How bees and foams respond to curved confinement: level set boundary representations in the Surface Evolver

TL;DR

This paper introduces a novel Surface Evolver framework for simulating bubbles and foams confined between curved surfaces with non-zero Gaussian curvature, including biological experiments with bees on curved surfaces.

Contribution

It develops a new method using level set constraints for simulating foams on curved geometries and explores biological adaptation of honeycombs on curved surfaces.

Findings

Successfully simulated foams on curved surfaces like spheres and tori.

First experimental attempt to create honeycombs on negatively curved surfaces.

Demonstrated bees can adapt honeycomb structures to curved geometries.

Abstract

We present a Surface Evolver framework for simulating single bubbles and multicellular foams trapped between curved parallel surfaces. We are able to explore a range of geometries using level set constraints to model the bounding surfaces. Unlike previous work, in which the bounding surfaces are flat (the so called Hele-Shaw geometry), we consider surfaces with non- vanishing Gaussian curvature, specifically the sphere, the torus and the Schwarz Primitive-surface. In the case of multi-cellular foams - our method is to first distribute a set of N points evenly over the surface (using an en- ergy minimisation approach), these seed points are then used to generate a Voronoi partition, that is clipped to the confining space, which in turn forms the basis of a Surface Evolver simulation. In addition we describe our ex- perimental attempt to generate a honeycomb on a negatively curved surface, by trapping bees between two Schwarz Primitive-surfaces. Our aim is to understand how bees adapt the usual hexagonal motif of the honeycomb to cope with a curved surface. To our knowledge this is the first time that an attempt has been made to realise a biological cellular structure of this type.