# Electrowetting on dielectric

Electrowetting on dielectric (EWOD) refers to the specific case of electrowetting in which the liquid of interest is resting on a dielectric layer. Electrowetting is the change in contact angle along the three-phase contact line, due to applied electric fields. In EWOD, a voltage can be applied across the liquid through an electrode beneath the dielectric which is referenced to an electrode directly in contact with the liquid. The applied voltage results in an increase in the surface energy at the liquid-dielectric interface, which in turn leads to an increase in the liquid's contact angle with the surface.

Lippman's Equation, shown below, shows the change in the liquid-dielectric surface energy with applied voltage.

- <math>\gamma_{SL}(V) = \gamma_{SL}|_{V=0} - \frac{1}{2}CV^2</math>

where <math>\gamma_{SL}</math> is the surface energy of the solid-liquid interface, and <math>C</math> is the specific capacitance of the dielectric layer in Farads per square metre. If we substitute this expression into Young's equation, the change of contact angle can be expressed as follows:

- <math>cos[\theta(V)] - cos \theta_o = \frac{\epsilon_o \epsilon}{2\gamma_{LG}t}V^2</math>

where <math>\theta_o</math> is the equilibrium contact angle with no applied voltage, <math>\epsilon_o</math> is the permittivity of free space, <math>\epsilon</math> is the dielectric constant of the dielectric layer, <math>t</math> is the thickness of the dielectric layer, and <math>\gamma_{LG}</math> is the surface tension of the liquid. Notice in particular that the change in contact angle is independent of the sign of the applied voltage, which verifies that the contact angle increases independent of the polarity of the applied voltage.

## References

- "Creating, Transporting, Cutting, and Merging Liquid Droplets by Electrowetting-Based Actuation for Digital Microfluidic Circuits". Sung Kwon Cho, Hyejin Moon, and Chang-Jin Kim. Journal of Microelectromechanical Systems (2003), 12(1), 70-80.