Abstract:
This thesis studies Some problems in the statics and dynamics of nematic liquid crystals. This thesis studies two broad classes of problems, using the GLdG approach. The first class deals with the static properties of the isotropic-nematic interface. The problem of interface structure for the nematic, provides a simple illustration of how the structure of an interface can differ substantially from structure in the bulk. The second class of problems involves study of dynamics of Q(alpha beta) for a nematic fluid in an external shear flow. This study impacts experiments on the flow behaviour of fluids with orientational order, a prototypical model for the understanding of complex fluid rheology, in particularly of chaos associated with unsteady rheological response or rheochaos. Such rheochaos is a consequence of constitutive and not convective non-linearities, originating in the coupling of the flow to structural or orientational variables, describing the local state of the fluid. This thesis discusses this requirement in the context of a model for rheochaos, proposing a local map as well as a coupled map description of regular and chaotic states obtained in sheared nematics.
