# Interdisciplinary Applied Mathematics

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The corresponding velocity profiles across the channel at Z = 4.5 are presented in Figure 7.7 (right plot). A pluglike velocity profile is observed for Uin    =    1.485,    as predicted    by    the theory.    Setting    Uin    =    2.5    corresponds

to a favorable pressure gradient case, which is a combination of a pluglike flow with a parabolic profile in the bulk of the channel. The corresponding pressure variation shown on the left indicates significant pressure drop at the entrance and exit portions of the channel. However, in the mixed zone, the pressure drop is relatively low due to the electroosmotic pumping.

The adverse pressure gradient case of Uin = 0.5 is an electrokinetically driven micropump. For this case, the inlet and the exit pressures are the same, corresponding to a laboratory-on-a-chip device that is exposed to atmosp pressure at both ends. The entire flow is driven by the electrokinetic forces, which overcome the drag force within the entire channel system. The pressure drop    at    the    inlet    and    exit    portions    of the    channel    (Z <    3.1    and

Z > 6.2) is due to the shear stress. A micropump must be able to raise the system pressure in order to drive the flow. The electroosmotic pump is doing precisely this. The net pressure gradient is positive within the pump, as shown in Figure 7.7. Here we note that:

• In a purely electroosmotic system, pluglike velocity profiles with zero-pressure gradient will be obtained. In the case of Uin = 0.5, the adverse pressure gradient is present to overcome the pressure drop at the inlet and exit sections.

Therefore, any mixed flow system should exhibit a behavior similar to the

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