Dispersion in Chromatography Columns - Alternative Equations for Peak Dispersion > The Huber Equation > Page 66

However, on consideration there is a difference between the Giddings equation and that of Van Deemter as the C term in the Van Deemter equation would now only describe the resistance to mass transfer in the mobile phase contained in the pores of the particles, and thus, would constitute an additional resistance to mass transfer in the stationary (static mobile) phase. This concept has some indirect experimental support in the development of the form of f1(k') from experimental data which will be discussed later. The form of f1(k') is shown to be closer to the original form given by Van Deemter for f2(k') that is appropriate for the resistance to mass transfer in the stationary phase. It is not known for certain, but it is possible and likely, that this was the reason why Van Deemter et al. did not include a resistance to mass transfer term for the mobile phase in their original form of the equation.

The Huber Equation

The next HETP equation to be developed was that of Huber and Hulsman in 1967 (17). These authors introduced a modified multipath term somewhat similar in form to that of Giddings and a separate term describing the resistance to mass transfer in the mobile phase contained between the particles. The form of their equation was as follows:-

                                       (47)

It is seen that the first term differs from that in the Giddings equation, in that it now contains the mobile phase velocity to the power of one half. Nevertheless, again when u1/2 >> E, the first term reduces to a constant similar to the Van Deemter equation. The additional term for the resistance to mass transfer in the mobile phase is an attempt to take into account the 'turbulent mixing' that takes place between the particles. Huber's equation implies (but, in fact, was not explicitly stated by the authors) that the mixing effect between the particles (that reduces the magnitude of the resistance to mass transfer in the mobile phase) does not commence until the mobile phase velocity approaches the optimum velocity (as defined by the Van Deemter equation). Furthermore, it is not complete until the mobile phase velocity is well above the optimum velocity. Thus, the shape of the HETP/u curve will be a little different from that predicted by the Van Deemter equation.