Flow in Cholesterics and Smectics

The equations for hydrodynamics of cholesterics are basically the same as for nematics, but there are some specific features related to the helical structure. 

Consider shear in three basic geometries shown in Fig. 9.8. In each sketch the helix axis h is aligned differently with respect to plane xy of the shear rate [15]. 

In the left part of the figure, the helical axis is parallel to the velocity gradient (shear) shown by two arrows. When cell thickness is less than the cholesteric pitch, d Pq, and the rate of shear is small, then an effective viscosity is given by averaging two Miesowicz coefficients  

For higher shear rates the helix is unwound, the director becomes almost parallel to the flow lines (nllv) and rji rib as in nematics. 

In the middle part of the figure, the helical axis is perpendicular to the flow direction and the effective viscosity at low shear rate equals 

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