We want to separate $15nm$ diameter polystyrene beads $(\{$:$D=1\mathrm{.}5{10}^{-14}\frac{m^2}{s})$ from

E$.$coli $(Decol{i}_e=1\mathrm{.}5{10}^{-12}\frac{m^2}{s})$ using a microfluidic $H-$filter. $H-$filter has channel height,

$h=10m$; width, $w=100m$ and length, $L=1cm.$

a$)$ What is the approximate particle speed and the flow rate that is needed for

separation of beads with purity of at least $80\%($assume that the input

concentrations are approximately equal for the beads and E$.$coli$)?$

b$)$ What is the Collection efficiency at this speed?

c$)$ What is the pressure needed to achieve this flow rate?

Use the following figure for your calculations and make assumptions when

necessary: