Abstract
In the magnetic-field-induced Freedericksz transition in a parallel oriented nematic liquid crystal cell, the one-dimensional liquid crystal orientation profile can become a two-dimensional transient splay periodic profile by the backflow effects. The backflow effects result in a reduction of the effective viscosity and thus gives a faster response than that of the one-dimensional orientation profile. We introduce a vector potential description for the liquid crystal director and flow velocity, and obtain the general solution for the two-dimensional splay Freedericksz transition. The vector potential method gives solutions which inherently satisfy the fluid incompressibility condition and overcome the difficulties in the conventional `free boundary conditions'. The method enables us to express the flow velocities and the nematic director by a single variable, and simplifies the equations of motion to one equation of motion for the new variable. The general solution is obtained. The particular solution on the fastest growing mode is in agreement with that obtained by Hurd et al [J. de Physique 46 (1985) 905].
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