M. Grinfeld, M. Langer and N.J. Mottram,
Nematic viscosity estimation using director kickback dynamics,
Liquid Crystals 38 (2011), 981–987
Abstract:
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.