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# Electrowetting

The electrowetting behavior of mercury and other liquids on variably charged surfaces was probably first explained by Lipmann in 1875 and was certainly observed much earlier. Froumkin used surface charge to change the shape of water drops in 1936. The term electrowetting was first introduced in 1981 to describe an effect proposed for designing a new type of display device . Digital microfluidic manipulation of chemical and biological fluids was first investigated by J. Brown in 1984-1989 , demonstrating valves, pumps and digitally relocatable nano droplets. In the past 25 years or so, a large number of devices based on electrowetting have been devised. In particular, electrowetting has been used successfully as one of several techniques to actuate microdroplets in a digital microfluidic device. In many of these applications, electrowetting allows large numbers of droplets to be independently manipulated under direct electrical control without the use of external pumps, valves or even fixed channels.

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.

## Electrowetting Theory

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:
$gamma_\left\{ws\right\} ,$ - The total, electrical and chemical, surface tension between the electrolyte and the conductor
$gamma_\left\{ws\right\}^0 ,$ - The surface tension between the electrolyte and the conductor at zero electric field
$gamma_s ,$ - The surface tension between the conductor and the external ambient
$gamma_w ,$ - The surface tension between the electrolyte and the ambient
$theta$ - The macroscopic contact angle between the electrolyte and the dielectric
$C$ - The capacitance of the interface, єrє0/t, for a uniform dielectric of thickness t and permittivity єr
$V$ - 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:

$gamma _\left\{ws\right\} = gamma _\left\{ws\right\}^0 - frac\left\{CV^2\right\}\left\{2\right\} ,$

The contact angle is given by the Young-Dupre equation, with the only complication being that the total surface energy $gamma_\left\{ws\right\}$ is used:

$gamma_\left\{ws\right\} = gamma_s + gamma_w cos\left(theta\right) ,$

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

$theta = cos^\left\{-1\right\}\left(frac\left\{gamma _\left\{ws\right\}^0-gamma_s-frac\left\{CV^2\right\}\left\{2\right\}\right\}\left\{gamma_w\right\}\right) ,$

An additional complication is that liquids also exhibit a saturation phenomena: 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. The ultimate and complete explanation of electrowetting, mainly because of this effect, is still missing.

## Materials

For reasons that are still under investigation, only a limited set of surfaces exhibit the theoretically predicted electrowetting behavior. Amorphous fluoropolymers are by far the best electrowetting materials discovered so far, and it has been found that their behaviour can be enhanced by the appropriate patterning. Three types of such polymers are commercially available: FluoroPel is sold by the Cytonix Corporation, CYTOP is sold by Asahi Glass Co., and Teflon AF is sold by DuPont.

## Applications

Electrowetting is now used in a wide range of applications from modulab to adjustable lenses, electronic displays and switches for optical fibers.