with \(C\left(t_{in}\right)=0\) and \(C_0\left(t\right):=\frac{F_s\left(t\right)}{F\left(t\right)}\)being the volumetric concentration of the solute in input, if F_s(t) is the input of solute. The same arguments apply to \(C\left(t\right):=\ \frac{V_s\left(t\right)}{V\left(t\right)}\)being the concentration of solute in output. After using the continuity equation for the solvent represented by equation (12), (23) results in: