# Interdisciplinary Applied Mathematics

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FIGURE 8.12. Sketches illustrating the basic principle of light actuation of liquid droplets (Optoelectrowetting). (Courtesy of M.C. Wu.)

FIGURE 8.13. Optoelectrowetting: Contact angle of a water droplet versus light intensity (Chiou et al., 2003). (Courtesy of M.C. Wu.)

to 7 mm/s were recorded, which are much higher than velocities achieved by thermocapillary but lower than standard electrowetting. The liquid microdroplet follows the path of the laser beam (4 mW power). A change in contact angle up to 30° was demonstrated in (Chiou et al., 2003). However, the saturation phenomenon encountered in conventional electrowetting was present here too. In Figure 8.13 we plot the measured contact angle as a function of the light intensity obtained in the experiments of (Chiou et al., 2003). The results are in agreement with the Young-Lippmann formula if

FIGURE 8.14. Sketch of bubble trains and details in the gap. Here V denotes voltage, h is the annular gap size, Zb is the zeta potential, U0 is the bubble velocity, and C0 is the KCL concentration.

we substitute V = 70 (rms value), d =1 ym, e = 4 x 8.854 x 10~12 F/m, and y = 73 N/m; the saturation angle is about 75°.

This technique, which exploits light actuation combined with electrowetting, enables a large number of electrodes to be addressed for multifunctioning lab-on-a-chip operation without wiring bottlenecks.

##### 8.7 Bubble Transport in Capillaries

Transport of long bubbles and organic liquid droplets is required in microgenerators, microreactors, and drug delivery applications. The droplets, for example, can be drugs, while air bubbles can be used as spacers to separate samples along a pathway in a network of microchannels. The air bubbles can also be used as pumps, e.g., as pistons that drive the flow, or as valves as in ink-jet printers. The motion of droplets and bubbles in pipes has been studied in the classical work of (Bretherton, 1961) and in many subsequent papers; see, for example, (Ratulowski and Chang, 1989), and references therein. In microfluidic applications it is interesting to determine the maximum speed of transporting bubbles in microchannels and to understand the physical mechanisms that control this transport.

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