# Interdisciplinary Applied Mathematics

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In the    next    example,    we    consider    the    chaotic    electroosmotic    stirrer    of

Qian and Bau (2002). The device consists of a spatially-periodic mixing

(a)

FIGURE 9.6. Schematic of the shear superposition micromixer and corresponding micrograph of the actual device. (Courtesy of I. Mezic.)

(b)

FIGURE 9.7.    (a)    Experimental    measurements    of    MVC    for    an    (x-y)    plane    and

numerical simulations for an (x-y) and a (y-z) plane for a single side-channel activated. (b) Numerical simulations for all three pairs of side-channels activated. (Courtesy of I. Mezic).

chamber, where the bottom and top surfaces each have two surface electrodes that are covered with a thin insulator. The zeta potential on the insulated surface can be altered by applying electrostatic potential on these electrodes (Schasfoort et al., 2001); see also Section 7.4.7. It is possible to create various flow patterns in the mixing chamber by using different zeta potentials under horizontal electric field. For simplicity, Qian and Bau utilized zeta potential combinations of ±Co, and obtained analytical solutions of Stokes flow in the rectangular chamber using the thin EDL approximation (i.e., the Helmholtz-Smoluchowski slip velocity (equation (7.24)) is assumed on electrode surfaces). Figure 9.8 shows four steady Stokes flow patterns obtained under different zeta potentials (shown by patterns A, B, C, and D). The arrows on the top and bottom of the mixing chambers show the electroosmotic flow direction. The main idea in the electroosmotic stirrer is to alter the zeta potential, and hence the flow patterns vary peri-

FIGURE 9.8. Four different electroosmotic flow patterns obtained by zeta potential alterations in (Qian and Bau, 2002). Arrows show the electroosmotic flow direction on electrode surfaces. The flow is maintained by a steady horizontal electric field.

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