  We numerically study the dynamics of quasi-two dimensional cholesteric liquid
crystal droplets in the presence of a time-dependent electric field, rotating
at constant angular velocity. A surfactant sitting at droplet interface is also
introduced to prevent droplet coalescence. The dynamics is modeled following a
hybrid numerical approach, where a standard lattice Boltzmann technique solves
the Navier-Stokes equation and a finite difference scheme integrates the
evolution equations of liquid crystal and surfactant. Our results show that,
once the field is turned on, the liquid crystal rotates coherently triggering a
concurrent orbital motion of both droplets around each other, an effect due to
the momentum transfer to the surrounding fluid. In addition the topological
defects, resulting from the conflict orientation of the liquid crystal within
the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in
contrast with a regular one occurring along circular trajectories observed in
nematics drops. Such behavior is found to depend on magnitude and frequency of
the applied field as well as on the anchoring of the liquid crystal at the
droplet interface. These findings are quantitatively evaluated by measuring the
angular velocity of fluid and drops for various frequencies of the applied
field.
