Multistable nematic wells: modelling perspectives, recent results and new directions

ABSTRACT

This review article is a consolidated but not exhaustive account of recent modelling and numerical work on nematic-filled square or cuboid shaped wells with planar degenerate boundary conditions. This seemingly simple geometry can be modelled with a simplistic Oseen–Frank approach or a more sophisticated two-dimensional and three-dimensional Landau–de Gennes approach. We discuss these approaches, reconcile the findings and in doing so, elucidate the complex interplay between material properties, temperature, geometry and boundary conditions in both equilibrium and non-equilibrium phenomena. We largely focus on static equilibria with some discussion on metastable or transient states of experimental relevance.

GRAPHICAL ABSTRACT

KEYWORDS:

• Modelling
• Oseen–Frank
• Landau–de Gennes
• multistability
• well order reconstruction solution

Acknowledgements

The authors are grateful to Oliver Dammone, Peter Howell, Dirk Aarts, Halim Kusumaatmaja, Radek Erban, Chong Luo and Samo Kralj for fruitful discussions and suggestions. In compliance with EPSRCs open access initiative, the data used in Figures 6 and 7, as well as the MATLAB codes that generated them, are available from http://dx.doi.org/10.5287/bodleian:E9R5RGgjP.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The integral equations in (44) and (45) are the weak form for the Euler–Lagrange equations for 2D LdG equilibria that have on the boundary and this is the standard form used by numerical analysts.

Additional information

Funding

A.M. is supported by an EPSRC Career Acceleration Fellowship EP/J001686/1 and EP/J001686/2, an OCIAM Visiting Fellowship, support from the Bath Internationalization Grant schemes and the Bath Institute for Mathematical Innovation. A.L. is supported by an Engineering Physical Sciences Research Council studentship.