Spherical polymer beads of 3.0 mm (0.3 cm) diameter contain residual solvent from the polymer-casting process. Initially, the bead contains 0.20 wt% of residual solvent uniformly distributed within the polymer. The residual solvent will be removed from the bead material by drying the beads in a fluidized bed of air. This sink for mass transfer will cause the solvent molecules inside the bead to transfer to the surface of the bead. The air flow through the fluidized bed is very high so that convective mass-transfer resistances are not present and the effective concentration of emitted solvent vapor into the bulk flowing air is equal to zero. At the process conditions of the fluidized bed, the effective diffusion coefficient of residual solvent molecules in the polymer material is 4.0 × 10-7 cm2/s.
a. How long will it take (in hours) for the solvent in the center of the bead to reach 0.002 wt%?
b. How long will it take (in s) for the solvent to reach 0.18 wt % composition at a depth of 0.1 mm from the surface of the bead?