Electrowetting - Electrowetting Theory

Electrowetting Theory

The electrowetting effect has been defined as "the change in solid-electrolyte contact angle due to an applied potential difference between the solid and the electrolyte". The phenomenon of electrowetting can be understood in terms of the forces that result from the applied electric field. The fringing field at the corners of the electrolyte droplet tend to pull the droplet down onto the electrode, lowering the macroscopic contact angle and increasing the droplet contact area. Alternatively, electrowetting can be viewed from a thermodynamic perspective. Since the surface tension of an interface is defined as the Gibbs free energy required to create a certain area of that surface, it contains both chemical and electrical components, and charge becomes a significant term in that equation. The chemical component is just the natural surface tension of the solid/electrolyte interface with no electric field. The electrical component is the energy stored in the capacitor formed between the conductor and the electrolyte.

The simplest derivation of electrowetting behavior is given by considering its thermodynamic model. While it is possible to obtain a detailed numerical model of electrowetting by considering the precise shape of the electrical fringing field and how it affects the local droplet curvature, such solutions are mathematically and computationally complex. The thermodynamic derivation proceeds as follows. Defining the relevant surface tensions as:

- The total, electrical and chemical, surface tension between the electrolyte and the conductor

- The surface tension between the electrolyte and the conductor at zero electric field

- The surface tension between the conductor and the external ambient

- The surface tension between the electrolyte and the external ambient

- The macroscopic contact angle between the electrolyte and the dielectric

- The capacitance of the interface, є_rє₀/t, for a uniform dielectric of thickness t and permittivity є_r

- The effective applied voltage, integral of the electric field from the electrolyte to the conductor

Relating the total surface tension to its chemical and electrical components gives:

The contact angle is given by the Young-Dupre equation, with the only complication being that the total surface energy is used:

Combining the two equations gives the dependence of θ on the effective applied voltage as:

An additional complication is that liquids also exhibit a saturation phenomenon: after certain voltage, the saturation voltage, the further increase of voltage will not change the contact angle, and with extreme voltages the interface will only show instabilities.

However, surface charge is but one component of surface energy, and other components are certainly perturbed by induced charge. So, a complete explanation of electrowetting is unquantified, but it should not be surprising that these limits exist.

It was recently shown that contact angle saturation can be explained if electrowetting is observed as a global phenomenon affected by the detailed geometry of the system. Within this framework it is predicted that reversed electrowetting is also possible (contact angle grows with the voltage).

It has also been experimentally shown by Chevaloitt that contact angle saturation is invariant to all materials parameters, thus revealing that a universal theory for saturation is still lacking, and that when good materials are utilized, most saturation theories are invalid. This same paper further suggests that electrohydrodynamic instability may be the source of saturation, a theory that is unproven but being suggested by several other groups as well.