Nematics flow alignment angle

X of a flow-aligning nematic with flow-alignment angle 9a in a steady shearing flow, with x the flow direction and... 

In ordinary nematics p and p are both negative and the flow alignment angle 0 is usually small. This equilibrium orientation of the director is... 

Gahwiller discovered that nematics that undergo a transformation to the smectic phase at lower temperatures exhibit an unusual type of instability as the temperature approaches the transition point. The limiting value of the flow alignment angle 0 defined as... 

Figure 7, The shear stress (left) and viscosity as functions of the shear rate for Xk = T25 and = 0, in the nematic phase, at the temperature = 0.8, where the flow alignment angle, at small shear rates, is about 10 degrees. The large gray dots stem from calculations with constant shear rates, with a maximum shear deformation 150. The smaller black dots are for imposed shear stress.

The flow alignment angle for discotics should therefore be approximately 90°. A stability analysis shows that the angle above 90° is the stable one [44]. Thus for both types of nematic liquid crystals the configuration with the large dimension nearly parallel to the flow direction is the stable alignment. Figure 12 demonstrates this phenomenon. 

A stable angle obviously requires that I- = IAI> 1. Indeed, in most nematics, I Al> 1, and there is an equilibrium with flow alignment angles in the range... 

This is analogous to the flow alignment angle in nematics (see (4.22)), which again shows that the behavior of the c-director within the layers is similar to the meaning of the director in the nematic phase. 

An interesting similarity of what we discussed here appears if one deals with mixtures of rodlike and disklike micelles. These systems could behave very similarly to a truly biaxial nematic, but show interesting differences to them. Whereas for the usual orthorhombic biaxial nematics both directors are perpendicular to each other by construction, in mixtures there is no need to impose this restriction. Pleiner and Brand [70] investigated how mixtures are influenced by an external field (magnetic field or shear flow) and found that the angle between the two directors exhibits a flow aligning behavior similar to the one studied in [42,43],... 

Problem 10.7 Derive Eq. (10.4) for the alignment angle 6 of the director in shearing flow of a flow-aligning nematic. 

Fig. 6.5.2. Flow alignment of the director in nematic liquid crystals, (a) For rodshaped molecules the alignment angle 0 with respect to the flow direction lies between 0° and 45°, while (b) for disc-shaped molecules it lies between —90° and —45° (or equivalently between 90° and 135°).

A second requirement for this instability to occur is that the two Leslie viscosity coefficients tt2 and Oi are of opposite signs [276,312]. If the ratio between the two viscosities is positive, the director exhibits different dynamics it aligns with respect to the velocity at an angle 6I9 such that tan (6b) = a2/ 3- Note finally that, despite a complex microstructure, the classification in terms of flow-aligning and tumbling nematics, as defined for low molecular weight liquid-crystals, still applied to lyotropic systems. 

In both possibihties there is therefore a flow alignment where the c-director makes an angle 0o to the direction of flow, as indicated by these results. This is somewhat sinwlar to the flow alignment that arises in nematics see Section 5.2. 

Assume that our capacitor is filled by a nematic mixture with 0 well aligned along the x-axis and let the same charge injection mechanism works. Then, in a dc regime, the periodic flow will inevitably interact with the director. The maximum realignment, i.e. the deflection of the director angle 9 in the z-direction, will be... 

The interpretation of the double-layer structure of the electrospxm APC fibers is based on the fact that APC solutions subjected to shear show a transition from cholesteric to nematic [104]. Calculation of the Reynolds number shows that the flow inside the needle is laminar. The velocity profile is parabolic and, since the solution becomes nematic, the director should align parallel to walls in the center of the flow, away from the walls of needle, there is some reorientation due to the flow and the director makes an angle with the flow direction. As the solution exits the needle, a rapid evaporation of the solvent freezes the orientation of the director in the different areas of the cross-section of the fiber. 

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