# Interdisciplinary Applied Mathematics

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FIGURE 7.7. Normalized pressure and velocity distribution in a mixed electroos-motic/pressure-driven channel    for    various    values    of    Uin.    The    case    Uin    = 1.485

corresponds to the pluglike flow. The electroosmotic forces are present only for 3.1 < £ < 6.2. Simulation results are for a =1, в = 10,000 and Re = 0.005.

FIGURE 7.8.    Pressure build-up    along    the    microchannel    for    zero    net    flow    (left),

and corresponding velocity distribution across the channel (right).

simulation results presented in Figure 7.7. The velocity profile for this case indicates a combination of plug and adverse pressure gradient channel flow behavior, and the net volumetric flowrate is positive, as shown in Figure

7.7.

For a closed system it is possible to create large pressure gradients using electroosmotic forces. This can be used for actuation of micropistons or microbellows mechanisms. Such a configuration is simulated by closing the exit of the channel. Due to the presence of electroosmotic forces, the pressure rises linearly within the electroosmotic region, as shown in Figure 7.8.

This pressure rise is accompanied by the electroosmotic flow near channel walls and a reverse flow in the middle of the microchannel, as shown in Figure 7.8.

###### 7-4-2 Time-Periodic and AC Flows

In this section we present an overview of the AC electroosmotic flows and time-periodic electroosmosis, where the flow is driven by an alternating electric field. The primary difference between these two flows is that in AC electroosmosis the electric field is nonuniform, and it creates a nonzero time-averaged flow (Morgan and Green, 2003), while the time-periodic electroosmosis utilizes a uniform electric field, and results in zero time-averaged flow (Dutta and Beskok, 2001b).

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