Abstract
Two-dimensional liquid foam systems comprised of an odd number 𝑁 of bubbles arranged in a staircase configuration are studied as they are packed within a confined straight channel. Energy minimization is employed to characterize the permitted topology and geometry of the system at equilibrium. It is known that in an infinite staircase, bubble films are flat. The configuration for a finite number of bubbles, however, deviates from that of an infinite staircase at the edges. It is known that films near the edges are not flat and structures with a few bubbles (up to 𝑁=3) are well characterized. To study what happens as more bubbles are added, and how the behaviour approaches that of an infinite staircase, structures comprised of 𝑁=[5,7,…] bubbles are studied here. For these 𝑁 values, minimum and maximum bubble areas are found that can pack in a staircase configuration within a straight channel. However, for an infinite staircase and also for 𝑁=3, there are maximum areas, but no minima. Staircases with very short films, which make the structure susceptible to break in various ways, are also identified
Original language | English |
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Article number | 20240151 |
Number of pages | 26 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 480 |
Issue number | 2300 |
DOIs | |
Publication status | Published - Oct 2024 |
Keywords
- dimensional bubbles
- energy minimization
- equilibrium foams
- mathematical modelling
- staircase structure
- two-