Electroosmotic and Pressure-Driven Flow in Open and Packed Capillaries: Velocity Distributions and Fluid Dispersion Ulrich Tallarek,* ,† Erdmann Rapp, ‡ Tom Scheenen, † Ernst Bayer, ‡ and Henk Van As † Laboratory of Molecular Physics and Wageningen NMR Centre, Department of Biomolecular Sciences, Wageningen University, Dreijenlaan 3, 6703 HA Wageningen, The Netherlands, and Research Center of Nucleic Acid and Peptide Chemistry, Institute of Organic Chemistry, University of Tu ¨bingen, Auf der Morgenstelle 18, 72076 Tu ¨ bingen, Germany The flow field dynamics in open and packed segments of capillary columns has been studied by a direct motion encoding of the fluid molecules using pulsed magnetic field gradient nuclear magnetic resonance. This non- invasive method operates within a time window that allows a quantitative discrimination of electroosmotic against pressure-driven flow behavior. The inherent axial fluid flow field dispersion and characteristic length scales of either transport mode are addressed, and the results demonstrate a significant performance advantage of an electrokinetically driven mobile phase in both open- tubular and packed-bed geometries. In contrast to the parabolic velocity profile and its impact on axial disper- sion characterizing laminar flow through an open cylin- drical capillary, a pluglike velocity distribution of the electroosmotic flow field is revealed in capillary electro- phoresis. Here, the variance of the radially averaged, axial displacement probability distributions is quantitatively explained by longitudinal molecular diffusion at the actual buffer temperature, while for Poiseuille flow, the pre- asymptotic regime to Taylor-Aris dispersion can be shown. Compared to creeping laminar flow through a packed bed, the increased efficiency observed in capillary electrochromatography is related to the superior charac- teristics of the electroosmotic flow profile over any length scale in the interstitial pore space and to the origin, spatial dimension, and hydrodynamics of the stagnant fluid on the support particles’ external surface. Using the Knox equation to analyze the axial plate height data, an eddy dispersion term smaller by a factor of almost 2.5 than in capillary high-performance liquid chromatography is re- vealed for the electroosmotic flow field in the same column. The actual flow pattern of a fluid undergoing slow, laminar flow in a packed bed of particles depends on the morphology (i.e., the topology and geometry) of the pore space that is available for the flow, and the existence of a point-to-point difference in flow velocity is a fundamental property of the fluid flow field under the most general conditions. 1 However, not only the inherent structural heterogeneity of the porous medium but also the actual physical origin(s) of the flow may very sensitively influence the correlation time and length which characterize velocity fluctuations in the mobile phase. In contrast to the more conventional pressure-driven mode, capillary electrochromatography (CEC) utilizes the hydrodynam- ics of an electroosmotic flow (EOF) to transport solute molecules through the interconnected pore space of capillary columns packed with small adsorbent particles. 2-7 The ideal EOF in a narrow cylindrical channel should be characterized by a flat, i.e., pluglike velocity profile at distances from the surface that are of the order of the electric double-layer thickness. This intrinsic property makes the channel cross-sectional profile and magnitude of the EOF independent of the actual channel diameter, provided that the latter is significantly larger than the electric double-layer thickness. 8 The situation is in sharp contrast to the parabolic (Poiseuille) velocity profile encountered in pressure-driven flow, which directly results from the distribution of shear stress in a viscous fluid under laminar flow conditions. Further, the cross- sectional average velocity in the (cylindrical) channel here depends on the square of its diameter. These characteristics have important implications for the eddy dispersion contribution to the overall band spreading expected in CEC and capillary high-performance liquid chromatography (CHPLC). 9 In general, eddy dispersion is caused by any velocity inequality of the flow pattern over the whole column cross section. Due to the anatomy of the available stream paths in the packed bed and local or systematic changes in packing density, fluctua- tions in permeability and mobile-phase velocity also exist at * To whom correspondence should be addressed: (phone) + 31 ( 317) 48- 2047; ( fax) + 31 ( 317) 48-2725; ( e-mail) ulrich.tallarek@ water.mf.wau.nl. † Wageningen University. ‡ University of Tu ¨ bingen. (1) Sahimi, M. Applications of Percolation Theory; Taylor & Francis: London, 1994. (2) Knox, J. H.; Grant, I. H. Chromatographia 1987 , 24, 135-143. (3) Dittmann, M. M.; Wienand, K.; Bek, F.; Rozing, G. P. LC-GC 1995 , 13, 800-814. (4) Crego, A. L.; Gonza ´lez, A.; Marina, M. L. Crit. Rev. Anal. Chem. 1996 , 26, 261-304. (5) Colo ´ n, L. A.; Reynolds, K. J.; Alicea-Maldonado, R.; Fermier, A. M. Electrophoresis 1997 , 18, 2162-2174. (6) Rathore, A. S.; Horva ´th, Cs. J. Chromatogr., A 1997 , 781, 185-195. (7) Colo ´n, L. A.; Guo, Y.; Fermier, A. Anal. Chem. 1997 , 69, 461A-467A. (8) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965 , 69, 4017-4024. (9) Knox, J. H. Chromatographia 1988 , 26, 329-337. Anal. Chem. 2000, 72, 2292-2301 2292 Analytical Chemistry, Vol. 72, No. 10, May 15, 2000 10.1021/ac991303i CCC: $19.00 © 2000 American Chemical Society Published on Web 04/12/2000