Flow-aligning

Phillips, M., 1997, Role of Flow Alignment and Inlet Blockage on Vaned Diffuser Perfonnance, Report No. 229, Gas Turbine Laboratory, Massachusetts Institute of Technology. 

The same flow-aligning side-chain liquid crystalline polymer has been studied [43] in extensional flow using a rheo-NMR method in which selective excitation of... 

Fig. 2.8.16 Director orientation, 0, as a function of shear rate for both flow aligning (solid squares) and tumbling (open squares 325 K, solid circles 328 K and open circles 333 K) nematic polymers. (From Siebert et al. [10].)...

Figure 11.3. Fluidic flow directed assembly of NWs. (a,b) Schematic (a) and SEM image (b) of parallel NW arrays obtained by passing an NW solution through a channel on a substrate (c.d) Schematic (c) and SEM image (d) of a crossed NW matrix obtained by orthogonally changing the flow direction in a sequential flow alignment process. [Adapted from Ref. 49.]...

For the reversible parts of the equations some coupling constants have been introduced the flow-alignment tensor... 

Fig. 9 Critical values as functions of the flow alignment parameter X for various viscosities (a, b) and compressibilities (c, d). In the upper row we plot this dependence for a set of (isotropic) viscosities ranging from v, = 1 (thick solid line,) down to V = 10 3 (thick dashed line,). The lower row illustrates the behavior for varying layer compressibility Bo with Bo 3 f°r the thick solid curve and Bo = 100 for the thick dashed curve. In all plots the thin solid lines give the behavior for some intermediate values. For an interpretation of this behavior see the text...

Out of the five viscosities, only two (V2 and V3) show a significant influence on the critical values. In Fig. 8 we present the dependence of 9C and qc on an assumed isotropic viscosity (upper row) and on these two viscosity coefficients (middle and lower row). Since the flow alignment parameter X has a remarkable influence on these curves we have chosen four different values of X in this figure, namely X = 0.7, X = 1.1, X = 2, and X = 3.5. The curves for X < 1 and X > 3 for an isotropic viscosity tensor are very similar to the corresponding curves where only V2 is varied. In this parameter range the coefficient V2 dominates the behavior. Note that the influence of V3 on the critical values is already much smaller than that of V2. We left out the equivalent graphs for the other viscosity coefficients, because they have almost no effect on the critical values. For further comments on the influence of an anisotropic viscosity tensor see also Sect. 3.4. 

All the parameters we have discussed up to now caused variations in the critical values that did not select specific values of the considered parameter. In this aspect the situation is completely different in the case of the flow alignment parameter X. As shown in Fig. 9 there is a clear change in behavior for X 1 and X 3. The... 

Clearly flow aligning behavior of the director is present and do increases linearly with the tilt angle, do. Above a threshold in the Spain rate, y 0.011, undulations in vorticity direction set in. In Fig. 14 the results of simulations for y 0.015 are shown. In Fig. 15 we have plotted the undulation amplitude obtained as a function of the shear rate. The dashed line indicates a square root behavior corresponding to a forward bifurcation near the onset of undulations. This is, indeed, what is expected, when a weakly nonlinear analysis based on the underlying macroscopic equations is performed [54], In Fig. 16 we have plotted an example for the dynamic behavior obtained from molecular dynamics simulations. It shows the time evolution after a step-type start for two shear rates below the onset of undulations. The two solid lines correspond to a fit to the data using the solutions of the averaged linearized form of (27). The shear approaches its stationary value for small tilt angle (implied by the use of the linearized equation) with a characteristic time scale t = fi/Bi. 

We start with the ground state (°), fi(° defined by the simple shear flow y(°), Fig. 17. The principal effect is, as expected, the appearance of a small tilt of the director from the layer normal (flow alignment), predominantly in z direction (Fig. 18). Note that the configuration of layers is also modified by the shear (Figs. 19 and 20), i.e., the cylindrical symmetry is lost. This is analogous to the shear-flow-induced undulation instability of planar layers (wave vector of undulations in the... 

Fig. 18 Ground state flow alignment director tilt in the Z direction at r = 0.1SR as a function of the polar angle 0. The tilt is zero at 0 = 0 and

Fig. 20 Radial profile of (°) and n close to (but not exactly at) = n/2. Note the regions of dilatation and compression of the layers caused by the flow alignment...

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],... 

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

Note that the period is inversely proportional to shear rate y hence, the strain period Py is independent of shear rate. When A < 1 the nematic is called a tumbling nematic, while when A > 1, the nematic is flow-aligning. As discussed in Sections 10.2.5 and 10.2.6, both cases (tumbling and flow-aligning) can occur in small-molecule liquid crystals. 

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.)...

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