Problem 1 (40 pts) One way to control the release of drug is to encapsulate it within a microparticle. Consider the case of the spherical microcapsule shown below. Here, an aqueous solution of drug is loaded at a concentration (C1) within a hollow sphere coated by a polymer layer of thickness that separates the drug from the exterior at concentration (C2), which is dilute enough to assume negligible. The total microparticle radius is R2 and the inner radius is R₁. In this way, the polymer coating acts as a rate-limiting membrane with a partition coefficient, D, such that the drug concentration in this polymer is C, and C2 at R1 and R2 respectively. R₁ R₂ Φ 'C₂ a) Assume the mass transfer across the shell is not steady-state, derive and simplify mass balance equation in radial direction by using shell balance. Write down any assumptions if you need. (10 pts) b) Simplify the resulting equation from (a) by applying Fick's Second Law and steady-state condition. (5 pts) c) What are the boundary conditions for the system? (5 pts) d) Derive the concentration profile of the drug along the microparticle. (10 pts) e) Determine the drug release rate. (10 pts)