Hydrodynamic instabilities of nematic liquid crystals under A. C. electric fields

This is the authors' abstract. We don't add key points for this paper.

We present an extension of the Helfrich theory of hydrodynamic instabilities to the case of alternating electric fields. The electrohydrodynamic effects are described by two coupled equations for the charge density (q) and the local curvature of the molecular alignment (ψ). The relaxation time for q is the dielectric relaxation time τ (∼ 10-2 s in typical samples). The relaxation time T for ψ is strongly dependent on the field magnitude. Provided that the sample thickness d is above a certain limit dc, the nature of the instability is very different, depending on the ratio of the field frequency ω to a critical frequency ω c. For ω < ωc the onset of instability corresponds to a charge q which oscillates at the frequency ω, while the curvature ψ is essentially time independent. For ω > ωc the situation at threshold corresponds to a constant q and an oscillating ψ. These predictions, together with the calculated curves of threshold voltage vs ω and d, are in reasonable agreement with a number of recent experiments.