Interdisciplinary Applied Mathematics

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Embedded surface electrodes can also be used to locally alter the zeta potential. Schasfoort et al. have built microchannels using conducting material,    and have    covered these    with    a    thin    layer    of insulator.    They    have

shown that the electroosmotic mobility can be altered by applying electrostatic potential on the walls (Schasfoort et al., 2001). A similar approach for direct zeta potential control has also been implemented in (Buch et al., 2001).

Active Mixing Using Electroosmotic Flows

Mixing in microfluidic systems is difficult due to the minute inertial effects (Re ^ 1) and small molecular diffusion coefficients (Sc ^ 1). Con-vective/diffusive mixing in microscales requires large length and/or time scales; see Chapter 9. Given these limitations, electroosmotically induced mixing has attracted the attention of several research groups. Jacobson et al. have developed parallel and serial mixing mechanisms using microcapillary networks (Jacobson et al., 1999).

In a series of experiments, Santiago and coworkers have observed an electrokinetic instability for flows that are practically in the Stokes flow regime (Oddy et al., 2001; Chen and Santiago, 2002; Chen et al., 2003). Their extensive studies have shown that the electrokinetic instability is due to the conductivity gradients in the fluid, imposed either by the concentration or temperature gradients. In Figure 7.15, we present the time evolution of the electrokinetic flow instability in a microchannel of lenth, 40 mm, width, 1 mm and depth, 100 /am. The image area shown in the figure is 1 mm in the vertical direction and 3.6 mm in the streamwise direction. The channel is filled with two streams of 10 mM HEPES-buffered aqueous solution. The top stream (shown by gray) also included potassium chloride, which increased its conductivity to 50 p,S/cm, while the bottom stream (shown by black) had conductivity of 5 p,S/cm. This created a conductivity gradient in the spanwise direction. It has been found that the electrokinetic instability initiates after applying a critical electric field in the streamwise direction (perpendicular to the conductivity gradients). Figure 7.15 (a) shows time evolution of the electrokinetic instability for a streamwise (horizontal) electric field of 50 V/mm. These experimental results show rapid growth of small-amplitude waves, resulting in fast stirring of the initially distinct buffer streams. Reproduction of dynamics from simplified two-dimensional nonlinear numerical computations are also shown in Figure 7.15. The numerical model reproduces the main features of the instability observed in experiments, including the wave number and time scales. However, the twodimensional approximation shows this rapid mixing at a lower field value of 17.5 V/mm. Details of this electrokinetic instability physics are given in (Lin et al., 2004). Considering the extensive use of electrokinetically driven flows in recent microflow applications, electrokinetic instability can be utilized to design efficient micromixers. For example, the work described in (Oddy et al., 2001), has demonstrated that time-periodic electroosmotic flows obtained by oscillatory electric fields can potentially result in fast mixing.

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