We wish to extract a dilute solution of the protein alcohol dehydrogenase from an aqueous

solution of $5wt\%$ poly $($ethylene glycol$)($PEG$)$ with an aqueous solution that is $10wt\%$

dextran. Aqueous two$-$phase extraction system is a very gentle method of recovering proteins

that is unlikely to denature the protein since both phases are aqueous. The two phases can be

considered to be essentially immiscible. The dextran phase is denser and will be the crossflow

solvent. The entering dextran phases contain no protein. The entering PEG phase flow rate is

$25k\frac{g}{h}.$

$K_d=0\mathrm{.}12$

a$.$ If $10k\frac{g}{h}$ of dextran phase is added to a single$-$stage extractor, find the total recovery fraction

of alcohol dehydrogenase in the dextran solvent phase.

b$.$ If $10k\frac{g}{h}$ of dextran phase is added to each stage of a cross$-$flow cascade with two stages,

find the total recovery fraction of alcohol dehydrogenase in the dextran solvent phase.