Non-spherical bubbles

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By Sung Hoon Kang

(not finished yet)


Title: Non-spherical bubbles

Reference: A. B. Subramaniam, M. Abkarian, L. Mahadevan, H. A. Stone, Nature 438, 930 (2005).

Soft matter keywords

surface tension, gas-liquid interface, bubble

Abstract from the original paper

Surface tension gives gas bubbles their perfect spherical shape by minimizing the surface area for a given volume. Here we show that gas bubbles and liquid drops can exist in stable, non-spherical shapes if the surface is covered, or ‘armoured’, with a close-packed monolayer of particles. When two spherical armoured bubbles are fused, jamming of the particles on the interface supports the unequal stresses that are necessary to stabilize a non-spherical shape.

Soft matter example

Gas bubbles have their spherical shape to minimize their surface area [1]. This surface tension effect is frequently observed in our lives. In this paper, the author showed that the gas bubbles and liquid drops could exist in stable non spherical shapes if the surface is covered with a close-packed monolayer of particles. When the surface of two bubbles, covered or 'armoured" with a closed-packed monolayer of particles, are fused, jamming of the particles on the interface supports the unequil stresses to stabilize a non-spherical shape. They found that the fusion of the armoured bubbles (done by squeezing the bubbles between two glass plates) produced a stable ellipsoidal shape as shown in Fig. 1 a-c. In this case, the jamming of the particles on the closed interface mediated by surface tension generates non-minimal shapes. If we consider the stress state in these kind of interfacial composite materials, a balance of normal stresses at the bubble surface results in

   ΔP = σ1/R1 + σ2/R2

where ΔP is the pressure jump across the surface, R1 and R2 are the local principal radii of curvature, and σ1 and σ2 are the corresponding principal resultants of surface stress. Thus, for a non-spherical bubble (R1 ≠ R2), σ1 ≠ σ2. While a simple fluid interface at equilibrium cannot support this unequal stresses, the bubble can do because of steric jamming of the armoured particles [3-4].


Fig. 1. Non-spherical gas bubbles. In a–d, the bubbles are covered with charge-stabilized, fluorescent polystyrene beads, each of 2.6 um diameter. a, Two initially spherical armoured bubbles. b, The bubbles are compressed between two glass plates (see supplementary information for details), which exposes naked interfaces that spontaneously coalesce. c, The gas bubble maintains a stable ellipsoidal shape even after the side plates are removed. d, Armoured bubble with a stable saddle shape. e, The ability to maintain a saddle curvature allows a hole to be introduced into the bubble to create a permanent change of topology into a genus-1 toroid; here the particles are ground zirconium, of average diameter 200 um. f,Non-spherical shapes can be similarly maintained on mineral-oil droplets in water armoured with 4.0-um fluorescent polystyrene particles. Scale bars (um): a–c, 100; d, 200; e, 500; and f, 16.

References

[1] C. V. Boys, Soap Bubbles - Their Colurs and the Forces which Mould Them (Dover, New York, 1959).

[2] A. B. Subramaniam, M. Abkarian, H. A. Stone, Nature Mater. 4, 553-556 (2005).

[3] D. Vella, P. Aussillous, L. Mahadevan, Europhys. Lett. 68, 212-218 (2004).

[4] A. J. Liu, S. R. Nagel, Nature 396, 21-22 (1998).