The Kelvin problem - what packing minimizes the surface area in 3D space?
For over 100 years, the Kelvin structure composed of truncated octahedrons was believed to be the unit cell, which divided 3D space with minimum surface area. In 1994, the Weaire-Phelan structure was proposed, which shows 0.3% less surface area than the Kelvin structure. Although monodisperse foams have been used to address this problem and realize the structure, high density difference between gas and liquid and lack of technology to make monodisperse bubbles at micron scale have severely restricted their production and observation.
We are studying this problem with monodisperse emulsion drops, instead of foam. Microfluidic technique facilitates the production of such small and uniform drops. As continuous phase evaporates, monodisperse drops are densely packed without coalescence, minimizing their interfacial area. Therefore, microfluidic approach provides an ideal model system to address Kelvin's problem. In addition, through polymerization of drops in densely packed state, we can permanently fix the structure and produce monodisperse polyhedron microparticles which are potentially useful as building blocks for assemblies.
Figure 1: Two layers of monodisperse emulsion drops (a) in a low volume fraction of drops (beehive structure) and (b) in a high volume fraction (Toth structure). (c) Polyhedron microparticles templated by Toth structure. [Scale bar = 200 microns]
This project is a collaboration with Shin-Hyun Kim.