The stability of a horizontal interface between two viscous fluids, one of
which is conducting and the other is dielectric, acted upon by a vertical
time-periodic electric field is considered. The two fluids are bounded by
electrodes separated by a finite distance. By means of Floquet theory, the
marginal stability curves are obtained, thereby elucidating the dependency of
the critical voltage and wavenumber upon the fluid viscosities. The limit of
vanishing viscosities is shown to be in excellent agreement with the marginal
stability curves predicted by means of a Mathieu equation. The methodology to
obtain the marginal stability curves developed here is applicable to any
arbitrary but time periodic-signal, as demonstrated for the case of a signal
with two different frequencies. As a special case, the marginal stability
curves for an applied ac voltage biased by a dc voltage are depicted. It is
shown that the mode coupling caused by the normal stress at the interface due
to the electric field leads to appearance of harmonic modes and subharmonic
modes. This is in contrast to the application of a voltage with a single
frequency which always leads to a harmonic mode. Whether a harmonic or
subharmonic mode is the most unstable one depends on details of the excitation
signal. It is also shown that the electrode spacing has a distinct effect on
the stability bahavior of the system
