# Difference between revisions of "Colloid Science - Non-spherical bubbles"

by Professor Stone

## General Introduction beyond the article

Bubble formation

This is a very famous article by Professor Howard Stone. The experimental pictures from this articles were feature on the front page of SEAS homepage. I carefully read the article and were indeed fascinated by the results obtained. All in all, most people would wonder how and why are bubbles formed. The simplest building block of bubble systems is a single gas bubble in still water. We expect that it rises straight upward, due to the buoyancy force that is directed opposite gravity. However, bubbles with a radius larger than about 0.8 mm spiral or zigzag as they rise. Why? Scientific articles show that Leonardo da Vinci were the first to point out this phenomenon and even drew rising spiraling bubbles. The question has now been tackled for decades, and although the phenomenon is ubiquitous in nature, technology, and even popular toys such as bubble columns, the full answer is not yet known. The difficulties arise from the bubble's interaction with its own wake, from the free and thus deformable surface, and from surface impurities that are unavoidable even in ultraclean water. For bubbles in turbulence or for many interacting bubbles, the question is even more difficult to answer. Accurately calculating the dynamics of a few air bubbles in turbulent flow is numerically still infeasible.

### Bubble formation

We see Bubbles in our lives everyday. However, few people have cared about how they form. By and large, bubbles can be injected in some fluids, but they can also form spontaneously. Such spontaneously formed bubbles mainly contain liquid vapor instead of some other gas. This process of bubble formation, just as boiling water, is called cavitation. Cavitation can occur in a liquid when the local pressure p(x) drops below the vapor pressure pv of the fluid. One way to achieve cavitation is to increase the liquid's temperature, because the vapor pressure is temperature dependent: For water at 20°C, the vapor pressure is 0.023 bar (2.3 kPa), but at 100°C, it is 1 bar, and thus the water boils.

Another way to achieve cavitation is to increase the local flow velocity U(x). An easy experiment is to reduce the cross section of a pipe in one region, making a so-called diffuser that produces large local flow velocities due to mass flux conservation. For steady potential flow, the corresponding local pressure p(x) can be estimated from Bernoulli's equation,

At an ambient reference pressure of 1 bar and at room temperature, a water velocity of about 14 m/s is sufficient to nucleate bubbles.

However, the weakness of Bernoulli's estimate is that it does not consider viscous effects, the gas content of the fluid, impurities, or walls and other inhomogeneities. Crevices at surfaces or remaining impurities to which submicron gas bubbles attach seem to play a prominent role in the bubble nucleation process, but our understanding of cavitation is still incomplete.

## Non-spherical 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.

Surface tension gives gas bubbles their perfect spherical shape by minimizing the surface area for a given volume. Researchers have shown 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. The rigid particles straddle the gas–liquid interface and have mechanical properties distinct from either constituent, forming what we call an interfacial composite material. The fusion of these armoured bubbles, achieved by squeezing the bubbles between two glass plates, produces a stable ellipsoidal shape as shown in the picture. The fused armoured bubble is unable to relax to a spherical shape by expelling particles: instead, the jamming 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. 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. These shape changes occur with apparently no hysteresis and at relatively low forces, which is equivalent to perfect plasticity in continuum mechanics.