Editing Digital microfluidics (section)

== Working principle ==
Droplets are formed using the [[surface tension]] properties of a liquid. For example, water placed on a hydrophobic surface such as wax paper will form spherical droplets to minimize its contact with the surface.<ref>{{Cite web|url=http://www.appstate.edu/~goodmanjm/rcoe/asuscienceed/background/waterdrops/waterdrops.html|title=Water Drops: Cohesion and Adhesion of Water| vauthors = Goodman J|website=www.appstate.edu|access-date=2017-05-21}}</ref> Differences in surface hydrophobicity affect a liquid’s ability to spread and ‘wet’ a surface by changing the [[contact angle]].<ref>{{Cite web |url= http://web.mit.edu/nnf/education/wettability/wetting.html |title=Wetting|website=web.mit.edu|access-date=2017-05-21}}</ref> As the [[hydrophobicity]] of a surface increases, the [[contact angle]] increases, and the ability of the droplet to wet the surface decreases. The change in contact angle, and therefore wetting, is regulated by the Young-Lippmann equation.<ref name="Jain_2017" /><ref name="Berthier_2008" /><ref name="Choi_2012" />
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<math>\cos(\theta)=\cos(\theta{_0})+\frac{\varepsilon{_0}\varepsilon{_r}V^2}{{2\gamma}d}</math>

where <math>\theta</math> is the contact angle with an applied voltage <math>V</math>; <math>\theta{_0}</math> is the contact angle with no voltage; <math>\varepsilon{_r}</math> is the relative [[permittivity]] of the dielectric; <math>\varepsilon{_0}</math> is the [[Vacuum permittivity|permittivity of free space]]; <math>\gamma</math> is the liquid/filler media surface tension; <math>d</math> is the dielectric thickness.<ref name="Choi_2012" />

In some cases, the [[hydrophobicity]] of a substrate can be controlled by using electrical fields. This refers to the phenomenon [[Electrowetting]] On Dielectric ([[EWOD]]).[[Digital microfluidics#cite note-Chang-3|[3]]][[Digital microfluidics#cite note-Kirby-4|[4]]]<ref name="Choi_2012" /> For example, when no electric field is applied to an electrode, the surface will remain hydrophobic and a liquid droplet will form a more spherical droplet with a greater contact angle. When an electric field is applied, a polarized hydrophilic surface is created. The water droplet then becomes flattened and the contact angle decreases. By controlling the localization of this polarization, we can create an interfacial tension gradient that allows controlled displacement of the droplet across the surface of the DMF device.<ref name="Fair_2007"/>