(Solved): 4. (WRF 27.8) It is desired to diffuse a blue dye molecule (solute A) into a solid material (sp ...

4. (WRF 27.8) It is desired to diffuse a blue dye molecule (solute A) into a solid material (species B) near the surface of the material, as shown in the figure below. Initially, there is no dye in the solid, and the maximum solubility of the dye in the solid is $0.010\mathrm{gmol}/{\mathrm{m}}^3$. Both the solubility of the dye and its diffusion coefficient in the solid are relatively small, so that the dye does not penetrate very far into the solid. The process is carried out at ambient conditions $\left(25^{?}\mathrm{C},1.0\mathrm{atm}\right)$. After $2.0\min$, the flux of the dye into the solid was observed to be $\mathrm{NA}(\mathrm{z}=0,\mathrm{t})=5.15\times 10^{?9}$ $gmol/\left(m^2\mathrm{s}\right)$ A. The process is considered complete when the dye concentration within the solid achieves a concentration of $0.0062\mathrm{gmol}/{\mathrm{m}}^3$ at a depth of $0.050\mathrm{cm}$ from the surface. How much time will this process take? B. Which of the following are reasonable attributes of solid B: transient source, transient sink, stagnant medium, semi-infinite medium? 5. (WRF 27.18) A small spherical bead is used as a controlled drug-release capsule in the gastrointestinal system. A $0.10\mathrm{cm}$ diameter bead has a uniform initial concentration of 0.20 $\mathrm{mmol}/\mathrm{L}$ of the drug griseofulvin (species A). The diffusion coefficient of griseofulvin within the bead material is $1.5\times 10^{?7}{\mathrm{cm}}^2/\mathrm{s}$. Upon release from the bead, the drug is immediately consumed so that the surface concentration is essentially zero. Using the concentration-time charts, determine the time it will take for concentration of the griseofulvin in the center of the bead to reach $10\%$ of its initial value.