Interdisciplinary Applied Mathematics

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FIGURE 9.4. A: Schematic of microchannel with the V-grooves and of streamlines showing the secondary induced motion at the two halves of the periodic array of grooves. Here h = 77 pm, a = 0.23,q = 2n/100 pm-1. B: Confocal micrographs of vertical cross-sections at different distances from the inlet. (Courtesy of H.A. Stone.)

inlet. By cycling bubble generation and collapse, a net pumping action is achieved. Steam bubbles can be generated by heat; upon heat removal the steam condenses and the bubble collapses. Electrolysis bubbles can also be used. This micromixer was fabricated using SOI (silicon on insulator) and quartz wafers bonded together using epoxy. Bubbles were created using polysilicon resistors on quartz, which act as heaters. The designs tested in    (Deshmukh    et    al.,    2000),    use    1 to 4    watts    per    pump,    which is    quite

inefficient. Another practical issue is that the valves and substrate, which are made of bare silicon, sometimes stick together, since water is a poor lubricant on silicon surfaces.

A novel concept of an active micromixer was introduced in (Volpert et al., 1999). It is based on mixing a sequence of shear flows at different angles, and it is called the “shear superposition micromixer,” or SSM. In contrast to the pulsatile micromixer we described above, the SSM is a continuous through-flow micromixer consisting of the main channel and three cross-flow side channels. The side-channels produce a time-dependent shear flow in the direction transverse to the main flow. The frequency of actuation in the three side-channels increases downstream to accommodate the decreasing scales that need to be further mixed downstream. A sketch of SSM and a micrograph of the actual device is shown in Figure 9.6; a typical range of

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