Interdisciplinary Applied Mathematics

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dispersion in pressure-driven or mixed electroosmotic/pressure-driven flows by modification of the channel geometry (Dutta and Leighton, 2001; Dutta and Leighton, 2003).

The results presented in Figures 7.22 and 7.23 characterize electrophoretic transport in simple channels. Similar techniques can be implemented in complex microchannel networks to enable flow and species transport control applications. (Ermakov et al., 1998) have developed a two-dimensional numerical model for electroosmotic/electrophoretic transport and species diffusion, which enabled them to analyze electrokinetic transport in two basic chip elements: cross-channel geometry for sample focusing and injection, and T-channel for sample mixing. Numerical results of electrokinetic sample focusing, injection, and separation steps are compared with the experimental data    (Ermakov    et    al.,    1999).    We    must    note    that    the    results

shown in Figures 7.22 and 7.23 differ from the numerical approach in (Ermakov et al., 1998), since the EDL region is fully resolved in the results presented here using spectral element discretization; see Section 14.1.

Finally, most practical applications of electrokinetically driven flows may experience variations in the wall charge (and hence the zeta potential) or variations in the channel cross-section. For example, proteins and peptides in capillary zone electrophoresis adsorb on the capillary walls, changing the zeta potential. This mismatch on the zeta potential locally changes the electroosmotic flow, and pressure-driven flow is initiated to conserve mass (see Figure 7.7). Since the flow conditions vary axially in the channel and there may be secondary flows, Taylor dispersion increases and becomes nonuniform. Such conditions have been investigated by Ghosal in a series of papers. Electroosmotic flow in a straight channel of arbitrary cross-sectional geometry and wall charge distribution is solved using the lubrication approximation (Ghosal, 2002c), while stepwise zeta potential variations are presented in (Ghosal, 2002a). Analyte adsorption and the corresponding changes in the flow pattern and the analyte dispersion are presented in (Ghosal, 2002b; Ghosal, 2003).

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