Sub-Diffusion in Electroconvective Turbulence of Homeotropic Nematic Liquid Crystals

Diffusion resulting from turbulence corresponding to dynamic scattering mode 1 (DSM1) of electroconvection was studied in experiments on homeotropically aligned systems of nematic liquid crystals. In such systems, electroconvection displays peculiar nonlinear phenomena arising from the interaction between its convection and the nematic director yielding Nambu-Goldstone modes. From an analogy with Brownian motion, the motion of tagged particles driven by the turbulence was analyzed using the time-dependent coefficient of diffusion, defined as the mean-square displacement divided by time. The results indicate that sub-diffusion occurs in a certain time range, suggesting that turbulence causes particles to rebound. Detailed observations of turbulence structures revealed that rebounding is induced by characteristic linear structures of the nematic director caused by turbulence. This sub-diffusion arising from the interaction between the nematic director and turbulence is specific to nematic liquid crystals.