Importance of the surface viscosity on the relaxation of an imposed deformation in a nematic liquid crystal cell

We analyze the influence of the surface viscosity on the relaxation of the nematic deformation induced by an external field on a nematic cell, when the distorting field is removed. The analysis is performed by assuming that the anchoring energy describing the anisotropic part of the nematic-substrate surface tension can be approximated by the form proposed by Rapini and Papoular, and that the viscous torque at the surface is characterized by a surface viscosity ηs. We consider a simple situation where by means of an external action the surface easy direction is modified, and investigate the evolution of the nematic orientation, from the initial state to the final one. The Green function approach is used to obtain the exact solution for the tilt angle profile. The results show that the surface viscosity modifies the relaxation process which becomes slower for increasing values of ηs.