Nonlinear dynamics of the alignment tensor in the presence of electric fields (Archives of Mechanics - Test, 1998)
In the mesoscopic theory field quantities are introduced, which depend not only on position and time, but also on an additional orientational variable, the microscopic director. The orientation distribution function (ODF) gives the fraction of particles of a particular orientation. An equation of motion for the second order alignment tensor, including the influence of electromagnetic fields and of spatial inhomogeneities, is derived. The starting point are the mesoscopic balance equations of mass and of angular momentum. A constitutive equation on the mesoscopic level is discussed. The two balance equations together with the constitutive equation yield an equation of motion for the ODF. This finally leads to a nonlinear partial differential equation for the alignment tensor, which involves also the fourth and the sixth moment of the ODF.