A membrane separator is \(3 \mathrm{~mm}\) in diameter, and the membrane permeability was estimated as \(2 \times 10^{-6} \mathrm{~m} / \mathrm{s}\). The solute being transported has a diffusivity of \(2 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\) in the liquid.

Estimate the overall permeability. What fraction of the resistance can be attributed to mass transfer?

The above membrane separator showed \(70 \%\) solute recovery under certain operating conditions. A new membrane with 10 times the permeability is being considered as a replacement. Estimate the solute recovery in this new case.