  We consider the problem of electrowetting on dielectric (EWoD). The system
involves the dynamics of a conducting droplet, which is immersed in another
dielectric fluid, on a dielectric substrate under an applied voltage. The fluid
dynamics is modeled by the two-phase incompressible Navier-Stokes equations
with the standard interface conditions, the Navier slip condition on the
substrate, and a contact angle condition which relates the dynamic contact
angle and the contact line velocity, as well as the kinematic condition for the
evolution of the interface. The electric force acting on the fluid interface is
modeled by Maxwell's equations in the domain occupied by the dielectric fluid
and the dielectric substrate. We develop a numerical method for the model based
on its weak form. This method combines the finite element method for the
Navier-Stokes equations on a fixed bulk mesh with a parametric finite element
method for the dynamics of the fluid interface, and the boundary integral
method for the electric force along the fluid interface. Numerical examples are
presented to demonstrate the accuracy and convergence of the numerical method,
the effect of various physical parameters on the interface profile, and other
interesting phenomena such as the transportation of droplet driven by the
applied non-uniform electric potential difference.
