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Hydrodynamic description of thin nematic films

Tuesday 21st May 2013 - 11:30 to 11:50
INI Seminar Room 1
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal. Firstly, we clarify how the elastic energy enters the evolution equation for the film thickness. We show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. Secondly, based on a gradient dynamics approach, we propose a film thickness evolution equation that describes a free surface thin film of nematic liquid crystals on a solid substrate under weak anchoring conditions at the free surface. We show that in the intermediate film thickness range anchoring and bulk energies compete what may result in a linear instability of the free surfa ce of the film.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons