Circular Shearing Flow of Homeotropic Nematic Liquid Crystals

Abstract

The equation of motion of director in a homeotropic liquid crystal cell with circular plates rotating against each other is derived with cylindrical coordinates. The optical pattern observed under crossed polarizers with monochromatic light is discussed. Numerical integrations for the case of MBBA have been carried out and the result is compared with the experimental observation reported by Wahl and Fischer in 1973, Mol. Cryst. Liq. Cryst., 22, 359. Instead of the linear relationship between (m/l)/(lv)² and (lv)² given by Wahl and Fischer, we suggest a parabolic relationship between (lv)²/(m/l) and (m/l), where m is the order of the dark ring, 1 is the thickness of the cell, and v is the velocity of flow of the liquid crystal at a distance r from the center of the cell.