Flows with Fixed Director Axis Orientation

Flows with Fixed Director Axis Orientation 

Consider here the simplest case of flows in which the director axis orientation is held fixed. This may be achieved by a strong externally applied magnetic field (see Fig. 3.11), where the magnetic field is along the direction h. Consider the case of shear flow, where the velocity is in the z direction and the velocity gradient is along the X direction. This process could occur, for example, in liquid crystals confined by two parallel plates in the y-z plane. 

In terms of the orientation of the director axis, there are three distinct possibilities involving three corresponding viscosity coefficients  

r 2- is parallel to the flow velocity, that is, along the z axis and lies in the shear plane x-z (0=0°, ( )=0°). 

These three configurations have been investigated by Miesowicz, and the rj s are known as Miesowicz coefficients. In the original paper, as well as in the treatment by deGennes, the definitions of r i and ri3 are interchanged. In deGennes notation, in terms of and we have r a = = ri2, and = ri3. The notation used 

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Flows with Fixed Director Axis Orientation... 

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