Hydrodynamic instabilities of nematic liquid crystals with a negative dielectric anisotropy in ac electric fields are theoretically studied. The instabilities considered are due to the development of bend modes coupled with flow fields of equal periodicity (Carr, Helfrich). A simple numerical procedure is developed which allows a convenient and exact calculation of threshold curves and instability regions which depend essentially only on two parameters, the reduced cutoff frequency and the reduced decay time of the bend-shear mode. Results of numerical calculations are presented in stability charts using reduced field and frequency coordinates. Characteristic features of threshold curves are discussed and a general survey is given on the position and the extent of instability regions.

• Received 19 February 1974

DOI:https://doi.org/10.1103/PhysRevA.9.2698