W. Muschik and B. Su
Mesoscopic Interpretation of Fokker-Planck Equation Describing Time
Behavior of Liquid Crystal Orientation
submitted to:
J. Chem. Phys.
Starting out with the mesoscopic mass balance for liquid crystals we derive
the balance equation for the orientation distribution function (ODF) of the
molecules which is of Fokker-Planck type. Comparison of this mesoscopic
generated Fokker-Planck equation to well-known statistically induced balance
equations of the ODF results in a slip relation between the rotation of the
liquid crystal and the angular velocity of molecules of different orientations.
The difference between these two angular velocities is caused by the torque of
the meanfield, by the velocity gradient, by the alignment, and by the
non-isotropy of the ODF.