Electric field along the helical axis

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). 

We shall consider the DC case first (neglecting, of course, any charge injection at the boundaries). If (7 and are the conductivities along and 

The threshold field is obtained by setting /eiec+/eias = 0. The optimum wavevector k is given by (4.6.26) and the threshold field by 

Hurault has extended the treatment to AC fields. The method is somewhat analogous to the one discussed in 3.10 for nematic instabilities and leads, in the conduction regime, to the following threshold for distortion  

For negative dielectric anisotropy (gp— j 0) the conduction regime occurs when co towhere 

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