A thin polymer film contains some residual liquid solvent. It is desired to evaporate the solvent (n-hexane, solute A) from the polymer using the process shown below. Both sides of the polymer film are exposed to the cross flow of air.
The evaporation rate of the solvent from the polymer film is limited by external convection. The dried polymer film is then rolled up into a bundle. During the drying process, the width of the thin polymer film is 0.5 m and the length of the polymer film is 2.5 m. The flowing air has a bulk velocity of 1.5 m/s, a temperature of 20°C, and the total system pressure of 1.0 atm. The wet polymer film is also maintained at 20°C. The vapor pressure of the solvent at 20°C is 0.16 atm, the diffusion coefficient of the solvent in air is 0.080 cm2 /s at 20°C and 1.0 atm, and the molecular weight of the solvent is 86 g/g mol. The partial pressure of the solvent in the bulk air flow can be assumed to be near zero. The kinematic viscosity of air is 1:5×10-5 m2/s at 20°C.
(a) Evaluate the Sc number and the average Sh number for the solvent evaporation process.
(b) What is the total evaportion rate of the solvent from the 0.5 m by 2.5 m polymer film, recognizing that both sides of the film are exposed to the following air?
(c) The solvent loading in the polymer film at the entrance of the drying process is 0.1 g solvent per gram of dry polymer (XAo = 0.1 g solvent/g dry polymer). The total mass flow rate of the polymer film on a solvent-free dry polymer basis is mo = 50:0 g dry polymer/s. What is the solvent loading in the polymer film exiting the drying process (XAf in g solvent/g dry polymer)?