# 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 (D_{s})
is likely to change linearly with (D_{m}). The diffusivity can also be
modified by choosing an *alternative mobile phase* in which case (D_{m)
}will be changed but (D_{s}) 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
(d_{f}) being much smaller than
(d_{p}) the assumption that
_{ }D_{m }= eD_{s
}will still be approximately true.

Assuming that
the diffusivity is varied by changing the nature of the solute and not the
mobile phase, then D_{s} can be replaced by eD_{s }and equation
(1) can be simplified to ,

_{} (65)

where,
_{}

Differentiating
with respect to (u), equating to zero and solving for u_{opt.}, it can
be seen that,

(66)