Analytical solutions for the moving interface problem in freeze-drying with or without back heating

A mathematical model for freeze-drying without back surface heating is established first in this paper by a combination of URIF (uniformly retreating ice front) and Sheng/Peck's theories. Explicit analytical expressions are obtained for the rates of interface movement and drying. The predicted drying rate and temperature profile are in good agreement with the Sheng/Peck's model results. Furthermore, the model is extended to the process of freeze-drying with back heating in which the temperature at the interface is assumed to increase along the path of movement. It is shown that the average rates for drying and interface moving may be obtained by assuming a quadric distribution for the interface temperature.