Consider the wetted wall tower shown in Fig. $3.$ A thin film of thickness $$ of a Newtonian liquid $B($water$)$ flows along $(z)$ a vertical wall while in contact with a gas mixture containing the solute $A($chlorine$).$ The solute A diffuses and absorbed in to the liquid $B.$ The length of contact between the two phases is relatively short during normal operation. The concentration of the solute at the liquid gas interface is constant $(C_{As})$ at the value of solubility of A$.$

$($i$)$ Derive the governing equation of transport of solute neglecting the curvature effect the cylindrical wall may $be$ assumed $tobe$ a rectangular wall $of$ width $2R,Ris$ the inner radius $of$ the tower