$26\mathrm{.}6$ 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?