Liquid crystals microstructured fluids

Micellar solutions are isotropic microstructured fluids which form under certain conditions. At other conditions, liquid crystals periodic in at least one dimension can form. The lamellar liquid crystal phase consists of periodically stacked bilayers (a pair of opposed monolayers). The sheetlike surfactant structures can curl into long rods (closing on either the head or tail side) with parallel axes arrayed in a periodic hexagonal or rectangular spacing to form a hexagonal or a rectangular liquid crystal. Spherical micelles or inverted micelles whose centers are periodically distributed on a lattice of cubic symmetry form a cubic liquid crystal. 

This transition from a homogeneous towards a nonhomogeneous flow has been reported in complex fluids of various microstructure such as lyotropic micellar and lamellar phases [44,121,122], triblock copolymers solutions [123,124], viral suspensions [125], thermotropic liquid crystal polymers [126], electro-rheological fluids [127], soft glassy materials [128], granular materials [129,130], or foams [131-133]. 

The microstructure of complex fluids such as ILs, surfactant systems, and liquid crystals can be profitably investigated by means of pulsed gradient spin-echo nuclear magnetic resonance (PGSE-NMR) experiments, a technique that allows the determination of the self-diffusion coefficients. 

The Eulerian description of the instantaneous motion of a fluid with microstructure employs two independent vector fields. The first is the usual velocity v(x, t) and the second is an axial vector w(x, t) which, in the case of polar fluids, represents the angular velocity of the polar fluid particle at position x at time t. In the context of liquid crystals, w is interpreted as being the local angular velocity of the liquid crystal material element, that is, it represents the local angular velocity of the director n. In ordinary continuum theory the only independent field is the velocity v of the fluid because the angular velocity in such theories equals one half of the curl of the velocity. We denote this particular angular velocity by w defined... 

The statics and dynamics of microstructures are governed by the forces that create or maintain them. Rarely can the forces be measured directly. But forces between special surfaces immersed in fluid can now be accurately gauged at separations down to 0.1 nm with the direct force measurement apparatus, an ingenious combination of a differential spring, a piezoelectric crystal, an interferometer, and crossed cyhndrical surfaces covered by atomically smooth layers of cleaved mica (Figure 9.4). This recent development is finding more and more applications in research on liquid and semiliquid microstructures, thin films, and adsorbed layers. 

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