ONE-DIMENSIONAL WALLS IN LIQUID-CRYSTALS

We study the geometry of the matter flow which leads to the formation of one-dimensional walls above the magnetic Freedericksz threshold in some nematic materials. The corresponding anisotropic Navier-Stokes eq uation, subject to the appropriate boundary conditions, is solved. We show analytically that the one-dimensional nature of the observed wall s arises from the combination of the planar geometry of the director, imposed before the magnetic field is turned on, the anisotropic viscos ity of the nematic material, and the saturated profile of the director along the direction of the magnetic field. The matter flow along the direction perpendicular to the magnetic field is analytically studied, and the conditions that restrict it to the edge of the sample are sho wn. The influence of this transverse flow of matter on the bending pro file of the director is also analyzed.