R Water Problem 2. Controlled drug release through a spherical shell (40 points) A drug encapsulated in a spherical shell of polymer gel is released to the surrounding water by diffusion through the gel layer (see figure). The spherical core containing the drug has an initial radius of R., which decreases as the drug is dissolved and released through the spherical shell with an outer radius of R, which remains unchanged. The gel layer is full of still water, and the concentration of the drug at the inner interface is equal to the solubility of the drug in water or C (R) = CA. You can also assume that the concentration of the drug is zero at the interface between the gel layer and outside water or C (R) = 0. We are interested to find the concentration profile of the drug CAC) in the spherical shell and the drug release rate. a. Starting from the continuity equation in spherical coordinates, write the differential equation and boundary conditions that determine the concentration profile of the drug in the gel layer. Justify all simplifications to the continuity equation. (10 points) b. Assuming pseudo-steady state, show that the concentration profile C4() in the gel layer is: (10 points) R. R CO) = csat where Ro