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

Lattice Boltzmann modeling of cholesteric liquid crystal droplets under an oscillatory electric field