Analysis of Electrowetting of a Conducting Droplet on a Dielectric Layer

Abstract

Electrowetting has been used to actuate and control the motion of droplets on solid surfaces. An analysis based on the theories of thermodynamics and thermal activation processes is presented for the electrowetting of a conducting droplet on a dielectric layer. The concept of release rate of electric energy is proposed. The release rate of electric energy is proportional to the square of the applied electric voltage and the derivative of electric capacitance with respect to the surface area of the corresponding electric system. The velocity of a contact line under the action of an electric voltage is a hyperbolic sine function of the release rate of electric energy. Using the release rate of electric energy and introducing line tension in the analysis, the contact angle of a droplet at a stationary state under the action of a constant electric voltage is found to be a linear function of the release rate of electric energy and the line tension. The line tension introduces the droplet-size effect on the contact angle. A critical contact angle as a function of the applied electric voltage, the thickness of the dielectric layer, and the radius of the contact area is obtained. There exist stable and unstable zones, depending on the relative value of the contact angle and the critical contact angle. There exists an upper bound of electric voltage with the corresponding contact angle of 65.89 degrees between 60 and 70 degrees of the saturated contact angle reported for electrowetting of conducting droplets. This result suggests that the saturation of contact angle likely is related to the condition determining the field-induced stability of the contact line.