S. Blenk, H. Ehrentraut and W. Muschik
Statistical Foundation of Macroscopic Balances for
Liquid Crystals in Alignment Tensor Formulation
Physica A 174, 1991, 119-138
Starting out with the global balance equations of mass, momentum,
angular momentum, and energy formulated on the so-called
ten-dimensional doubled phase space of position, velocity,
orientation, and orientation change velocity, the appropiate local
balances are derived, which are defined on the five-dimensional half
of the doubled phase space including time, position, and the
microscopic director. These so-called orientation balance equations
describe nematic liquid crystals whoose alignment need not to be
uniform as it is presupposed in theories using macroscopic director
fields. In Rü we get the usual phenomenological balance equations of
micropolar media having the advantage that the balanced quantities are
defined statistically. By expanding the orientation distribution
function into a series of multipoles we get alignment tensor fields
and an additional alignment tensor balance equation on Rü.