Analysis of electrowetting-driven spreading of a drop in air

Abstract

A set of shape mode equations is derived to describe unsteady motions of a sessile drop actuated by electrowetting. The unsteady, axially symmetric, and linearized flow field is analyzed by expressing the shape of a drop using the Legendre polynomials. A modified boundary condition is obtained by combining the contact angle model and the normal stress condition at the surface. The electrical force is assumed to be concentrated on one point (i.e., three-phase contact line) rather than distributed on the narrow surface of the order of dielectric layer thickness near the contact line. Then, the delta function is used to represent the wetting tension, which includes the capillary force, electrical force, and contact line friction. In previous work [J. M. Oh et al., Langmuir 24, 8379 (2008)], the capillary forces of the air-substrate and liquid-substrate interfaces were neglected, together with the contact-line friction. The delta function is decomposed into a weighted sum of the Legendre polynomials so that each component becomes a forcing term that drives a shape mode of motion. The shape mode equations are nonlinearly coupled between modes due to the contact line friction. The equilibrium contact angle of electrowetting predicted by the present method shows a good agreement with the Lippmann–Young equation and with our experimental results. The present theoretical model is also validated by predicting the spreading of a drop for step input voltages. It shows qualitative agreement with experimental results in temporal evolution of drop shape.