H. Ehrentraut and W. Muschik
Balance laws and constitutive equations for liquid crystals
Extracta Mathematicae 11, 1996, 41-50
Liquid crystals consist of form-anisotropic particles which posses in
most cases a uniaxial symmetry but in general the particles have a
biaxial shape.
We want to show how both cases can be treated within a uniform mathematical
model. This model can be used to obtain a set of "mesoscopic" balance
equations containing the orientation as additional
variable. Introducing an orientation distribution function (ODF) for
the rotational degrees of freedom the moments of the ODF - called
alignment tensors - can be used as order parameters of the liquid
crystal. Constitutive equations are formulated on the mesoscopic level
and can be lifted to macroscopic fields by an averaging
procedure. The resulting equations are valid for the whole physical
range of the order parameters, covering the isotropic phase as well
as the completely ordered nematic phase. To demonstrate the usefulness
of the method we shortly discuss the viscous properties of nematic liquid
crystals.