Modeling and measurements of water-vapor flow and icing at low pressures with application to pharmaceutical freeze-drying

A modeling and computational framework for analysis of rarefied water vapor flow and icing in application to pharmaceutical freeze-drying is developed. The direct simulation Monte Carlo (DSMC) technique is applied to model the relevant gaseous transport processes in a low-pressure environment encountered in freeze-drying. The developing ice front on a supercooled surface is simulated based on the water vapor mass flux computed from DSMC. Verification of icing simulations has been done by comparison with the analytical solution for a free-molecular flow over a circular cylinder. To validate the vapor flow and icing simulations, measurements of ice accretion in a laboratory-scale freeze-dryer are conducted with the use of time-lapse photography. The simulations corresponding to the measured time-average water sublimation rate agree well with the observed patterns and rates of ice accretion. The developed computational framework has been applied to investigate factors underlying the observed non-uniformity of ice growth. It has been shown that two key factors impact the uniformity of ice accretion: (i) the direction of the vapor flow at the inlet to the condenser which is governed by the geometry of a duct connecting the product chamber to the condenser; and (ii) the pressure of non-condensable gases in the condenser reservoir. The DSMC simulations demonstrate that by tailoring the condensing surfaces topology to the flowfield structure of the water vapor jet expanding into a low-pressure reservoir, it is possible to significantly increase the total rate of vapor removal and improve the overall efficiency of the freeze-drying process.