Shape minimisation problems in liquid crystals

ABSTRACT

We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air–liquid or fluid–liquid crystal interfaces and elastomers. We develop a finite element algorithm to solve such problems with dynamic mesh control, achieved by supplementing the free energy with an auxiliary functional that promotes mesh quality and is minimised in the null space of the energy. We apply this algorithm to a flexible capacitor, as well as to determine the shape of liquid crystal tactoids as a function of the surface tension and elastic constants. These are compared with theoretical predictions and experimental observations of tactoids from the literature.

GRAPHICAL ABSTRACT

KEYWORDS:

• Tactoids
• shape minimisation
• regularisation
• finite elements

Acknowledgements

The authors wish to thank the Tufts Graduate School of Arts and Sciences for provision of a summer scholarship for ADB. Both TJA and ADB are grateful for funding from a Cottrell Award from the Research Corporation for Science Advancement.

Disclosure statement

No potential conflict of interest was reported by the authors.

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Funding

This work was supported by the Research Corporation for Science Advancement [Cottrell Award];