Numerical and analytical solutions for the column length-dependent band broadening originating from axisymmetrical trans-column velocity gradients

Trans-column velocity gradients arising from radial variations in packing density or mobile phase temperature lead to a plate height contribution that, in the case of for example a 4.6 mm column, may increase over several tens of centimeters before it reaches a constant value. Considering a wide variety of different trans-column velocity profiles, including Giddings’ general polynomial expression and several simplified partially flat profiles, and performing a set of analytical calculations (to establish an expression for the long time-limit constant value H∞) and numerical simulations (to calculate the band broadening in the transient regime), it was found that the column length-dependent variation of this plate height contribution can be very closely approximated by a simple exponential-law expression. The availability of the latter will greatly simplify the experimental analysis of radial column heterogeneity effects, especially considering that this expression is independent of the radial dispersion, the column diameter, and the average velocity and maximum velocity difference. Surprisingly, the exponential-law expression is to a first approximation also independent of the shape of the velocity profile, provided the velocity profile does not become flat over a substantially large part of the cross-section. In the latter case, the transient curve obeys a more complex law, but can nevertheless still be approximated by an exponential-law expression, though with a different (larger) decay constant.