October 25, 2021

I, Science

The science magazine of Imperial College

The most recent financial crisis caused by the housing bubble, which popped as subprime mortgages in the US and many Western European countries defaulted, has been having dramatic consequences in many aspects of Western Europe and US economies such as high rate of unemployment and economical policies based on ”cut if you can”. Stock market bubbles, whose origin have been not completely understood by economists, are events that have occurred frequently in the past, even as far back as 1637 with the tulips mania.

When we think of bubbles, we always imagine those objects that we can make out of blowing a solution of soap and water through an empty hole, with kids getting all mad and enthusiastic wanting to play with them. These soap bubbles are much older than those in the economy, but some aspects of their nature and physics still fascinates scientists and they are still capable of revealing new enigmatic phenomena and interesting properties.

Bubbles consist of air or other gas enclosed within a thin film of liquid soap-water solution, which in turn is in contact with air (soap bubbles) or other liquid (like fizzy drinks). Bubbles can only exist due to a fundamental intrinsic property of all liquids called surface tension. This is a net force which characterises liquid surfaces, and it is due to the lack of complete compensation of intermolecular forces among molecules at the surface when compared to those in the bulk. In virtue of this force, liquids surfaces behave like a sort of soft elastic mattress for some objects in contact with the liquid surface.

A solid object which is denser than the liquid it is placed in will sink to the bottom, but if the surface of the object is relatively large and its weight is not much bigger than the force arising from the liquid surface tension, then the object will be able to float on top of the liquid surface without showing any minimal buoyancy. This effect is entirely due to the surface tension of the liquid and it is this force which makes a needle floating on water surface when placed horizontally and it helps water striders walking on water.

Surface tension varies for different liquids and in the case of water is high because of the very strong hydrogen bond interactions among water molecules. This force determines the spherical shape of a drop of water from the tab. Mathematicians demonstrated that a spherical shape is the one which guarantees the minimum surface of any isolated object, so that it results the energetically must stable surface.

This is also the case of bubbles. They can assume different shapes when in contact with other solid surfaces or assembled geometries (cubes, prisms, etc.), but no matter the initially generated shape they will turn to a sphere when individually isolated in air for a long enough time.

The formation of a bubble results from the balance between competitive forces such as the surface tension of the liquid and the air we blow for its formation. The surface tension is too strong to allow bubble formation, but when soap is added to water surface tension of water is lowered, making the pressure of air induced by blowing competitive to form the bubble.

The pressure of the air inside a bubble is different from the pressure outside and Pierre-Simon Laplace, a French mathematician and astronomer at the end of the eighteenth century, demonstrated that the pressure is related to the radius of the bubble. The smaller the bubble the bigger is the pressure inside it.

Bubbles are metastable structures, which pop after a certain time, with pressure increasing inside them or when in contact with another object. Nevertheless they can last also long time and can merge with each other forming different structures. The encounter of two bubbles always obeys to the principle of minimum surface area and this leads to the law of the survival of the fittest: the smaller bubble will bulge into the larger. On the other hand if the bubbles are identical they will couple together separated by a flat wall. Bubbles are very discreet too. In the nineteenth century the Belgian mathematician Joseph Antoine Ferdinand Plateau found that only three bubble walls can meet along a line with angles of 120o and that four bubble walls can meet at one point with angles of 109.5o.

Bubbles fascinate not only babies and kids but adults too. They exhibit very interesting optical, acoustic and mechanical properties when organized in soapy foams. For instance a phenomenon known as iridescence is what gives bubbles different beautiful colours and reflections. This is not the same phenomenon at the origin of rainbow colours. Contrary to the latter, which are generated by the refraction and internal reflection of light inside a drop, some rays of light impinging on the film are reflected off of the outer surface of the bubbles, while other rays penetrate the film and re-emerges after being reflected by the second surface. The different rays undergo interference with each other, which might be either constructive or destructive allowing only certain wavelengths (colours) to survive. Thicker walls cancel out red wavelengths, giving blue-green reflections, while thinner walls give blue light by cancelling yellow wavelengths.

Bubbles in liquids have an oscillatory behaviour. We can notice it looking at bubbles in a glass of coke or champagne in their ascent motion and Leonardo Da Vinci was among the first to study this behaviour. If a pressure-wave (oscillations in pressure) passes through the bubble, it activates an oscillatory motion which will rapidly tune to a specific resonant frequency of the bubble. This produces a sound corresponding to that frequency. Bubbles show this behaviour in superheated liquid (when it is brought to a temperature above its boiling point) or when rain droplets fall into a lake. In fact after rain drops hit the surface of the lake a tiny bubbles form as result of the droplet impact with the surface. Their oscillations underneath the surface will occur in a narrow range of resonant frequencies, producing a sounds which is that we can listen when we try to dive underwater during a rainy day, if lighting does not kill us beforehand.

Finally a fascinating and still very enigmatic phenomenon of gas bubbles is that known as sonoluminescence, which consists of the capacity of a bubble containing noble gases such as xenon or argon and vapour to generate light under sound wave adsorption. The phenomenon was first observed for many bubbles in 1934 by two Germans scientists H. Frenzel and H. Schultes. In 1989 the same phenomenon was observed from a single bubble. The acoustic wave induces a bubble expansion followed by a sudden collapse with simultaneous emission of light. Another striking peculiarity of the phenomenon is that approximate estimates have revealed the temperature inside the bubble to be higher than that necessary to fuse a metal. Different explanations of the phenomenon have been proposed and different claims about the actual temperature inside the bubbles from 20,000 Kelvin to millions of Kelvin and some scientists have evoked evidence of occurrence of nuclear fusion reactions inside the bubbles. Many observations are still controversial and have been not reproduced by the international scientific community and nobody still knows what exactly happens in this phenomenon. Nevertheless something new happens for sure and bubbles still leave us open-mouthed and make us dreaming like children.