Nematic Liquid Crystal reorientation with a Photosensitive layer

We assume a nematic cell in a planar configuration for which one of their confining plates, is submitted to a hard-anchoring boundary condition and the other plate has a coating monolayer of azo dye molecules, such that the change of the orientation of azo dye isomers, due to light, causes changes in the nematic director. We find an approximated expression for the density of isomers, written in terms of the director angle, which allows us to close the equation for the director's angle on the boundary having a photosensitive plate. We have managed to decouple the director's angle and the isomer densities by assuming extremely different temporal time scales between them. We show that switching times inversely depend on trans-cis transition rate of photo-excitation meanwhile relaxation times do not depend on it, for a given sample. On the other hand, switching and relaxation times linearly depend on surface viscosity values.