If we use the formulation of D_{ax} obtained from moment analysis of the equilibrium dispersive model, if I recall correctly, we can see that it is dependent on the column efficiency.

D_{ax} = \mathrm{HETP} \left(\frac{u}{2\varepsilon_e}\right), where u is the superficial velocity and \varepsilon_e is the interstitial porosity. Here, \mathrm{HETP} can be determined using pulse injections under non-binding conditions.

Using this expression, calculated values of D_{ax} will increase over resin cycles—assuming that column efficiency decreases. This is because plate height will increase with band broadening as the column degrades. This analysis suggests an opposite trend to that stated:

We can also consider the correlation by Rastegar and Gu for the Péclet number and obtain an expression to directly estimate D_{ax}.

D_{a x}=0.7 D_o+\frac{d_p u}{0.18+\left(u d_p \nu^{-1}\right)^{0.59}}, where D_o is the free solution diffusivity, d_p is resin particle diameter, u is the superficial velocity, and \nu is kinematic viscosity.

Assuming D_o and \nu are constant, d_p would have to change to alter D_{ax} for a certain u. Seems like we are missing something.

@jaymax, I think this calls for further investigation. Here are some ideas for you to pursue.

Putting the experimental data aside for a moment, you can simulate the salt concentration transition using a range of D_{ax} values and linear velocities. You can also simulate salt pulse injections and sample the same parameters. You can even vary \varepsilon_e and d_p, if for some reason these parameters change over cycles.

From this analysis, it should be clear what the expected trends should be—from a theoretical standpoint. There are, of course, factors that we cannot easily consider, such as changes in packing heterogeneity, compression, and flow distribution. If you are feeling ambitious, you can also account for the particle size distribution.