# Interdisciplinary Applied Mathematics

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PR — Pa =—^-(cOS0 + COS0b) < 0,

where d is the channel height, which is equal to the droplet height. The pressure difference within the liquid droplet is then

Y i

PL — PR = Y~(cOSeb — COS 060),

which shows that the surface angle on the cover glass does not influence the spreading process. Using the Young-Lippmann equation (8.19) we can eliminate the contact angles alltogether to obtain

cU2    eoeV2

PL~PR-^d-^r’

where t is the thickness of Teflon (1 pm in (Lee et al., 2002)), d = 10pm, e0 = 8.854x 10~12 C/V is the vacuum permittivity, and e = 2.0 is the Teflon permittivity. As pointed out in (Lee et al., 2002), it is somewhat surprising to see, at least for this application, that the surface tension is not present in the above equation, although flow motion occurs due to surface tension changes between the liquid and the solid! Clearly, if hysteresis effects are present, then Ysi will be involved explicitly in the above pressure equation. With regards to efficiency, a large voltage is required in EWOD (about 100 volts compared to EW of about 1 volt) due to the relatively thick layer of the Teflon dielectric layer. For a very thin dielectric layer on the order of 0.1 pm or less, the required voltage is about 20 volts (Lee et al., 2002).

In summary, the EW method is appropriate for electrolytes and is energetically quite efficient. In contrast, the EWOD method can handle any

aqueous liquids, but it requires substantially higher voltage. Switching between hydrophobic and hydrophilic surfaces using electric potential is, in principle,    a    reversible    process,    but    other parasitic    effects    may    affect    re

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