Drug delivery through the skin can be done using a solid membrane or a patch loaded with drugs on the skin. Consider such a patch in the figure below. Here we will estimate the diffusion of this drug across the dermis and then into the capillary bed underneath the skin. One benefit of saturating the patch with drug is that the concentration of drug at the patch surface remains nearly constant at Cp = 5 mg/mL until the drug is used up. The rate of blood flow through the capillary bed is 5 x 10-4 mL/min. The drug's diffusivity across the dermis is 5 x 10-8 cm2 /s, while that across the interstitium (the tissue between the dermis and the capillaries) is 8 x 10-6 cm2 /s. The capillaries are oriented primarily as shown in the figure (which is not draw to scale), and the drug can freely penetrate the capillary walls. The dermis is 2 mm thick; the interstitium is 3 mm thick. (a) Derive an expression for the concentration of drug in a capillary as a function of x, the distance from the beginning of the patch in the direction in which blood in the capillaries is flowing. You may assume that the concentration of drug in the capillaries is a function only of x and does not vary with the radial position in the capillary. (b) an equation to estimate how long the patch will last if it is initially loaded with 50 mg of drug