Flow nematics

In the absence of elastic stresses, the stress tensor for a flowing nematic is given by (Ericksen 1960, 1961)... 

In a flowing nematic, the viscous and distortional stresses must satisfy the balance of linear... 

The expression for the irreversible entropy production of a flowing nematic liquid crystal given in Section 4 did not include the contribution from the streaming angular velocity and its conjugate torque density. Therefore we present a more general expression that includes this contribution [26],... 

Feng, J.J. Sgalari, G. Leal, L.G. A theory for flowing nematic polymers with orientational distortion. J. Rheol. 2000, 44 (5), 1085-1101. 

Continuum theory has also been applied to analyse tire dynamics of flow of nematics [77, 80, 81 and 82]. The equations provide tire time-dependent velocity, director and pressure fields. These can be detennined from equations for tire fluid acceleration (in tenns of tire total stress tensor split into reversible and viscous parts), tire rate of change of director in tenns of tire velocity gradients and tire molecular field and tire incompressibility condition [20]. 

C. Characteristically, these nematic melts show the persistence of orientational order under the influence of elongational flow fields which result in low melt viscosities under typical fiber formation conditions even at high molecular weights. 

Molecules of nematic Hquid crystals also are aligned in flow fields which results in a viscosity that is lower than that of the isotropic Hquid the rod-shaped molecules easily stream past one another when oriented. Flow may be impeded if an electric or magnetic field is appHed to counter the flow orientation the viscosity then becomes an anisotropic property. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

The rigid nature of the mesophase pitch molecules creates a strong relationship between flow and orientation. In this regard, mesophase pitch may be considered to be a discotic nematic liquid crystal. The flow behavior of liquid crystals of the nematic type has been described by a continuum theory proposed by Leslie [36] and Ericksen [37]. 

J. Fukuda. Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals. Eur Phys J B 7 173, 1998. 

General Flow Properties for Nematic-like Ordered Fluids... 

A nematic flows very much like a conventional organic liquid with molecules of similar size. In the vicinity of the... 

Leslie, F. M., "Theory of Flow in Nematic Liquid Crystals, The Breadth and Depth of Continuum Mechanics—A Collection of Papers Dedicated To J. L. Ericksen, C. M. Da-fermos, D. D. Joseph, andF. M. Leslie, Eds., Springer-Verlag, Berlin, 1986. 

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].)...

Note 1 The three Miesowicz coefficients (//i, 772, and 773) describe the shear flow of a nematic phase with three different director orientations, (see Fig. 31) namely 771 for the director parallel to the shear-flow axis 772 for the director parallel to the velocity gradient and 773 for the director perpendicular to the shear flow and to the velocity gradient. 

Fig. 31. Scheme of director alignment in the shear flow of velocity u of a nematic phase and... 

Regions in a liquid crystal having a specific cellular periodic flow-pattern in the form of long rolls induced by the application of an electric field perpendicular to a nematic layer with an initial planar alignment of the director. 

Note 1 The nematic liquid crystal must have a negative dielectric anisotropy (Af < 0), and a positive anisotropy (Aa > 0). The optical texture corresponding to the flow pattern consists of a set of regularly spaced, black and white stripes perpendicular to the initial direction of the director. These stripes are caused by the periodicity of the change in the refractive index for the extraordinary ray due to variations in the director orientation. 

In order to discuss the rheological properties of stiff-chain polymer solutions, we need an expression for stress. The stress a induced in a homogeneous isotropic or nematic solution by a macroscopic flow was formulated by Doi [114], who used the Kirkwood general theory [116] to show... 

Here a is the elastic stress which arises from the change in the (dynamic) free energy in the macroscopic flow, while o(V) and a(S) are the viscous stresses produced by the polymer-solvent friction and the solvent-solvent friction, respectively. In concentrated isotropic polymer solutions, the elastic stress overwhelms the viscous stresses, so the latter are often neglected. However, it should be noticed that the viscous stresses may become significant in more dilute solutions as well as in nematic solutions where the elastic stress diminishes. 

Actual calculations of w,E) for isotropic and nematic solutions will be described in Sects. 8 and 9 respectively. Furthermore, derived approximately for isotropic solutions in a steady shear flow in Sect. 8, but it will be neglected for nematic solutions in Sect. 9. 

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