Calculating Water Diffusion Rates in Hygroscopic Polymers during Desiccant Drying
Calculate water diffusion in hygroscopic polymers using Crank's spherical solution with Arrhenius-derived diffusivity to establish minimum hopper drying times.
Mass Transfer Biot Number
Meaning
Dimensionless ratios of convective mass transfer at the boundary of a solid to the internal diffusive mass transfer of a solute within the solid govern the drying rate of polymer pellets. This dimensionless parameter is the mass transfer Biot number, which determines whether the speed of pellet drying is limited by moisture migration inside the pellet or by evaporation from the pellet surface. It ceases to be useful if the resin degrades or melts during the drying process.
Drying Kinetics
External resistance dominates the transport process when the ratio is low, meaning moisture evaporates slower than it migrates to the surface. For a high mass transfer Biot number, the internal diffusion of water molecules through the solid polymer is the rate-limiting step. This scenario requires longer heating times rather than higher airflow rates.
Process Control
Resin dryers adjust temperature and air velocity based on the transport limitations of the specific polymer grade. Incorporating the mass transfer Biot number into dryer programming allows processors to optimize energy usage for both virgin and regrind resins. This prevents the moisture-induced hydrolysis that causes brittle parts during injection molding.
Pellet Dimension
Large pellets exhibit high internal diffusion resistance. The mass transfer Biot number increases with pellet size. This requires longer dryer run times.