Abstract
We develop a one-dimensional theory of electrohydrodynamic instabilities in nematics under AC excitation by incorporating the flexoelectric terms. The results account for the following observations which were not adequately explained earlier: (1) the occurrence of oblique rolls (OR) at a threshold voltage Vth (ν) up to a certain well defined frequency νo which depends on the conductivity of the sample, (2) the occurrence of OR at voltages > Vth at which normal rolls are seen for some frequency range νc>ν>νo, (3) the observation of ‘chevrons’ in the dielectric regime and (4) the occurrence of ‘longitudinal’ rolls with a field threshold for materials with a negative dielectric anisotropy close to the nematic—smectic transition point.