Macroscopic constitutive equations for liquid crystals induced by their mesoscopic orientation distribution (Q1199200)

To derive a theory that is able to represent a change in the degree of orientational order in liquid crystals, this paper adopts a mesoscopic approach that employs a microscopic director and an orientational distribution function. Treating the liquid crystal formally as a mixture, the authors begin by stating the mesoscopic orientational balance equations for mass, momentum and spin and showing that an integration over all orientations results in the usual unchanged balance equations for a micropolar fluid together with mesoscopic definitions of spin, internal energy density etc. Replacing the microscopic director by a second order alignment tensor, for which a macroscopic balance equation is derived, the authors choose a set of independent macroscopic variables, which includes the alignment tensor and its derivatives, to form a state space. They then proceed to propose appropriate constitutive equations by using Coleman and Noll's method of exploiting the dissipation inequality. In addition the Landau condition for equilibrium in homogeneous alignment is obtained and extended to the case of inhomogeneous alignment. Finally results for a uniaxial distribution function are derived and compared with those obtained by \textit{J. L. Ericksen} [Arch. Ration. Mech. Anal. 113, No. 2, 97-120 (1991; Zbl 0729.76008)] using a macroscopic director together with an order parameter. As the authors observe, the mesoscopic approach is obviously more general than the theory proposed by Ericksen and Leslie. However the theory is considerably more complicated and hence the paper is only likely to appeal to researchers interested in constitutive theory.