7.3 Passive Micromixers
7.3.2 Electrically Driven Passive Micromixers
Micromixers 185 be promising for integration into multifunction biochips especially if man- ufactured successfully on various biocompatible materials.
The potential of attaining improved mixing by placing obstacles in micro- channels has also been explored. While it is well known that at very low Reynolds numbers obstacles cannot generate secondary flows such as recir- culations, it is possible to achieve this at higher Reynolds numbers. This was also shown in a numerical study by Wang et al.,40 who investigated the effect on mixing due to various arrangements of cylindrical obstacles in a micro- channel. An effective micromixer incorporating staggered cylindrical obsta- cles in a mixing chamber was demonstrated by Lin et al.41 on a silicon chip generating fluid streams of high Reynolds numbers (approximately 380). A ceramic cross-junction microchannel mixer with sidewall obstacles was dem- onstrated also at high Reynolds numbers (greater than 100) by Wong et al.42 This configuration produces essentially a serpentine channel and the benefits are predominantly due to the successive bends. Micromixers employing obstacles can be realized with relative ease using single-layer or wafer man- ufacturing processes, yet the high Reynolds number requirements imply high operating pressures, which is the major drawback of this approach.
Swirl chambers have also been employed on the microscale to achieve effective mixing. The multi-inlet design of Böhm et al,43 realized in a glass- covered silicon chip using two wafers and DRIE is an early example of this type. It was a very effective mixing device, but required very high pressures (15 atmospheres) and a costly manufacturing process. Recently Lin et al.44 simulated and demonstrated a multi-inlet swirl-chamber micromixer with performance at low Reynolds numbers (less than 20) realized in a multilayer silicon chip. Swirl-chamber mixers can be effective micromixing devices, but in general they require multilayer manufacturing, high pressures, and increased volume.
A combination of a microvalve and chamber design was realized by Vold- man et al.45 to provide both mixing and valving action on a glass-covered silicone chip. This was micromanufactured in two silicon wafers, one of which incorporated a cantilevered flap-valve element, and required DRIE.
This dual-function device, which performed reasonably well in terms of mixing time for batch applications, could also be used as an active mixer with improved performance by pulsing the supply of the valved fluid.
186 Bio-MEMS: Technologies and Applications
mixing performance was improved by approximately an order of magnitude relative to a reference Y-junction electroosmotically driven mixing channel.
A variety of chamber-based electroosmotic mixers were proposed by Yager et al.47 relying on recirculations generated by pressure gradients imposed by the conservation of mass. The simplest realization of the device involves a microscale mixing channel with electrodes (A and B) at each end as in Figure 7.1a. When a potential difference is applied between electrodes A and B, the fluid will be set into motion near the wall region with a velocity in proportion to the electroosmotic mobility of the wall material. Because the ends of the mixing channel (between A and B) cannot be penetrated by the flow, con- servation of mass will dictate a flow inside the core of the cross-section in the opposite direction to that near the walls. Thus a recirculating flow will be established within the mixing channel with shear layers in the proximity of the walls. This is shown in the numerical simulation results of Figure 7.148 for a channel incorporating material nonhomogeneity. The upper part of the channel has a different elecroosmotic mobility than the lower part. The resulting recirculating flow field is shown in Figure 7.1 where it is clearly visible that the fluid is moving in one direction in the proximity of the wall, while it is moving in the opposite direction in the core. Because of the unequal mobility of the top and bottom parts of the channel, flow is not symmetrical with respect to all the geometrical axes of symmetry. The near wall velocity is higher on the top half compared to the bottom half, and as a result the return velocity is higher in the lower part of the core. Consequently, the shear layers on the top half and bottom half are of unequal strengths. The top-to- bottom asymmetry will be absent if the channel has homogeneous mobility.
This flow is effective in mixing because it folds material lines multiple times in a short period of time, depending on the potential difference level (88 material lines caused by the recirculating flow, which is responsible for the effective mixing function. A plug of liquid with a substantially low mass diffusion coefficient (1.2 10–10 m2/sec) is mixed with a second liquid to form approximately 40 nL of a 2.78% mixture in less than one second. This illus- trates the effectiveness of this type mixer.
FIGURE 7.1
Main velocity component contours in chamber electroosmotic micromixer (a) streamwise mid- plane, x = 0 µm; (b) cross-flow midplane, y = 0 µm.
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volts in this example). Figure 7.2 illustrates this stretching and folding of
Micromixers 187
Based on the analytical work of Ajdari,49 recent technological advances in microfabrication have enabled the development of a variety of complex
50).
This ability has motivated a number of efforts to explore electroosmotic passive micromixers based on inhomogeneous surface-charge distribution in microchannels. These generate secondary flows much like geometrical nonhomogeneous patterns do in pressure-driven flows. Numerical predic- tions by Erickson and Li51 on an electroosmotically driven T-junction micro- channel mixer with alternating surface-charge (or zeta potential) sign on its side walls demonstrated that mixing can indeed be improved in this manner.
Similar simulations on a broader variety of surface-charge patterns were conducted by Qian and Bau,52 who also demonstrated how chaotic advec- tion and associated mixing benefits can be generated in such heteroge- neously charged devices. Another numerical study by Hong et al.53 demonstrated improved mixing using angled and herringbone patterns of
FIGURE 7.2
Concentration contours in chamber electroosmotic micromixer on streamwise midplane, x = 0 µm (a) t = 10 µs, (b) t = 200 µs, (c) t = 500 µs, (d) t = 780 ms; mass diffusion coefficient is 1.2 10–6 cm2/s and 2.78% mixture.
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microscale charge patterns on material surfaces (e.g., see Stroock et al.
188 Bio-MEMS: Technologies and Applications inhomogeneous surface-charge distributions based on the grooved channel configurations used by Stroock et al.36 in a counterpart pressure-driven flow.
T-junction mixers with inhomogeneous surface-charge distributions have been successfully demonstrated on a microchip by Wu and Liu54 in a low- aspect-ratio (0.3) PDMS microchannel on a silicon substrate by implanting patterned electrodes into the silicon substrate. Applying voltage of alternating signs to successive electrodes generated a nonuniform charge distribution on the bottom wall of the channel, resulting in secondary flows during operation and improved mixing performance. Glass T-junction micromixers with vari- ous heterogeneous zeta potential patterns in very low aspect- ratio micro- channels (0.04) have been manufactured by Biddiss et al.55 They used soft lithography techniques to chemically pattern the glass microchannel bottom surface. Both physical realizations54,55 of this very interesting concept achieved significant mixing enhancement relative to their homogeneous counterparts.
Widespread practical usage in integrated chips of these types of enhanced micromixers may be hampered by the manufacturing process complexity and the durability and shelf life of surface modification when the latter is the chosen method of introducing surface-charge nonuniformity. Much like many electrokinetically driven devices, these micromixers are limited to very low flow rates dictated by the requirement of keeping the driving voltages low.
Secondary flows associated with electrohydrodynamic (EHD) instability generated by conductivity gradients in the working fluid have also been shown through simulation and experimentation to enhance mixing by Lin et al.56 and could be promising for a practical mixing device of fluids with inherent or imposed conductivity gradients in the practical environment.
Coupled electrorotation of latex microspheres has been proposed and dem- onstrated by Wilson et al.57 on a glass chip with two electrodes separated by a PDMS wedge, and although intrusive, may be promising for inducing fast local mixing in microfluidic environments.