$26\mathrm{.}14$ The mass$-$transfer device shown in the figure below is

used to carry out the controlled release of a vapor$-$phase phero$-$

mone drug used in pest control. The solid drug sublimes at a vapor

pressure $P_A^{**}$ within the gas space of the reservoir. A polymer layer

of thickness $L=0\mathrm{.}15cm$ covers the drug reservoir. The drug

vapor $($species $A)$ absorbs into a polymer diffusion layer by a

linear relationship $p_A=S*C_A^{\text{'}},$ where $C_A^{\text{'}}$ is the concentration of

the pheromone drug dissolved in the polymer $($gmole species $A/$

$c{m}^3$ polymer$),p_A$ is 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 $(c{m}^3-at\frac{m}{m}ol).$ 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 "fluid boundary layer." The flux of the

drug vapor across this boundary layer is given by

$N_A=k_G(p_{As}-p_A)$

where $k_G$ is the gas$-$phase mass$-$transfer coefficient $($gmole$/$

$c{m}^2*s*atm).$ 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: $N_A,D_{Ae},P_A^{**},p_A,L,S,k_G.$ State all

assumptions for analysis.

b$.$ Determine the maximum possible drug vapor flux associ$-$

ated with the mass$-$transfer device, in units of $mol\frac{e}{c}{m}^2*s$

mole $=1\mathrm{.}0{10}^{-6}$ mole