Electrowetting films on parallel line electrodes

A lubrication analysis is presented for the spreading dynamics of a high permittivity polar dielectric liquid drop due to an electric field sustained by parallel line electrode pairs separated by a distance R-e. The normal Maxwell stress, concentrated at the tip region near the apparent three-phase contact line, produces a negative capillary pressure that is responsible for pulling out a thin finger of liquid film ahead of the macroscopic drop, analogous to that obtained in self-similar gravity spreading. This front-running electrowetting film maintains a constant contact angle and volume as its front position advances in time t by the universal law 0.43R(e)(t/T-cap)(1/3), independent of the drop dimension, surface tension, and wettability. T-cap=pi(2)mu R-l(e)/8 epsilon(0)epsilon V-l(2) is the electrocapillary time scale where mu(l) is the liquid viscosity, epsilon(0)epsilon(l) the liquid permittivity, and V the applied voltage. This spreading dynamics for the electrowetting film is much faster than the rest of the drop; after a short transient, the latter spreads over the electrowetting film by draining into it. By employing matched asymptotics, we are able to elucidate this unique mechanism, justified by the reasonable agreement with numerical and experimental results. Unlike the usual electrowetting-on-dielectric configuration where the field singularity at the contact line produces a static change in the contact angle consistent with the Lippmann equation, we show that the parallel electrode configuration produces a bulk negative Maxwell pressure within the drop. This Maxwell pressure increases in magnitude toward the contact line due to field confinement and is responsible for a bulk pressure gradient that gives rise to a front-running spontaneous electrowetting film.