S. Blenk and H. Ehrentraut and W. Muschik
Macroscopic Constitutive Equations for Liquid Crystals
induced by their mesoscopic Orientation Distribution
Int. J. Engng. Sci. 30(9), 1992, 1127-1143
By starting out with mesoscopic orientational balance equations for
each orientational component of a liquid crystal which is described as
a formal mixture, a set of independent macroscopic variables forming
the state space is included. This set includes a second-order
tensorial measure of alignment, called alignment tensor, and its
derivatives. In terms of these state space variables constitutive
equations are proposed by exploiting the dissipation inequality due
to coleman and Noll. The results are compared to those of Ericksen and
Leslie, who described the alignment in a liquid crystal with only a
macroscopic unit director field d(x,t) indicating the
"mean orientation" of the media. In a recent paper Ericksen introduced
beside the macroscopic director an additional scalar order parameter
S(x,t) and its derivatives (Maier-Saupe theory) which turns
out to be the uniaxial case in the alignment tensor formulation. Also
in this case the restrictions to the constitutive equations caused by
the dissipation inequality are discussed.