Nematic viscosity estimation using director kickback dynamics

The coupling between director rotation and bulk flow of a liquid crystal can cause many interesting, and often unwanted, effects. The associated 'backflow' and director 'kickback' have been observed and modelled over a number of years and have been used in the determination of nematic elastic constants and viscosities, usually through complicated fitting procedures. In this paper we develop a simple model of the flow and director dynamics during switch-off in a standard Freedericksz cell which, together with the classical switch-on dynamics, can be used to develop a relatively accurate, computationally inexpensive, two-mode fitting procedure capable of estimating splay and bend elastic constants, cell thickness and two combinations of the nematic viscosities. We do this by using an eigenfunction expansion for the director dynamics equation together with an analytical expression for the coefficients of the relaxing modes. This allows a simple estimation for the maximum director angle during kickback and the time after which the director has recovered to its initial state, which are comparable with a full numerical simulation, and leads to confidence in the accuracy of a two-mode eigenfunction expansion.