Fluid Dynamics of Nematics

Abstract

In this chapter we deal with the basic aspects of nematodynamics which will be described from a variational point of view using Rayleigh’s dissipation function as a starting point. First of all we briefly review the essentials of the fluid dynamics of simple isotropic liquids. Then the theory is generalized to nematics, i.e. anisotropic liquids. This generalization involves the so-called Leslie viscosity stress tensor, which for an incompressible fluid, contains five viscosity coefficients as follows directly from symmetry arguments. Apart from the effect of the anisotropy on the viscosity stress tensor, the orientation of the uniaxial axis will be influenced in most cases by the occurrence of flow. This effect on the orientational field is described by equations of motion, which will be derived taking into account the elastic and viscous forces. Next viscosity measurements are briefly discussed. Finally, as an example of the various types of instabilities that can occur, we consider the one-dimensional theory of electrohydrodynamic instabilities.