Inertial mode, instabilities

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. 

Figure 31. Optical patterns accompanying different EHD processes, (a) Electrolytic mode for the homeo-tropic orientation of a nematic liquid crystal, (b) Ka-pustin-Williams domains (KWD) in homogeneously oriented nematic, (c) Anisotropic EHD mode for the planar texture of a cholesteric, (d) A chevron structure due to interference of two instabilities (KWD and inertial mode).

In systems with return flows, as is the case in floating or supported zones, stationary roll cells were shown not to exist in slots heated from the side. Surface waves were found to be the prevailing cause of instability at very low Pr. However, it seems tenuous to try to extrapolate their results to the return flows with significant inertial effects and surface heating which we studied because the nonlinear inertia terms have a profound influence on the velocity profile, the surface deflection and the pressure distribution therefore they would influence strongly all modes of instability. 

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). 

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