Mass transfer in rectangular chromatographic channels

Rectangular channels are explored nowadays for use in chromatographic and electrophoretic separations, especially after the possibilities of micromachining have become available to separation scientist. Expressions for plate heights expected for such experiments with an infinite channel width has been given by Giddings, while Golay derived the effect of finite channel width for unretained components. However, it remains unclear how the classical equations for plate height for retained components should be modified when the effect of finite channel width is taken into account. Also, the application of electroosmotic propulsion of the mobile phase leads to a flow profile different from the Poiseuille-type profile assumed in the above treatments, and no equations seem to be available for this situation. In this work, these problems have been addressed by an approach involving numerical Fourier transforms. Expressions for the plate height contribution from mobile phase mass transfer as a function of characteristic length dc (the height of the channel, or the diameter for open cylindrical systems, OT), mean mobile phase velocity, um, diffusion coefficient Dm, retention factor, k', and width-to-height ratio, phi, can always be written as: H = dc2um/DmF(k', phi). For cylindrical open systems, F(k', phi) equals 1/96 (1 + 6k' + 11k'2)/(1 + k')2, the well-known Golay equation. In the present work, this is taken as a reference point; results are cast in the form F(k', n) = (A + Bk' + Ck'2)/(1 + k')2, where A, B and C replace the factors 1/96, 6/96 and 11/96 of the Golay equation. Values of A, B and C are reported for various values of phi. This is done for a selection from the large variety of conditions that can be imagined: Coating on one, two or four walls of the channel, non-uniform or uniform coating, pressure-driven (Poiseuille-type) or electro-osmotically-driven flow, surface charge on one, two of four walls, etc. It is found that the effect of finite channel width is large for unretained solutes (plate height for a wide channel is nearly eight times larger than that predicted when the finite channel width is ignored), whereas the plate height increase with retention is in many cases influenced only slightly.