Homogeneous instability in shear flow

11 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. 

The physical interpretation of this distortion is as follows. (We shall assume throughout this discussion that the material is an ordinary nematic like MBBA with 0.) Let us suppose that there is a fluctuation 0 0 in the xy plane that rotates the director from its initial orientation (1,0,0). The flow now exerts a viscous torque, which is given by SO (fig. 

There is, in fact, another torque that comes into effect. As we have seen in 3.6.5, a deflection of in the director orientation gives rise to a secondary flow v. The secondary velocity gradient causes a torque F that makes an additional destabilizing contribution (except close to the boundaries). 

It is possible to define a dimensionless quantity called the Ericksen number 

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