# Interdisciplinary Applied Mathematics

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odically to induce chaotic mixing. Although the flow is time-periodic here, the particle paths for two-dimensional unsteady flow may become noninte-grable, resulting in chaotic advection/mixing even in the Stokes flow regime. We must indicate that the actual device requires precise control over the zeta potential magnitude and the time scales for zeta potential alterations. In addition, the results presented in (Qian and Bau, 2002), ignore possible interactions between the insulated electrodes and the flow transients.

In Section 7.6 we have briefly described applications of dielectrophoresis to mixing. The final example of this section describes one such micromixer developed by (Deval et al., 2002). It is appropriate for microflows that contain charged or polarizable particles that can move under the influence of a nonuniform AC electric field. The spherical particles used in (Deval et al., 2002), are polystyrene spheres, but in principle, bacteria or cells may be present in the flow.

Assuming a spherical particle of radius a and conductivity a subject to an electric field with rms value Erms, the time-averaged force on the particle is given by equation (7.49). The real part of the Clausius-Mossotti factor, K(u>), is in the range [—1/2,1], and thus both attractive and repulsive forces can be induced simply by changing the frequency u>. The conductivity of polysterene spheres is on the order of 10 mS/m, and correspondingly, the

 Inlet channels 100 um

FIGURE 9.9. Top view of the DEP micromixer. (Courtesy of C.-M. Ho.)