Consider the "drug patch" shown below. The patch consists of a drug reservoir mounted on top of a gel diffusion barrier. A $3cm3cm$ patch has a diffusion barrier with a thickness of $2\mathrm{.}0mm.$ The diffusion barrier is in direct contact with the skin. The drug release vs$.$ time profile is shown below. The drug is only slightly soluble in the gel diffusion barrier, with a maximum solubility of $0\mathrm{.}5mo\frac{l}{c}{m}^3$ at the top of the barrier. Other experiments show the drug is immediately absorbed into the bloodstream after exiting the patch $($i$.$e$.,$ it is instantly cleared$).$

a$.$ State the boundary conditions for this system.

b$.$ Explain why this system can be modeled as steady$-$state.

c$.$ Solve the differential mass balance to find the concentration profile.

d$.$ Calculate the drug release rate, equivalent to $N(x{)}^{**}A(x),$ and use Fick's Law to estimate the diffusion coefficient of the drug in the diffusion barrier.