Spatial and temporal behavior of pattern formations and defect motions in the electrohydrodynamic instability of nematic liquid crystals

Pattern-formation processes and the associated defect motions are experimentally studied for various rectangular cells with aspect ratios Γ ranging from 8 to 15 in the electrohydrodynamic instability (EHD). Wave-number selection arises from the competition between the most rapidly growing mode $k_c$, which dominates initially, and the final stable mode $k_m$ in the Williams domain (WD) state, which is influenced by the cell boundaries as well as nonlinear effects. Defect motion is associated with such competitive growth into the final stage. The fluctuating Williams domains (FWD’s) are strongly related to the oscillatory gliding motion of defects. A temporally nonperiodic change of the number of defects is observed in the FWD state with a power spectrum of 1/f type (defect chaos). For a step change in the external voltage, a clear threshold for the onset of FWD is determined. On the other hand, when the voltage is increased continuously no defect is formed at the threshold for WD, and nondecaying defect motion starts at a certain threshold value. A large hysteresis is observed near the onset of FWD.