$.$ Diafiltration: Using UF membranes is typically used to concentrate the diluted stream containing the purified Mab protein $($which does not pass the UF$-$membrane$)$ while exchanging its buffer solution $($which can pass the membrane$).$ In SPD$,$ diafiltration is modelled parallel to a storage$/$holding vessel that represents the retentate vessel. At the end, a diafiltered MAb solution will leave the unit. At this point, we don$$t know the concentration of the purified protein in the$1$ tream from the chromatography unit, and assume it is $5$ g$/$L$.$ We want to concentrate the protein $5$ fold, while removing the eluent components such as salts that pass the membrane, using WFI $($purified wate$).$

a$.$ Determine amount of protein and liquid volume per batch $($VF$)$ to the dialysis unit. $($If youcan$$t determine this, take $0\mathrm{.}5$ kg Mab per batch$).$

b$.$ Determine a concentrating$-$dialysis strategy, while minimising $($expensive$)$ WFI use. How much WFI do we need for removing $95\%$ of the eluent components $?$

c$.$ If processing time needs to be maximum of $4$ hours $($due to degradation$),$ what is the required membrane area A $?$ For this UF module, you may take the mass transfer coefficient and the concentration where gel formation occurs as k $=10\backslash$mu m$/$s and a gel polarization concentration of cGEL $=100$ kg m$-3.$ Flux can be calculated using J $=$ k ln $($c GEL $/$c$)$ see Wesselingh and Krijgman p $52-53($which is also the model implemented in SPD$).$Assume average flux if flux varies $($as it does in a batch$).$