Assigment: UF description by the osmotic pressure model

A pharmaceutical industry concentrates a current of a peptide that is at $40C$ by ultrafiltration using a tubular membrane with an internal

diameter of $1\mathrm{.}8cm$ and with a permeability of $240L*m^{-2}{h}^{-1}at{m}^{-1}.$ In the characterization tests of the concentration process at a feed rate

of $2\mathrm{.}5\frac{m}{s}$ and with a peptide concentration in the feed stream of $9\frac{g}{L},$ a rejection concentration of $310\frac{g}{L}$ was reached. Calculate:

i$)$ The mass transfer coefficient.

ii$)$ The maximum permeate flow and the transmembrane pressure difference under these conditions.

iii$)$ If the concentration of peptide is increased to $18\frac{g}{L}$ by operating error, what will be the difference in transmembrane pressure under

conditions of maximum permeate flow.

iv$)$ Due to this change of operation the membrane permeability is reduced by $80\%$ as a result of fouling processes. Calculate what the

transmembrane pressure difference will be under conditions of maximum permeate flow

Data on the feed peptide solution: viscosity $=1,2*{10}^{-3}$Pas; density $=1013k\frac{g}{m^3}$;$D_v$ peptide average diffusion coefficient $=3,9*{10}^{-11}$

$\frac{m^2}{s}.,$ Osmotic pressure $,(atm)=3,{910}^{-3}c-1,5*{10}^{-6}{c}^2+7,7*{10}^{-8}{c}^3$ where $c$ is la peptide concentration $(\{$:$\frac{g}{L}).$