You are a bioprocess engineer working for a major pharmaceutical company on downstream process development. Your supervisor asks that you do some preliminary scaling calculations based on isotherm data generated by colleagues in laboratory experiments $($figure$).$ Specifically, you should calculate the shock front velocity for a loading concentration of $3\mathrm{.}0$ g L$-1$ in $50$ mM phosphate buffer. You can expect the column to have a diameter of $0\mathrm{.}16$ m with an inter$-$particle porosity of $0\mathrm{.}35.$ The volumetric flow rate will be $4$ mL min$-1.$ Also calculate the chromatographic velocity after the shock front for which you know that dq$/$dc is $0\mathrm{.}5.$ In addition, which bed height should the column have to ensure a typical contact time?