Computation of Equilibrium Bilayer Monodisperse Foam Structures Using the Surface Evolver

Fuyang Li,Zuosheng Lei,K A Brakke,Chengchuan Zhang

doi:10.1038/s41598-017-05490-y

Abstract

The Surface Evolver is used to minimize the surface energy of two ordered structures for bilayer monodisperse wet foams with arbitrary liquid fraction. Previous researchers have found a reversible structural transition in bilayer monodisperse foams by changing the foam liquid fraction in a physical experiment. We simulated this phenomenon by analyzing the interfacial energy of two bilayer foam systems with varying liquid fractions. The calculations reported here show that the Tóth structure is energy minimizing when the liquid fraction is below a critical value, around 2.26%, above which point the honeycomb structure becomes preferable, although the Tóth structure remains metastable.

Highlights

Researchers believe the structural transition described above is a product of foam self-organization for minimizing system energy
The only reason we can put forward is that λ = 1.03 is best for dry foam, and the liquid Plateau borders do not perturb the surface enough to change that noticeably in our investigated range of liquid fractions
Because the honeycomb structure and the Tóth structure are very close in energy, it is important to take extreme care in the evolution to get accurate results to at least six decimal places

Summary

Introduction

Researchers believe the structural transition described above is a product of foam self-organization for minimizing system energy. If we can introduce numerical simulation and accurately analyze how the energy of these bilayer foam systems changes with liquid fractions and geometric parameters, it would be informative to transition mechanism research. A foam consists of gas cells (bubbles) in a liquid medium, separated by thin films wherever the cells impinge on one another. Depending on their size and the pressure of the liquid in their interstices, the bubbles may remain approximately spherical with little contact (wet foam) or be pressed together to form polyhedra with possibly curved faces (dry foam). The liquid content is contained in two regions[6]: the thin foam films that separate adjacent bubbles, and the Plateau borders where several films meet. The topology and geometry of a dry foam system[7] were described by Plateau in 1873 using what are named Plateau’s rules: each film has uniform mean curvature; three films meet symmetrically in a Plateau border at equal angles of 120°; and four Plateau borders meet symmetrically in a vertex at the tetrahedral angle of cos−1(−1/3) ≈ 109.47°

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Results

Conclusion