOL Multiphysics 6.1. The accuracy was verified by the ±10% relative deviation of drying time between the model and experimental data. Drying kinetics were calculated under different conditions (product thickness 3-11 mm, equivalent pore diameter 2.0-6.0 μm, dry air temperature 263.15-273.15 K, dry air velocity 1.0-3.0 m/s). The results showed that the drying rate and time decreased with the decrease in product thickness and the increase in air temperature. But there was no outstanding influence of equivalent pore diameter and air velocity on the drying rate and time. Unlike the three stages of standard drying, only the initial accelerating and falling rate stages were observed in the AFD procedure. The absence of the constant rate stage was attributed to the assumption of material homogeneity and low moisture of the top surface. At the same time, the post-processing was carried out to calculate the external heat and mass transfer resistances between the external flow and the product, together with the internal heat and mass transfer resistances between the top surface of the product and the sublimation interface. The external heat/mass transfer resistances decreased, while the internal heat/mass transfer resistances increased linearly from zero, with the decreasing moisture content. The internal heat/mass transfer resistances exceeded the external heat/mass transfer resistances at a critical moisture content, indicating the transition from external heat/mass transfer control to internal heat/mass transfer control during AFD. There was some effect of condition parameters on the transfer resistances. The equivalent pore diameter shared no significant effect on either internal or external resistances. While the temperature increased to bring about a slight decrease in the internal heat-transfer resistance. By contrast, there was a decrease in the external and internal heat transfer resistance, due to the increasing air velocity. Especially, the reduction of product thickness was a significant contribution to the decrease of both internal and external transfer resistance. Therefore, small thickness product was more suitable for the AFD process, according to the drying kinetics and heat/mass transfer. It was expected to simultaneously realize both the reduction in the drying time and energy consumption. The findings can provide guidance to optimize the process parameters during atmospheric freeze-drying.