We study the geometry of the matter flow which leads to the formation of one-dimensional walls above the magnetic Fréedericksz threshold in some nematic materials. The corresponding anisotropic Navier-Stokes equation, subject to the appropriate boundary conditions, is solved. We show analytically that the one-dimensional nature of the observed walls arises from the combination of the planar geometry of the director, imposed before the magnetic field is turned on, the anisotropic viscosity 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 shown. The influence of this transverse flow of matter on the bending profile of the director is also analyzed.

• Received 7 April 1997

DOI:https://doi.org/10.1103/PhysRevE.56.3061