# Interdisciplinary Applied Mathematics

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sample distribution along the channel center at various times. Minute diffusion effects are visible for this Pe = 500 flow. Figure (e) shows the velocity distribution across the channel, which corresponds to the pluglike velocity distribution of “pure electroosmotic flows.” It is this pluglike velocity that maintains the initial sample distribution in the bulk flow region, as shown in Figures (a-c). Velocity distribution within the EDL region is visible in Figure (e),    where    the    velocity    rapidly decays    from the    bulk    flow    value    in

the edge of the EDL region to zero on the wall. Hence, we observe slower sample motion within the EDL region. This generates a retardation and smearing of sample distribution near the walls due to the mixed convec-tive/diffusive transport. The effect of convective/diffusive transport on the cross-section-averaged sample shape is known as the Taylor dispersion; see the next section. In most electrokinetic flow applications, the EDL thickness is three to five orders of magnitude smaller than the channel height. Hence, the EDL/electrophoresis interactions become negligible with increased disparities between the EDL and channel length scales. For such cases, the retarded sample in the vicinity of walls quickly diffuses due to the small diffusion length scales that are on the order of the Debye length. Hence, sample transport in electroosmotic flows in straight channels experiences “minimal” Taylor dispersion effects.

###### 7.5.3 Taylor Dispersion

Taylor dispersion has adverse effects in identifying the species type using capillary electrophoresis measurements. The electrophoretic motion of the sample experiences both convection and diffusion effects. For the cases in which the radial diffusion (or diffusion across the microchannel) is more dominant than the axial diffusion of the species Pe ^ 1, we can analyze the species transport equation to obtain a cross-sectionally averaged species transport equation in the following form (see (Probstein, 1994), Section 4.6,

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