Orientational Balances ffor Nematic Liquid Crystals

Abstract

Abstract Starting from the global balance equations of mass, momentum, angularmomentum and energy for discrete systems, new balances are derived byregarding the nematic liquid crystal as a formal mixture of fluids, whosecomponents are defined by the orientation of the particles. The resulting balanceequations for the components are called orientational balances. The connectionsbetween the dynamical quantities for the components and the mixture itself, suchas the stress tensors are discussed. 1. Introduction To describe the behavior of an anisotropic fluid, such as a nematic liquid crystal,there are two well known theories in use. One approach is the director theory[5,7], introducing a director field d(x, t) with d as an unit vector indicating themean orientation of the media. But in fact these theories are not able to describea change in the degree of orientational order as will be shown below. The secondapproach is to describe the orientation by an order parameter [6] by whichchanges in the degree of orientational order can be represented. But in thesetheories the problem arises how the mechanical properties of the particles such asmomentum, angular momentum and energy are related to the orientationaldistribution function which is necessary to calculate the order parameter. Thuswe want to combine both approaches by introducing a microscopic director,related to the orientation of one particle only, so that it is easy to get the balanceequations. Then we treat the anisotropic fluid as a formal mixture by regardingall particles of a volume element with the same orientation as one component ofthe fluid [3]. Thus the orientational distribution function results as the fractionof the mass density of a component by the mass density of the mixture.Consequently particles can change the degree of orientational order in themixture by considering formal chemical reactions between the components [2].