The spherical gel capsule shown in the figure at the top of the next column is used for long-term, sustained drug release. A saturated liquid solution containing the dissolved drug (solute A) is encapsulated within a rigid gel-like shell. The saturated solution contains a lump of solid A, which keeps the dissolved concentration of A saturated within the liquid core of the capsule. Solute A then diffuses through the gel-like shell (the gel phase) to the surroundings. Eventually, the source for A is depleted, and the amount of solute A within the liquid core goes down with time. However, as long as the lump of solid A exists within the core to keep the source solution saturated in A, the concentration of A within the core is constant. The diffusion coefficient of solute A in the gel phase (B) is D_AB= 1.5 × 10^-5cm²/s. The maximum solubility of the drug in the gel capsule material is c*_A= 0.01 gmole A/cm³. 

a. Starting from the appropriately simplified differential forms of Fick€™s flux equation and the general differential equation for mass transfer relevant to the physical system of interest, develop the final, analytical, integrated equation to deter mine the total rate of drug release (W_A) from the capsule under conditions where the saturated concentration of A within the liquid core of the capsule remains constant. 

b. What is the maximum possible rate of drug release from the capsule, in units of gmole A per hour, when c_Ao ‰ˆ 0? 

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Saturated solution of drug (solute A) Surrounding liquid Lump of solid species A Gel capsule shell r = R. CA = CAO r = R; CA= CAS