Time and length scales of eddy dispersion in chromatographic beds

Time and length scales as well as the magnitude of individual contributions to eddy dispersion in chromatographic beds are resolved. We address this issue by a high-resolution numerical analysis of flow and mass transport in computer-generated bulk (unconfined) packings of monosized, nonporous, incompressible, spherical particles and complementary confined cylindrical packings with a cylinder-to-particle diameter ratio of d_c/ d _p = 20. The transient behavior of longitudinal and transverse dispersion is analyzed and correlated with the spatial scales of heterogeneity in the bulk and confined packings. Simulations were carried out until complete transcolumn equilibration in the confined packings was achieved to facilitate a quantitative study of the geometrical wall effect. Longitudinal plate height data calculated over a wide range of reduced velocities (0.1 ≤ ν ≤ 500) were fitted to the comprehensive Giddings equation. The determined transition velocities for individual contributions to eddy dispersion were found to be widely disparate. As a consequence, the total effect of eddy dispersion on the plate height curves can be approximated in the practical range of chromatographic operational velocities (5 ≤ ν ≤ 20) by a composite expression in which only the short-range interchannel contribution retains its coupling characteristics, while transchannel and transcolumn contributions appear as simple mass transfer velocity-proportional terms.