# Interdisciplinary Applied Mathematics

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The basic electrowetting mechanism was discovered over a century ago by (Lippmann, 1875), who observed that electrostatic charge may modify capillary forces. This principle was introduced to microfluidics by (Mat-sumoto and Colgate, 1990), who attempted to design micropumps based on controlling surface tension using electric potentials. Perhaps the simplest implementation is continuous electrowetting (CEW), which uses liquid metal droplets (e.g., mercury) in a filler liquid, thus requiring two liquids in the system. CEW exploits changes in the surface tension of the liquid metal-liquid (electrolyte) system at the liquid-solid-gas interface. This is demonstrated in the sketch of Figure 8.8(a) adopted from the work of (Lee et al., 2002). Flow motion is induced due to the different surface tension at the two menisci caused by the electric potential.

Two other forms of electrocapillary are electrowetting (EW) and electrowetting-on-dielectric (EWOD). Unlike CEW, these methods can be used to move aqueous liquid in microchannels without the presence of a second liquid medium, so    the    droplet    in    this case is in    contact    with    air,    just    as

in thermocapillary. EW and EWOD exploit changes in the solid-liquid surface tension, which in turn changes the contact angle. Specifically, in EW an electrical double layer (EDL) is formed between the electrode and aqueous solution that is between 1 nm and 10 nm thick. Applying a voltage difference as shown in the sketch of Figure 8.8(b) may cause a hydrophobic surface to behave like a hydrophilic one. In essence, the electric energy counterbalances the free surface energy and lowers the surface tension %. In EWOD there is no electric double layer, but the change in the energy balance takes place in the hydrophobic dielectric layer; in (Lee et al., 2002), a Teflon layer 0.8 /am thick was used. The basic principle is demonstrated in the sketch of Figure 8.8(c) adopted from the work of (Lee et al., 2002).

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