Constitutive Relations

Abstract

In this chapter is devoted to constitutive laws describing equilibrium and non-equilibrium properties in anisotropic media. Firstly, general principles, viz. the Curie principle, energy requirements, positive entropy production and Onsager-Casimir symmetry relations of irreversible thermodynamics are introduced. Secondly, phenomenological considerations and microscopic expressions are presented for the elasticity coefficients describing linear elastic deformations of solids, with emphasis on isotropic and cubic symmetries. Thirdly, the anisotropy of the viscous behavior and non-equilibrium alignment phenomena are studied for various types of fluids. The influence of magnetic and electric fields are analyzed for plane Couette and plane Poiseuille flows. Results of the kinetic theory are presented for the Senftleben-Beenakker effect of the viscosity. Consequences of angular momentum conservation are pointed out for the antisymmetric part of the pressure tensor. The flow birefringence in liquids and in gases of rotating molecules is treated as well as heat-flow birefringence in gases. The phenomenological description of visco-elasticity and of non-linear viscous behavior is discussed. Vorticity-free flow geometries are considered. The fourth part of the chapter deals with the viscosity and alignment in nematic liquid crystals. Viscosity coefficients are introduced which are needed to characterize the anisotropy of the viscosity in an oriented liquid crystal as well as in a free flow. Flow alignment and tumbling are considered. Model computations are presented for the viscosity coefficients as well as the application of a generalized Fokker-Planck equation for the non-equilibrium alignment. A unified theory for the isotropic and nematic phases is introduced and limiting cases are discussed. Equations governing the dynamics of the alignment in spatially inhomogeneous systems are formulated.