# Interdisciplinary Applied Mathematics

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Young-Lippmann equation that we will study in the next section.

A proof-of-concept    experiment    for    EW    was    conducted    in    (Lee    et    al.,

2002), with a liquid droplet (Na2SO4) squeezed between an electrode and a cover glass, as shown in the schematic of Figure 8.9, subject to about 1 volt. Without the cover glass, microdroplets evaporate very quickly. The contact angle on the cover glass (coated with a hydrophobic layer) is not changed, but the wettability of the lower surface is changed by the electric potential. The pressure difference inside the liquid droplet and the air (p — pa) can be computed from Laplace’s equation, assuming a spherical geometry, to obtain

Y l

p~Pa = “» ( COS 0 ~~ COS ),

where d is the microchannel height.

Similarly, a proof-of-concept experiment was conducted in (Lee et al., 2002), to test EWOD. A water droplet was placed on a Teflon-coated surface (hydrophobic), and it was demonstrated that upon applying a voltage of about 100 V, the surface switched to hydrophilic, causing spreading of the droplet. To compute the pressure build-up in this case we refer to the schematic of Figure    8.10 adopted from    (Lee    et    al.,    2002).    On    the    left    end

of the meniscus, we have

Y i

PL ~Pa = “T» (COS 0 T COS \$50 ) > 0,

d

 Glass . A. ‘Teflon’* iquid >=> Aqueous __ ■
##### Teflon*

FIGURE 8.10. Electrowetting-on-dielectric (EWOD) device with electric potential on corresponding to a hydrophilic lower surface (Lee et al., 2002). (Courtesy of C.-J. Kim.)

while on the right end of the meniscus, we have

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