Part $2$ specifically!!! $(10$ points$)$ Experiments are being conducted to determine the suitability of a cellophane membrane

$0\mathrm{.}029mm$ thick for use in an artificial$-$kidney device. In an experiment at $37C$ using urea as the

diffusing solute, the membrane separates two components containing stirred aqueous solutions of urea,

where $c_1=100$gmo$\frac{l}{m^3}$ and $c_2=0\mathrm{.}5$gmo$\frac{l}{m^3}.$ The mass$-$transfer coefficients on either side of the

membrane have been estimated as $k_{C1}=k_{C2}=5\mathrm{.}24{10}^{-5}\frac{m}{s}.$ Experimental data obtained gave a flux

$N_A=4\mathrm{.}19{10}^{-4}$gmol urea $\frac{?}{m^2.s}$ at pseudo$-$steady$-$state conditions.

a$.$ Calculate the permeance $\frac{?}{\text{b}\text{a}\text{r}}(P{)}_M$ and permeability of the membrane.

b$.$ Calculate the percent resistance to diffusion in the liquid films.

$(30$ points$)$ A prototype of a dialyzer is built using $2m^2$ of the membrane in Problem $1$ to test how long

it will take to reduce the urea concentration of the blood in the reservoir to a desired level $($see schematic

in Figure $1).$ Due to the flow conditions in the dialyzer, the mass transfer coefficients in the blood$-$side

and the dialysate$-$side are $5\mathrm{.}5{10}^{-5}\frac{m}{s}$ and $1\mathrm{.}1{10}^{-5}\frac{m}{s},$ respectively. You may assume that the

blood inside the dialyzer is well mixed and the concentration of urea inside the dialyzer, $c_1(t)$ is uniform

everywhere and is the same as the urea concentration in the exiting blood stream. Furthermore, the

dialysate does not contain any urea and its concentration remains close to zero during the process. The

flow rate, $F$ during the hemodialysis process is assumed to remain constant at $0\mathrm{.}5\frac{L}{m}in.$ If the total

volume of blood in the reservoir is $6L$ and urea is added to the reservoir $($to simulate generation in the

body$)$ at $G_o=0\mathrm{.}1$mmo$\frac{l}{?}$ day, determine the time it will take for the urea concentration of the blood in

the reservoir to go from ${10}^{-2}$gmo$\frac{l}{L}$ to $3{10}^{-3}$gmo$\frac{l}{L}.$ You may assume that the addition of urea

to the reservoir does not change the volume of fluid in the reservoir.