LITMIR.BIZ

Figure 3.8. Plot of dn_||/dT and dn_⊥/dT for the liquid crystal for temperature near T_c (after Khoo and Normandin [14] and Horn [15]). Solid curve is for visual aid only.

3.5. FLOWS AND HYDRODYNAMICS

      One of the most striking properties of liquid crystals is their ability to flow freely while exhibiting various anisotropic and crystalline properties. This dual nature of liquid crystals makes them very interesting materials to study; it also makes theoretical formalism very complex.

The main feature that distinguishes liquid crystals in their ordered mesophases (e.g. the nematic phase) from ordinary fluids is that their physical properties are dependent on the orientation of the director axis ; these orientation flow processes are necessarily coupled, except in very unusual cases (e.g. pure twisted deformation). Therefore, studies of the hydrodynamics of liquid crystals will involve a great deal more (anisotropic) parameters than studies of the hydrodynamics of ordinary liquids.

      We begin our discussion by reviewing first the hydrodynamics of an ordinary fluid. This is followed by a discussion of the general hydrodynamics of liquid crystals. Specific cases involving a variety of flow‐orientational couplings are then treated.

      3.5.1. Hydrodynamics of Ordinary Isotropic Fluids

Consider an elementary volume dV = dx dy dz of a fluid moving in space as shown in Figure 3.9. The following parameters are needed to describe its dynamics:

In later chapters where we study laser‐induced acoustic (sound, density) waves in liquid crystals, or generally, when one deals with acoustic waves, it is necessary to assume that the density is a spatially and temporally varying function. In this chapter, however, we “decouple” such density wave excitation from all the processes under consideration and basically limit our attention to the flow and orientational effects of an incompressible fluid. In that case, we have