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Isaac Newton Institute for Mathematical Sciences

Hydrodynamic description of thin nematic films: weak anchoring model

Presenter: Te-Sheng Lin (Loughborough University)

Co-author: Uwe Thiele (Loughborough University)


Based on a gradient dynamics approach, we propose a film thickness evolution equation that describes the long-wave dynamics of a free surface thin film of nematic liquid crystals on a solid substrate under weak anchoring conditions at the free surface. As limiting cases the model recovers two hydrodynamic long-wave models reported in the literatures: (i) For thick films the surface anchoring energy dominates the bulk energy, i.e., one obtains the strong anchoring case. The director has to bend across the film (HAN state) leading to strong 'elastic diffusion' of the free surface height; (ii) For thin films the bulk elastic energy dominates the anchoring energy. The director orientation is homogeneous across the film (P state) and does not influence the stability of the free surface. In the intermediate film thickness range anchoring and bulk energies compete what may result in a linear instability of the free surface of the film. Finally, we show that the P state is linearly neutrally stable, but nonlinearly unstable.