Multiple solution for a nematic liquid crystal flowing in converging and divergent channels

Abstract

We consider a nematic liquid crystal flowing in converging and divergent channels delimited by two intersecting solid planes forming angular sector region. There is a source or sink of nematic, at the planes intersection, whether the nematic flow is outwards or inwards. We find the planar multiple configurations of the director of the nematic satisfying in-plane planar hard-anchoring boundary conditions for 4′-n-pentyl-4-cyanobiphenyl (5CB). Also, we obtain the corresponding velocity profiles parametrised by the Reynolds number for non-slip boundary conditions. We have obtained both symmetric and asymmetric velocity profiles for outwards and inwards flows, nevertheless, none of these profiles has counterflows regions as it occurs for isotropic liquids. Finally, we calculate the mass rate and Frank’s elastic energy for the same multiple velocity profiles and nematic textures we found. We hope this model can be useful as an extreme confining case which helps to understand the industrially important processes of blade coating and cavity filling of liquid crystalline materials.

Keywords:

• liquid crystal
• nematic
• nematodynamic
• channel

Acknowledgements

J. A. R. Acknowledges partial support from Grant DGAPA UNAM IN110012-3.