  The wetting properties of immiscible two-phase systems are crucial in a wide
range of applications, from lab-on-a-chip devices to field-scale oil recovery.
It has long been known that effective wetting properties can be altered by the
application of an electric field; a phenomenon coined as electrowetting. Here,
we consider theoretically and numerically a single droplet sitting on an
(insulated) conductor, i.e., within a capacitor. The droplet consists of a pure
phase without solutes, while the surrounding fluid contains a symmetric
monovalent electrolyte, and the interface between them is impermeable. Using
nonlinear Poisson--Boltzmann theory, we present a theoretical prediction of the
dependency of the apparent contact angle on the applied electric potential. We
then present well-resolved dynamic simulations of electrowetting using a
phase-field model, where the entire two-phase electrokinetic problem, including
the electric double layers (EDLs), is resolved. The simulations show that,
while the contact angle on scales smaller than the EDL is unaffected by the
application of an electric field, an apparent contact angle forms on scales
beyond the EDL. This contact angle relaxes in time towards a saturated apparent
contact angle. The dependency of the contact angle upon applied electric
potential is in good compliance with the theoretical prediction. The only
phenomenological parameter in the prediction is shown to only depend on the
permeability ratio between the two phases. Based on the resulting unified
description, we obtain an effective expression of the contact angle which can
be used in more macroscopic numerical simulations, i.e. where the
electrokinetic problem is not fully resolved.
