Instability Carr-Helfrich

Electric field effects are more complicated because of conduction. The Carr-Helfrich instability, which occurs in nematics of negative dielectric anisotropy (see 3.10.2), may be expected to take place in this case too, only the bend and twist distortions are now coupled. Moreover, the fluid motion along z can occur only by the process of permeation ( 4.5.1). 

The other two instabilities shown in Fig. 28 may be observed only in liquid crystals (nematic, cholesteric, and smectic C). The first is the Carr-Helfrich instability, which is caused by a low-frequency electric field and occurs in the form of elongated vortices with their axis perpendicular to the original director alignment. The vortices cause a distortion of the director orientation, which is observed optically as a one-dimensional periodic pattern (Kapustin-Williams domains). The other anisotropic mode is observed only in highly conductive liquid crystals. For its interpretation the inertial term dvidt for the fluid velocity must be taken into account, which is why this mode may be called inertial mode. 

Fig. 11. 33 Carr-Helfrich EHD instability in nematic liquid crystals (a) onset of the instability showing a competition of the elastic and hydrodynamic torques (b) photo of Williams domains observed at a voltage 7.5 V in a 20 pm thick cell filled with liquid crystal MBBA...

References [59] investigate the static and dynamic behavior of the electrohydrodynamic instability in fireely suspended layers of nematic liquid crystals. The existence of a domain mode was shown, which consists of adjacent elongated domains with a spatial period proportional to the thickness of the layer. This mode occurs only if the thickness of the layer exceeds a critical value 7 /x), and can be understood in terms of the same anisotropic mechanism as the Carr-Helfrich-type, as in the case of the Kapustin-WiUiams modulated structure. 

Thus, to date we have three theoretically predicted modes for a high-frequency instability caused by the Carr-Helfrich anisotropic mechanism. They are the conductance and dielectric regimes and the inertia mode. Two of these (the conducting regime and the inertia mode) correspond to the steady-state motion of the liquid and the stationary deviations of the... 

We now explicitly include in the discussion the anisotropy of the electrical conductivity (Xj of a liquid crystal. This anisotropy itself turns out to be a reason for electrohydrodynamic destabilization. First, we discuss the Carr-Helfrich mode of the instability [236, 237], which arises in a homogeneously oriented liquid crystal layer in a sandwich cell between transparent electrodes. 

Carr-Helfrich one in nematics and may be studied quantitatively theoretically [280]. At high frequencies, an instability is observed with a characteristic frequency dependence of the threshold field Elayer thickness (fundamental domains). This has been regarded as an analog of the dielectric regime [282], but it can also be interpreted as the electrolytic mode [283] with some specific features. In some special cases a new domain mode is observed [284], which has been referred to the inertial (anisotropic) mode (discussed in Section 9.4.1.3 of this Chapter). 

The basic mechanism for electric field induced instabilities is now very well understood in terms of the Carr-Helfrich model based on field induced space charges due to conductivity and dielectric anisotropies [16, 31], Helfrich [16] made derivations for only DC fields, which were further extended to AC fields by Dubois-Violette and co-... 

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