$26\mathrm{.}6$ Consider the $$drug patch$$ shown in Problem $26\mathrm{.}4.$ The

patch consists of a pure solid drug source mounted on top of a

water$-$swollen polymer, which acts as a controlled diffusion

barrier. The square patch is $4\mathrm{.}0$ cm $4\mathrm{.}0$ cm$.$ The bottom

surface of the diffusion barrier is in direct contact with the skin.

The desired amount of cumulative drug release is $0\mathrm{.}02\backslash$mu mole

after $10$ hours. Independent experiments have shown that the

drug is immediately taken up into the body after exiting the

patch. The maximum solubility of the drug in the water$-$swollen

polymer is $0\mathrm{.}50\backslash$mu mole$/$cm$3$

$,$ which is dilute. The effective

diffusion coefficient DAe of the drug in the water$-$swollen

polymer is $208107$ cm$2/$s$.$ What is the required thickness

$($L$)$ of the diffusion barrier component of the drug patch needed

to achieve the desired drug release profile?