In order to study the drug release from a new manufacture cylindrical drug capsule, the drug capsule l$)$ tested in a $S^{-}$ A small reservoir of water $($component B$)$ was kept a $37C$ and the capsule was inserted into the reservoir. The drug capsule has a diameter of $0\mathrm{.}65mm$ and height of $6\mathrm{.}9mm.$ Pure solid drug $A$ is loaded into the drug capsule to a depth of $4\mathrm{.}3mm.$ The drug $($component $A)$ dissolves into the water $($component $B)$ inside the reservoir.

You may assume that the diffusion process is a $\sqrt[\phantom{2}]{p}$ seudo$-$steady state. dilute system, and one$-$dimensional in the $2-$direction. The water reservoir aets as apintinite sing for the drug so that $C_{A2}=0,$ and the drug does not chemically react inside the water.

The density of the Drug $($A$)$ i $50\mathrm{.}9g_{cm}3$ the molecular weight of the drug is $150\frac{g}{m}ol,$ The maximum solubility of drug $A$ in water is $C_{AS}=2\mathrm{.}7{10}^{-3}mo\frac{l}{c}{m}^3,$ Diffusion coefficient, $D_{AB}$ of the drug $($s $4\mathrm{.}510)c\frac{m^2}{s}$

Simplify the differential equation of mass transfer?

Simplify the flux equation of mass transfer?

State the assumption you have used in part $1$&$2?$

Develop a simple model, in final integrated form to predict the flux of the drug from the drug $..$ capsule?

Calculate the Gotal drug belease rate from the capsul $\frac{W}{m}o\frac{l}{s}?$

Calculate thd fimo it will take the entirc drug to be released? Water, $C$

grad$*N_A+\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}-R_A=0,N_A=-c{D}_{AB}grad{y}_A+y_A(N_A+N_B)$

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{del{N}_{A,x}}{\text{d}\text{e}\text{l}\text{x}}+\frac{del{N}_{A,y}}{\text{d}\text{e}\text{l}\text{y}}+\frac{del{N}_{A,z}}{\text{d}\text{e}\text{l}\text{z}}]=R_A$ Rectangular coordinates

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{1}{r}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}(r{N}_{A,r})+\frac{1}{r}\frac{del{N}_{A,}}{\text{d}\text{e}\text{l}}+\frac{del{N}_{A,z}}{\text{d}\text{e}\text{l}\text{z}}]=R_A$ Cylindrical coordinates

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{1}{r^2}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}(r^2{N}_{A,r})+\frac{1}{rsin}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}}(N_{A,}sin)+\frac{1}{rsin}\frac{del{N}_{A,}}{\text{d}\text{e}\text{l}}]=R_A$ Spherical coordinates

Rectangular coordinates

Spherical Cylindrical coordinates

grad$*N_A+\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}-R_A=0,N_A=-c{D}_{AB}grad{y}_A+y_A(N_A+N_B)$

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{del{N}_{A,x}}{\text{d}\text{e}\text{l}\text{x}}+\frac{del{N}_{A,y}}{\text{d}\text{e}\text{l}\text{y}}+\frac{del{N}_{A,z}}{\text{d}\text{e}\text{l}\text{z}}]=R_A$ Rectangular coordinates

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{1}{r}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}(r{N}_{A,r})+\frac{1}{r}\frac{del{N}_{A,}}{\text{d}\text{e}\text{l}}+\frac{del{N}_{A,z}}{\text{d}\text{e}\text{l}\text{z}}]=R_A$ Cylindrical coordinates

$\frac{del{c}_A}{\text{d}\text{e}\text{l}\text{t}}+[\frac{1}{r^2}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}(r^2{N}_{A,r})+\frac{1}{rsin}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}}(N_{A,}sin)+\frac{1}{rsin}\frac{del{N}_{A,}}{\text{d}\text{e}\text{l}}]=R_A$ Spherical coordinates

coordinates