Electro-hydrodynamic instability

From macroscopic electrodynamics laws [3] it follows that at the phase boundary we have  

This latter equation shows that the longitudinal electric field, while acting on the charges adsorbed at the interface, will induce an inevitable convective flow both exactly at the boundary and in adjacent areas of each phase. If either the strength E of the external field or the surface density F of the adsorbed particles is a function of time, one can analyze the stabihty of the system of the hydrodynamic equations (l)-(2) with an x-component for each phase velocity in the form of Eq. (26). Various kinds of electrohydrodynamic instability result from such an analysis and are described in the literature [28-31]. More details on the problems of electrohydrodynamic instability will be given below using particular model systems as examples. 

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Hydrodynamic instabilities 3.11.1 Homogeneous instability in shear flow The anisotropic properties of nematics give rise to certain novel instability mechanisms that are not encountered in the classical problem of hydro-dynamic instability in ordinary liquids. Theoretical work on electro-hydrodynamic instability stimulated systematic studies on two other types of convective processes, viz, thermal and hydrodynamic instabilities, and it was soon established that the basic mechanisms involved in all three cases are closely similar. " In this section we shall examine the problem of hydrodynamic instabilities in nematics. 

If (5.20) is not valid other types of electrooptical effects take place and the modulated FVederiks transition cannot be observed in experiment. Figure 5.4 shows how doping liquid crystals with conducting and dielectric impurities can violate the inequality (5.20) and, consequently, the electro-hydrodynamic instabilities 1 and 5 (Table 5.1) are observed within the whole frequency range (curve B). Considerable change in the threshold voltage and inversion frequency also takes place for different values of the low-frequency dielectric anisotropy (curves A and C). 

Helfrich [49] was first to propose electro-hydrodynamic instability in cholesterics with negative dielectric anisotropy. Harault [56], combining Helfrich theory with time-dependent formalism, calculated a voltage frequency relationship similar to that observed for Williams domains. The existence of conduction and dielectric regimes was experimentally verified. The domain periodicity is proportional to wherepo... 

D. Meyerhofer, Electro Hydrodynamic Instabilities in Nematic Liquid Crystals, Chapter 9. 

A. Joets, R. Ribotta Electro-hydrodynamical convective structures and transitions to chaos in liquid crystals, in J. E. Wesfreid, S. Zaleski (eds.) Cellular Structure in Instabilities, Springer, Berlin, p. 294 (1984)... 

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