Interdisciplinary Applied Mathematics

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FIGURE 7.26. Optical micrograph of a growing microwire. Contours show nanoparticle concentration around the wire (a). The microwires generate complex connections    with    conductive    islands    (b),    which    is    achieved    by electric    field

disturbance imposed by the conductive surfaces. (Courtesy of O. Velev.).


Surface Tension-Driven Flows

Capillary phenomena involving wetting and spreading of liquid thin films and droplets have been studied for a long time for modeling of classical engineering applications such as coating and lubrication. This same body of theoretical and experimental knowledge can be of great use in microfluidic research and design. For microfluidic delivery on open surfaces, electrowetting and thermocapillary along with dielectrophoresis have been employed to move continuous or discrete streams of fluid, for example droplets along specified paths on glass surfaces (Sammarco and Burns, 1999; Kataoka and Troian, 1999;    Lee et    al.,    2002).    A    new    method    of actuation    exploits    opti

cal beams and photoconductor materials in conjunction with electrowetting (Ichimura et al., 2000). Such electrically or lithographically defined paths can be reconfigured dynamically using electronically addressable arrays that respond to electric potential, temperature, or laser beams and control the direction, timing, and speed of fluid droplets. Mixing two fluids in T-junctions creates interesting structures that can be manipulated in a controlled fashion. An example is shown in Figure 8.1, which shows droplet breakup by extensional flow, i.e., a flow in which fluid elements are only stretched in a network of T-junctions. Specifically, water slugs are broken into    droplets    in    oil,    a scaled-up    version    of    the    experiment    shown

in Figure 1.24. Here the microchannels have a rectangular cross-section 50 pm x 25 pm. Exploiting this concept, one can produce more than a few hundred droplets per second. The size of the droplets can be controlled by the lengths of the arms of the corresponding T-junction (Link et al., 2004).

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