Lagrangian chaos and particle diffusion in electroconvection of planar nematic liquid crystals

Two types of spatiotemporal chaos in the electroconvection of nematic liquid crystals, such as defect turbulence and spatiotemporal intermittency, have been statistically investigated according to the Lagrangian picture. Here fluctuations are traced using the motion of a single particle driven by chaotic convection. In the defect turbulence (fluctuating normal rolls), a particle is mainly trapped in a roll but sometimes jumps to a neighboring roll. Its activation energy is then obtained from the jumping (hopping) rate. This research clarifies that diffusion in the defect turbulence regime in electroconvection can be regarded as a kind of hopping process. The spatiotemporal intermittency appears as a coexistent state of ordered grid domains and turbulent domains. The motion of a single particle shows weak and strong diffusion, respectively, in the ordered and turbulent domains. The diffusion characteristics intermittently change from one to another with certain durations as the domains change. This research has found that the distribution function of the duration that a particle remains in an ordered area has a power-law decay for which the index is different from that obtained by the Eulerian measurement.