  We present a lattice-Boltzmann method that can simulate the coupled
hydrodynamics and electrostatics equations of motion of a two-phase fluid as a
means to model electrowetting phenomena. Our method has the advantage of
modelling the electrostatic fields within the lattice-Boltzmann algorithm
itself, eliminating the need for a hybrid method. We validate our method by
reproducing the static equilibrium configuration of a droplet subject to an
applied voltage and show that the apparent contact angle of the drop depends on
the voltage following the Young-Lippmann equation up to contact angles of
$\approx 50^\circ$. At higher voltages, we observe a saturation of the contact
angle caused by the competition between electric and capillary stresses. We
also study the stability of a dielectric film trapped between a conducting
fluid and a solid electrode and find a good agreement with analytical
predictions based on lubrication theory. Finally, we investigate the film
dynamics at long times and report observations of film breakup and entrapment
similar to previously reported experimental results.
