3. (18 pts) A medicine tablet or pill is being used to deliver naproxen sodium (abbreviated NS', material at core of spherical tablet). NS diffuses through three outer, coating layers which ensure the drug is released uniformly through the body. The tablet can be assumed to be a sphere. The thickness and diffusivity of each of the coating materials is described in the table below: Thickness (mm) Diffusivity (mm/s) 9.7 * 10-2 0.89 Layer 1 (Methocel K100, inner most, near NS core) 2 (Methocel E10) 3 (PVA, outer most layer) 0.76 0.13 0.15 * 10-2 0.24 * 10-2 = a) Write the simplified governing equation for steady-state, radial diffusion of NS through any layer. Include any assumptions. There are no chemical reactions. b) Apply specified surface concentration boundary conditions of c(r = ri) = Ci and c(r = r.)=co to solve the governing equation for c as a function of r, where ri and ro are the inner and outer most radii of any layer, respectively. You need to perform the integration to derive the solution, even though the solution is available in the lecture slides. c) Derive the equation for mass flow (mass/time) for a layer in terms of co, Ci, o, and rj. d) Rewrite the equation from part c in terms of a concentration difference divided by resistance and write the equation for diffusion resistance. e) The concentration between the NS core and layer 1 is 1.062 mg/mm and the concentration of the outer surface of layer 3 is 0. Using this information and the information in the table what is the mass flow rate from the core to the surface of the tablet