Hyperbolic Interfaces

TL;DR

This paper explores how fluid interfaces with orientational order can naturally form surfaces of constant negative Gaussian curvature, revealing new hyperbolic geometries in soft and biological materials due to competing physical forces.

Contribution

It demonstrates the emergence of hyperbolic interfaces in fluid systems with orientational order, linking geometry with material properties and physical interactions.

Findings

Hyperbolic interfaces arise in nematic liquid crystals and biological materials.

Surface tension and orientational elasticity compete to produce negative Gaussian curvature.

The morphology results from a balance between surface tension and elastic distortions.

Abstract

Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as scientists. Here I show that a special class of surfaces of constant negative Gaussian curvature can be obtained in fluid interfaces equipped with an orientational ordered phase. These arise in various soft and biological materials, such as nematic liquid crystals, cytoskeletal assemblies, or hexatic colloidal suspensions. The purely hyperbolic morphology originates from the competition between surface tension, that reduces the area of the interface at the expense of increasing its Gaussian curvature, and the orientational elasticity of the ordered phase, that in turn suffers for the distortion induced by the underlying curvature.