Surface viscosity in nematic liquid crystals

Abstract

We consider the effect of a localized surface viscosity on the relaxation of an imposed deformation in nematic liquid crystal cells. The simple case in which the samples are in the shape of a slab and the differential equations can be linearized is considered. The apparent inconsistence between the initial values of the time derivatives at the border evaluated by means of the bulk equation and of the boundary condition is related to the assumption that the distorting field is removed in a discontinuous manner. In this framework we shall see that the dynamical problem relevant to the relaxation of the deformation is a well posed problem. In particular, the time derivatives of the nematic director evaluated on the surface by means of the bulk differential equation and by means of the dynamical boundary condition are identical for times larger than the switching time of the deforming field. The analysis of the relaxation of the imposed deformation based on the diffusion equation, with the boundary condition containing the surface viscosity, is then valid only for times larger than the switching time of the deforming field. From this observation we conclude that the concept of localized surface viscosity is useful in the description of slow dynamics of nematic liquid crystals.