Dispersion in Chromatography Columns - Experimental Validation of the Van Deemter Equation > Page 89
where (e) is a constant, probably close to unity.
However that there are two ways in which the diffusivity of the solute in the mobile phase can be changed. It can be modified as a result of changing the solute which is being eluted, in which case the above assumptions are valid as (Ds) is likely to change linearly with (Dm). The diffusivity can also be modified by choosing an alternative mobile phase in which case (Dm) will be changed but (Ds) will remain the same. Under these circumstances the above assumptions are not likely to be precisely correct. Nevertheless, if the resistance to mass transfer in the stationary phase makes only a small contribution to the overall value of (H) due to the magnitude of (df) being much smaller than (dp) the assumption that Dm = eDs will still be approximately true.
Assuming that the diffusivity is varied by changing the nature of the solute and not the mobile phase, then Ds can be replaced by eDs and equation (1) can be simplified to ,
Differentiating with respect to (u), equating to zero and solving for uopt., it can be seen that,