A size-exclusion based molecular separation process is being developed to purify a mixture of proteins dissolved in aqueous solution at 20°C. The solution is dilute and approximates the properties of water, which has a viscosity of 1.0 cP at 20°C. One protein of interest (protein A) is spherical with a mean molecular diameter of 25 nm. It is desired to design a porous membrane that has a stearic partition coefficient of no more than 0.64 for this protein— i.e., F₁ (j) = 0.64.

a. Estimate the molecular diffusion coefficient of protein A in dissolved in solution at 20°C.

b. What is the effective diffusion coefficient of the protein A within a single cylindrical desired membrane material?

c. At what pore diameter will all proteins other than protein A will be “excluded” from the membrane?