An extracellular protein therapeutic needs to be separated from the cell

broth. Economic and processing demands indicate that the use of a rotary vacuum filter is the

best choice. $2000$ L$/$hr of the broth $($density $1\mathrm{.}01$ g$/$cm$3,$ viscosity: $1\mathrm{.}1$cp$)$ needs to be processed.

Preliminary experiments show that the best cake characteristics are obtained when diatomaceous

earth is added to achieve a solid$$s density of $0\mathrm{.}015$ kg dry cake per liter of filtrated.

Unfortunately, the chemists forgot to determine the compressibility of such a cake. Using a

Buchner filter $10$ cm in diameter you obtained the following data,

$\backslash$Delta P$=30000$ g$/$cm sec$2\backslash$Delta P$=40000$ g$/$cm sec$2$

Time $($sec$)$ Volume of Filtrate

$($L$)$

Time $($sec$)$ Volume of Filtrate

$($L$)$

$0000$

$50\mathrm{.}01650\mathrm{.}012$

$100\mathrm{.}023100\mathrm{.}017$

$200\mathrm{.}032200\mathrm{.}024$

$300\mathrm{.}040300\mathrm{.}029$

$\backslash$Delta P$=150000$ g$/$cm sec$2\backslash$Delta P$=200000$ g$/$cm sec$2$

Time $($sec$)$ Volume of Filtrate

$($L$)$

Time $($sec$)$ Volume of Filtrate

$($L$)$

$0000$

$50\mathrm{.}01850\mathrm{.}013$

$100\mathrm{.}026100\mathrm{.}018$

$200\mathrm{.}037200\mathrm{.}026$

$300\mathrm{.}043300\mathrm{.}032$

a$)$ Determine the specific cake resistance and how it depends on the pressure drop across the

filter.

b$)$ You ran a new set of experiments to determine the washing efficiency.

Retained solutes $($mg$/$g dry cake$)$ Volume of wash$/$g of dry cake $($ml$/$g$)$

$200$

$14\mathrm{.}40\mathrm{.}6$

$12\mathrm{.}60\mathrm{.}86$

$9\mathrm{.}61\mathrm{.}26$

$81\mathrm{.}52$

$7\mathrm{.}41\mathrm{.}72$

$52\mathrm{.}4$

$42\mathrm{.}7$

$3\mathrm{.}82\mathrm{.}8$

Find the washing efficiency