Flow-aligning nematics

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

Figure 10.38 Temperature-shear-rate phase diagram for 8CB in the vicinity of the transition temperature Tan = 33.58°C from the nematic to the smectic A phase. At temperatures more than 5.5°C above Tan, 8CB is a flow-aligning nematic, and it orients close to the flow direction in orientation b. As the temperature is lowered, the nematic becomes a tumbler, preferring the a orientation, mixed with either b or c. The a orientation prevails even in the smectic-A state at temperatures within a degree of Tan, especially at high shear rates. At lower temperatures, the orientation is a mixture of a and c. The globes show the ranges of orientations obtained in each of the states ac, a, a i, and b inferred from x-ray scattering. (From Safinya et al. 1991, reprinted with permission from the American Physical Society.)...

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

Zuniga, I. Leslie, F.M. Shear-flow instabilities in non-flow-aligning nematic liquid crystals. Liq. Cryst. 1989, 5, 725-734. 

Gu, D., Jamieson, A. M., and Wang, S. Q., Rheological characterization of director tumbling induced in a flow-aligning nematic solvent by dissolution of a side-chain liquid crystal polymer, J. RheoL, 37, 985-1001 (1993). 

The last part of the book deals with Hquids crystals and ceramic microelectronic devices. Chapter 12, by Mendoza et al. reviews recent theoretical results on the rheology of systems consisting of a flow-aligning nematic contained in cells and capillaries under a variety of different flow conditions and under the action of applied electric fields. Finally, chapter 13, by Alias and Shapee, stresses the impact of silver paste rheology in the fabrication of ceramic microelectronic devices (low temperature co-fired ceramic LTCC devices). 

For a flow-aligning nematic, that is, for a nematic where 020 3 > 0 and a2 0 and therefore the solution for 0 t) is given by (5.183). This solution oscillates aroimd its initial value of zero with an amplitude that is clearly independent of the frequency lj. The amplitude increases as the amplitude a of the oscillation on the upper plate increases, as can be seen from (5.182)2 it is also evident from (5.183) that the amplitude is uniformly bounded, since it is never greater than tan ((5) for any value of a. 

For a non-flow-aligning nematic, that is, a nematic where 0203 < 0, we have that e < 0 and the solution 9 t) is provided by equation (5.184). The amplitude of this oscillating solution is independent of cj, as before. However, in this case the amplitude of the oscillation in the solution can increase without bound as the amplitude a of the oscillation on the upper plates increases. Further, if <5 < 1, then the amplitude of the solution remains relatively small until the value a increases to a critical value Uc defined by... 

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