The mass transfer device shown in the figure at the top of the next column is used to carry out the controlled release of a vapor-phase pheromone drug used in pest control. The solid drug sublimes at a vapor pressure P*_Awithin the gas space of the reservoir. A polymer layer of thickness L = 0.15 cm covers the drug reservoir. The drug vapor (species A) absorbs into a polymer diffusion layer by a linear relationship p_A= S · C'_A, where C'_Ais the concentration of the pheromone drug dissolved in the polymer (gmole species A/cm³polymer), p_Ais the partial pressure of the drug vapor (atm). and S is the partitioning constant for the drug between the vapor phase and the polymer phase (cm³-atm/mol). The pheromone is highly soluble in the polymer. The drug then diffuses through the polymer layer with diffusion coefficient D_Ae, and then exits to the surroundings as a vapor. Air flow over the top surface of the polymer layer generates a €œfluid boundary layer.€™ The flux of the drug vapor across this boundary layer is given by 

N_A = k_G(p_As €“ P_Aˆž) 

where k_G is the gas-phase mass-transfer coefficient (gmole/ · s · atm). Generally, k_G increases as the air flow rate over the surface increases. At steady state, the flux of drug (species A) through the polymer layer equals the flux through the boundary layer. 

a. Develop a mathematical model, in final integrated form, for the drug vapor flux N_A. The final model can only contain the following terms: N_A, D_Ae, P_A*, P_Aˆž, L, S, k_G. State all assumptions for analysis. 

b. Determine the maximum possible drug vapor flux associated with the mass-transfer device, in units of pmole/cm²· s (1 µmole = 1.0 × 10^-6 mole), under conditions where P_Aˆž ‰ˆ 0, 30°C, and 1.0 atm total system pressure. The diffusion coefficient of drug vapor through polymer, D_Ae, is 1.0 × l0^-6 cm²/s. The Henry€™s law constant for absorption (dissolution) of drug vapor into polymer, S, is 0.80 cm³€™atm/gmole. The €œmass-transfer coefficient€ for boundary layer. k_G, is 1.0 × 10^-5 mol/cm² · s · atm. The vapor pressure of pheromone drug at 30°C is 1.1 atm.

Transcribed Image Text:

Bulk air PAo Air Boundary layer flow -z = L, PA = PAS L = 1.5 mm Polymer layer, C'A -z = 0 100% drug vapor PA"= 1.1 atm Drug reservoir (drug crystals + vapor) - 2.0 cm/side