Regular and chaotic flow behavior and orientational dynamics of tumbling nematics

The flow behavior of (both low molecular weight and polymeric) liquid crystals is strongly affected by the coupling between the flow and the molecular orientation. Nematic liquid crystals which respond with a time-dependent orientational behavior to an applied steady shear flow rather than a stationary flow alignment are called ’tumbling nematics’. The time-dependent phenomena can be rather complex. Different types of periodic behavior referred to as (ordinary) tumbling, wagging, kayaking tumbling and kayaking wagging have been idendified in experiments and in theoretical descriptions [1]. A relatively simple model based on a nonlinear equation for the second rank alignment tensor which can be derived form irreversible thermodynamics [2, 3, 4] or from a generalized Fokker-Planck equation [5, 6] revealed a more complex and even chaotic behavior for certain model parameters and specific values of the applied shear rate [7]. Chaotic behavior was also found from a solution of a Fokker-Planck equation for the orientational distribution function involving 65 components rather than the 5 independent components of the second rank alignment tensor [8]. Further theoretical studies on the periodic and chaotic orientational and rheological behavior were presented in [9] and in [10]. Here the following further points are addressed: