As part of a process to fabricate materials with ordered pore arrays, the diffusion-limited solvent etching process shown in the figure (next column) is used to remove a contaminant (solid solute A, lithium carbonate) from an array of pores within a slab. There are presently 16 cylindrical pores, each of 0.10 cm diameter and 0.5 cm depth, and the overall dimensions of the slab are 4.0 cm per side and 0.60 cm deep. Liquid solvent (species B) flows over the surface of the slab at a high rate so that the concentration of dissolved solute A is essentially zero; also, dissolved solute A is not very soluble (sparingly soluble) in solvent B. The process is carried out at ambient conditions (25 C, 1.0 atm). Other potentially useful information: c_A* = 90 μmole/cm³ (maximum solubility of solute A in solvent B), ρB 1.0 g/cm³ (density of solvent B) ρ_A,solid = 2.1 g/cm³, M_A = 74 g/gmole, M_B = 18 g/gmole, D_AB = 1.6 X 10^–5 cm²/s at 25 C and 1.0 atm.

a. Initially, the solid solute A is loaded to a depth of 0.20 cm within each 0.5 cm length pore, as shown in the figure below. At this point, what the total transfer rate of solute A out of the entire slab, in units of μmole/s?

b. How much time will it take for all of the solid solute A to be removed from each pore, units of hours?

c. The process takes a long time. What changes to the process (e.g. solubility of solute A, pore diameter, diffusion path length, process temperature) would likely reduce the time required?