# Interdisciplinary Applied Mathematics

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Zone electrophoresis utilizes a supporting medium to hold the sample, while an external electric potential is applied at the end of the supporting media. Typically, filter paper, cellulose, cellulose-acetate, and gel are used as the supporting media (Westermeier, 1990).

Capillary electrophoresis is applied in capillaries and microchannels (Janos, 1999). It has utmost potential for development of automated analytical equipment with fast analysis time and on-line detection possibilities. Today, many separation techniques rely on combined capillary electrophoresis and electroosmotic flow to pump solutes toward the detector. Through a set of experiments, (Polson and Hayes, 2000) demonstrated flow control using external electric fields in capillary electrophoresis. (McClain et al., 2001) have developed a microfluidic array for E. coli detection, which utilized pure electrophoretic transport.

In the following, we demonstrate numerical simulations of electrophoretic motion in a microchannel. The electrode configuration and channel surface conditions are consistent with the schematic shown in Figure 7.4. The elec-

tric field is from left to right, the zeta potential on the channel surface is negative (Z < 0), and the sample is positively charged. Simulation parameters are chosen such that the electroosmotic mobility of the buffer is twice the electrophoretic mobility of the sample (peo = 2pep), and the Debye length is (1/100) of the channel height. The electric field generates pure electroosmotic flow with Helmholtz-Smoluchowski velocity (whs) given by equation (7.18), resulting in Re = 0.03 and Pe = 500 flow. Figure 7.22 shows sample motion with an initial Gaussian distribution under electrophoresis and electroosmosis. Since we assume a positively charged sample, the electrophoretic motion is toward the cathode (right), which is augmented by the electroosmotic flow in the same direction. Figures (a-c) show snapshots of sample contours at various times. The sample maintains its initial    distribution    in    the    bulk flow region. In    Figure    (d),    we    present    the

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