A thin polymer film contains some residual solvent. It is desired to evaporate the volatile solvent (n-hexane, solute A) from the polymer using the process shown in the figure below. The wet polymer film enters the drying process. Both the top and bottom surfaces of the polymer film are exposed to a cross flow of air. The evaporation rate of the solvent from the polymer film is limited by external convection mass transfer. The dried polymer film is then rolled up into a bundle. During the drying process, the width of the thin polymer film is 0.50 m, and the length of the polymer film is 2.5 m. The flowing air has a bulk velocity of 1.5 m/s, temperature of 20°C, and total system pressure of 1.0 atm. The wet polymer film is also at maintained at 20°C, and the evaporation process is assumed to be limited by convection mass transfer. The vapor pressure of the solvent at 20°C is 121 mm Hg. 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/gmole. The partial pressure of the solvent vapor itself within the drying chamber can be assumed to be close to zero with P_A>> p_Aˆž.

a. What are the Schmidt number and the average Sherwood number for the solvent evaporation process? 

b. What is the total evaporation rate of the solvent from the 0.50-m by 2.50-m polymer film, in units of gmole A/s? Remember: Both sides of the polymer film are exposed to flowing air. 

c. The solvent loading in the polymer film at the entrance of the drying process is 0.10 g solvent per g dry polymer €“i.e., X_A0 = 0.10 g solvent/g dry polymer. The total mass flow rate of the polymer film on a solvent-free dry polymer basis is ṁ_s = 50.0 g dry polymer solid/s. What is the solvent loading in the polymer film exiting the drying process, X_Af ? Perform a material balance on the solvent in the film as the polymer film moves through the drying process.

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air cross flow (1.0 atm, 20°C) Voo = 1.5 m/s NA wet polymer film entrance 0.5 m т, exit drying drying process 2.5 m process Х до Ao Xaf