Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -101

Mechanisms and Importance of Zone-Spreading 91\ntotal plate height: sum of contributions\n\nh\n3\n\n2\n\n1\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n 10 20 30\n v = Re.Sc \n\nFigure 5 Reduced plate height plot, showing the most important contributions.\n\nvalid for capillary columns (see Sec. II.E.4.e) in which the stationary phase is supposed to be present as a thin film at the column wall. This idea arises from the capillary models for packed beds as described in Sec. II.E.2.c.\n\nAlthough the mathematical structure of the coupling Eq. (39b) and our result Eq. (43a,b) is identical, there are several more or less important differences.\n\nThe A Term. In the coupling equation, there is no explicit term for the longitudinal eddy diffusion or streamline-splitting along the column axis. Only if C_m(v_m) -> 0 (i.e., either for v = 0, or in the ideal case, if there are no velocity profile effects in the mobile phase) there appears a constant A term. This term, however, both in Giddings' theory and in our approach, reflects the hydrodynamic contribution to radial mass transfer, called A_g in Eq. (43). Giddings' coupling theory thus does not provide a specific term for this realistic effect that is also recognized in technological and hydrological sciences. As said before, many experiments in these and also in chromatographic sciences support the existence of a constant A term also if v = 0. Hence, we prefer the relation in Eq. (43) over the coupling Eq. (39b).\n\nThe Mobile Phase Term as a Whole. It should be pointed out, however, that Giddings' coupling theory [1,5] does provide more than one coupling term stemming from mobile-phase dispersion processes for velocity differences on different scales in the column cross section. The complete coupling equation reads:\n\nh_coupling = 2γ_m/v + Σ { 1/{(1/λ_a) + (1/σ_w)} } + (2/3)g(k^2)D_v\n\n(44)\n\nHere, the summation Σ_i over all possible velocity differences that might arise in the column cross section, such as:\n