The effect of a stationary electric field on a water droplet with a diameter
of several tens micrometers in oil was examined. Such a droplet exhibits
repetitive translational motion between the electrodes in a spontaneous manner.
The state diagram of this oscillatory motion was deduced; at 0-20 V the droplet
is fixed at the surface of the electrode, at 20-70 V the droplet exhibits
small-amplitude oscillatory motion between the electrodes, and at 70-100 V the
droplet shows large-amplitude periodic motion between the electrodes. The
observed rhythmic motion is explained in a semi-quantitative manner by using
differential equations, which includes the effect of charging the droplet under
an electric field. We also found that twin droplets exhibit synchronized
rhythmic motion between the electrodes