NOTE: In the following there is some ambiguity upon which I have to reflect a little. We are going to do the hypothesis of an instantaneous release of solute, this in order to obtain back Newman results. This does not automatically implies that the solvent is released just instantaneously which would require, \(F\left(t\right)\ \to F\left(t,t_{in}\right)=M_0\delta\left(t-t_{in}\right)\). I have certainly to compare the result below with what obtained in Rigon et al., 2016 (section 10) and \cite{Duffy_2010} to clarify all the issues. Please note that in Rigon et al., 2016, we did not fully exploited the concentration equation simplification (as Duffy 2010 does and we are required to do also here below) using the continuity equation (we did consciously for not adding further equation to the 104 ones already present) .
Assuming that we have an instantaneous input of both solvent and solute, i.e. \(C_0\left(t\right)=C_0\delta\left(t-t_{in}\right)\), then the
equation can be written: