The Contact Angle Saturation Influence on a Drop Dynamics in a Non-uniform Alternating Electric Field

A theoretical model of electrowetting on a dielectric substrate is proposed taking into account the saturation of the dynamic contact angle from the electric voltage in this article. As an example, forced oscillations of an electrolyte droplet placed between two parallel solid surfaces in an alternating electric field are considered. In the state of mechanical equilibrium, the droplet has the shape of a round cylinder whose symmetry axis is perpendicular to the plates. The velocities of the contact lines on both surfaces depend on the external periodic force of the electric field and the deviation of the contact angle from its equilibrium value. To describe the surface inhomogeneity, it is assumed that the proportionality coefficient is a function of coordinates. This function is individual for each surface. It is shown that this leads to the excitation of additional azimuthal modes, in contrast to the case of homogeneous surfaces. The external alternating electric field is also spatially inhomogeneous, since it is difficult to achieve a uniform field in experiments with finite conductor sizes. It is found that the inhomogeneity of the plates changes the value of the saturation angle. Qualitative agreement with experiments was demonstrated.