Question #$1($Total: $50\%)$

An external flow of water was applied on top of the planar surface of a fibrous solid membrane $($made of polymer with finite thickness$).$ You are told that moxifloxacin $($an antibiotics which is water soluble$)$ was initially encapsulated within the matrix of polymer solid membrane as mentioned above. You are told that the flux of moxifloxacin from the polymer membrane surface was determined as $2\mathrm{.}4{10}^{-5}$mol$\frac{e}{m^2(s)}$ under water flow with constant velocity profile. The partition coefficient ${}_{\text{A}\text{f}\text{s}}$ was given as $0\mathrm{.}35.$ Also, the concentration of moxifloxacin in the water far away from the surface of polymer solid membrane was known to be $0\mathrm{.}6$mol$\frac{e}{L}.$ The mass transfer coefficients values were known too as follows: $k_{AS}=3\mathrm{.}5{10}^{-9}\frac{m}{s}$;$k_{AF}=9\mathrm{.}7{10}^{-9}\frac{m}{s}.$

Please determine the concentration of moxifloxacin inside the polymer solid membrane $($at the region just next to the water layer$).$ Some basic conversion factors can be found in the tables in the Appendix.