# Difference between revisions of "Non-spherical bubbles"

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ΔP = σ<sub>1</sub>/R<sub>1</sub> + σ<sub>2</sub>/R<sub>2</sub> | ΔP = σ<sub>1</sub>/R<sub>1</sub> + σ<sub>2</sub>/R<sub>2</sub> | ||

− | where ΔP is the pressure jump across the surface, R<sub>1</sub> and R<sub>2</sub> are the local principal radii of curvature, and σ<sub>1</sub> and σ<sub>2</sub> are the corresponding principal resultants of surface stress. Thus, for a non-spherical bubble where R<sub>1</sub> | + | where ΔP is the pressure jump across the surface, R<sub>1</sub> and R<sub>2</sub> are the local principal radii of curvature, and σ<sub>1</sub> and σ<sub>2</sub> are the corresponding principal resultants of surface stress. Thus, for a non-spherical bubble where R<sub>1</sub> is not equal to R<sub>2</sub>), σ<sub>1</sub> is different from σ<sub>2</sub>. 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]. |

## Revision as of 01:24, 4 April 2009

By Sung Hoon Kang

Title: Non-spherical bubbles

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

## Contents

## 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 = σ_{1}/R_{1}+ σ_{2}/R_{2}

where ΔP is the pressure jump across the surface, R_{1} and R_{2} are the local principal radii of curvature, and σ_{1} and σ_{2} are the corresponding principal resultants of surface stress. Thus, for a non-spherical bubble where R_{1} is not equal to R_{2}), σ_{1} is different from σ_{2}. 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].

The armoured bubbles can have various stable anisotropic shapes through particle-scale rearrangements to adapt external inhomogeneous stress. Fig. 1d shows high aspect ratio shapes with saddle curvature on the armoured bubbles. This characteristic can be used to modify the topology of the bubbles by having a hole into the object as the case of a stable genus-1 toroid shown in Fig. 1e. The authors foudnt that the interfacial jamming is a general phenomenon for materials such as polymethylmethcrylate (PMMA), gold and zirconium oxide and parcile and bubble sizes that spans four orders of magnitude. Fig. 1f shows liquid droplets of mineral oil that are covered with rigid particles. There are many more examples in nature such as dirty air bubbles in the ocean, various cellular organelles [5-6]. The authors conclude the paper by proposing that a general interfacial jamming transion may expalin the mechanical properties and structural stability of diverse systems mentioned above.

## 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).

[5] B. D. Johnson, R. C. Cooke, *Science* 213, 209-211 (1981).

[6] S. Joachim, E. Jokitalo, M. Pypaert, G. Warren, *Nature* 407, 1022-1026 (2000).