Surface tension gives gas bubbles their perfect spherical shape by minimizing the surface area for a given volume1. 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.
We have previously described a microfluidic method for producing spherical armoured bubbles that are all the same size2. The rigid particles straddle the gas–liquid interface and have mechanical properties distinct from either constituent, forming what we call an interfacial composite material.
We find that fusion of these armoured bubbles, achieved by squeezing the bubbles between two glass plates, produces a stable ellipsoidal shape (Fig. 1 a–c) (for methods, see supplementary information). The fused armoured bubble is unable to relax to a spherical shape by expelling particles: instead, the jamming2 of the particles on the closed interface, which is mediated by surface tension, leads to non-minimal shapes.
The non-trivial geometry of these bubbles provides a natural means of understanding the state of stress in the interfacial composite material. A balance of normal stresses at the bubble surface demands that
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. Therefore, if R1≠R2, as is the case for non-spherical bubbles, then σ1≠σ2 of the armour particles, so we term the interfacial composite material a solid.
The armoured bubbles can be remodelled into various stable anisotropic shapes because the interfacial composite material is able to undergo extensive particle-scale rearrangements in order to accommodate external inhomogeneous stresses (our manuscript in preparation). These shape changes occur with apparently no hysteresis and at relatively low forces, which is equivalent to perfect plasticity in continuum mechanics.
High aspect-ratio shapes with saddle curvature can be maintained on the armoured bubbles (Fig. 1d). This feature may be exploited to change the topology of the bubble by introducing a hole into the object, thereby creating a stable genus-1 toroid (Fig. 1e). The change in topology is irreversible5, and seems to be the only permanent change associated with the manipulation of the interfacial composite material.
We have found that interfacial jamming is a general phenomenon that occurs with particle types such as polymethylmethacrylate, gold and zirconium oxide, and that spans four orders of magnitude in particle and bubble sizes. Similar effects are evident with liquid droplets of mineral oil that are covered with rigid particles (Fig. 1f).
Stable, non-spherical shapes of pressurized systems that have no obvious source of a stress-bearing network have been reported for dirty air bubbles in the ocean6 and for various cellular organelles7. Also, systems such as gelled lipids on air bubbles8 and protein-coated vesicles9 show plasticity. We propose that a generic interfacial jamming transition may explain the mechanical properties and structural stability of these diverse systems.
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The authors declare no competing financial interests.
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Bala Subramaniam, A., Abkarian, M., Mahadevan, L. et al. Non-spherical bubbles. Nature 438, 930 (2005). https://doi.org/10.1038/438930a
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