Interdisciplinary Applied Mathematics

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192 +

where AD is the Debye length (see equation (7.1) normalized with the tube radius or the channel half-height. This equation is valid for small surface potential, since it is derived from the solution of the Debye-Huckel equation (7.6). In    the    limit    of large Debye    length    (AD    ^ 1),    the    EDL    on    both

sides of the channel (or tube) overlaps, resulting in a parabolic velocity profile for the pure electroosmotic flow. For such cases, equation (7.48) gives ao ^ 48, as expected. For large zeta potential, the effective diffusion coefficients in a tube or a two-dimensional channel have been presented in (Griffiths and Nilson, 2000). Dispersion coefficients for pure electroosmotic flows in various cross-section channels were presented in (Zholkovskij et al., 2003). In a subsequent work, hydrodynamic dispersion for mixed electroosmotic/pressure-driven flows in arbitrary cross-section channels was presented for electric double layers that are much smaller than the channel dimensions (Zholkovskij and Masliyah, 2004). This study was valid for a relatively small contribution of the pressure-driven flow.

In Figure 7.23, we demonstrate electrophoretic transport under mixed electroosmotic and pressure-driven flow conditions. The electrochemical conditions for this case are identical to those presented in Figure 7.22, with the exception of the favorable pressure gradient imposed on the bulk flow by regulating the channel flowrate. We have deliberately increased the mass flowrate    in    the    channel by a factor    of    two.    Analysis    of    the    electroos

motic flow for mixed electroomostic/pressure-driven flows was presented in Section 7.4.2. In Figure 7.23, we show snapshots of sample contours at various times. Although the initial sample distribution was uniform across the channel, due to the mixed electroosmotic/pressure-driven flow, the sample distribution across the channel quickly becomes parabolic. This parabolic profile is constantly stretched as the material points move with different streamwise velocities. Hence, Taylor dispersion effects are dominant for this flow. Here    we must    note    that    in addition    to the    convective    transport    due    to

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