Surface Tension

Liquids sometimes form drops, and sometimes spread over a surface and wet it. Why does this happen, and why are raindrops never a metre wide? A clue to the answer to the second question may be found in pictures of astronauts playing with large blobs of water in their space-craft.

It all comes down to the forces between atoms or molecules, and the forces between them. These particles are unimaginably small. In one gram of water the number of molecules is about 3.3 X 10²², or 33000000000000000000000. If the gram of water were in the form of a 1 cm cube, there would be about 23000000 molecules on a side.

The force between two atoms or molecules is generally repulsive if they are pushed too close together. The force increases so strongly as the distance is reduced that they behave almost as if they were hard objects. Try compressing some water or steel. But at larger distances the force are attractive. Try pulling pulling the bung from a tube which contains only water and no air. Or try pulling a piece of piano wire in two.

So between these two regimes, two molecules prefer very strongly to sit at a distance where there is no force between them, where their total energy is a minimum. Of course, they are not stationary - they are jiggling about because of thermal motion. This changes the optimum distance very slightly, and that is why most things expand when heated. Below a certain temperature, molecules cannot easily get away from their position - in this condition, the substance is a solid. At a higher temperature they can wander around, and we have a liquid. Given a high enough temperature, molecules may may escape - this is evaporation. At higher temperature the liquid turns into a gas. As you might expect, adding pressure changes things.

So in a solid or a liquid, the atoms or molecules are in a state of average equilibrium. On average, each one feels no net force from the ones all around. There will be fluctuations in the force on each one as they jiggle around, and in a liquid the molecules will slowly wander about. Two layers of differently coloured water will gradually diffuse into each other. Even in a solid, there can be very slow diffusion.

What has all this to do with water drops? The answer is already implied in the statements given. Every molecule is on average in a sate of lowest available energy, with no net force on it. If a molecule experienced a net force it would move until it didn't. Molecules in the body of a liquid are surrounded by neighbours . You might imagine that there could be around twelve packed around it - six in a ring, with three above and three below. Any molecule is, on average, in equilibrium with all of these.

But a molecule at the edge has fewer neighbours, perhaps by about three. What is the consequence? Imagine just two molecules coming together. They are attracted until they reach equilibrium, and so when they are together, they have less energy than when they apart. This is like water in a reservoir - water at the surface has more energy than water at the bottom - that is why it can drive a turbine. Ten molecules together have lost about ten lots of energy in coming together. A molecule in the surface has lost less energy because it has joined together with fewer neighbours.

So a molecule in the surface has higher energy than one inside the liquid. What do things do in a position of high energy? They tend to go to a position of lower energy. In the case of gravity this is called falling. But not all the surface molecules can go inside - whatever happens, there has to be a surface. What actually happens is that the surface becomes very slightly depopulated, until all the molecules are in equilibrium.

So at, and very near, the surface of a water drop, the molecules are a little further apart than the normal equilibrium distance. So the surface behaves as if it is in a state of tension. And because this region has higher energy for a given area, it will tend to behave so as to minimize its area in any situation. For a free blob of liquid, the smallest area is obtained with a sphere. In more complicated cases the shape of the surface reflects the complexity of the situation. Click here

The drops in the middle of the picture show the spherical shape, while those on the wire are influenced by gravity, adhesion to the wire, and surface tension.

Larger drops of water that sit on a non-wetted surface are not spherical - the shape is the result of the combination of the surface effect with the force of gravity. Because some surfaces have an affinity for water, drops can hang from them.

Some liquid and solid combinations have little or no affinity. In these cases a liquid drop sits on the surface. But if there is a degree of affinity, the shape of the drop is modified. With strong affinity, the liquid wets the surface and spreads out as a thin layer. What matters is the relative energy of the three interfaces - air-liquid, liquid-solid, and air-solid. In practice, because of surface variations, impurities and foreign bodies, the situation is complex, and real drops may take shapes that cannot be computed, as you can see in some of the photographs above.

What are the shapes of water-drops in ideal circumstances? To some extent they reflect the symmetry of the situation. Very small drops floating in a space craft are close to being spherical, because there is no preferred direction, but as larger and larger drops are more and more affected by effects that can dominate the short-range inter-molecular forces. The kinetic energy and momentum of different parts of large drops makes them wobble around in a rather unstable manner. If the waves that travel around a drop should add in a suitable manner (Interference) the drop may split.

A similar effect is a part of the explanation of the finite list of chemical elements found on earth, which terminates at number 92, uranium. The particles in an atomic nucleus experience short range forces analogous to those between molecules in a liquid. So larger and larger nuclei can behave like large liquid drops. Other considerations, such as quantum mechanics, modify the behaviour, but a large enough nucleus can be quite unstable. Furthermore, some of the particles (protons) in a nucleus carry electric charge. These repel each other, like similar magnetic poles. Because the electric force has long range, each proton feels the effect of all the others, whereas it feels only he nearest neighbours for the nuclear force.

So adding particles to a nucleus doesn't make it bind more strongly, while the electric repulsion gets bigger. So very large nuclei are very unstable. Large enough nuclei have such short lives that they have not survived the age of the earth, even if they were originally present. Nevertheless, during the last sixty years, scientists have been able to create those bigger nuclei and some that probably never existed on earth. An exciting recent development is the discovery of very heavy ones which have anomalously long lives. On the chart of nuclear types this would appear as an island of stability, which was predicted to exist many years ago. This has no counterpart in drops of water - it is a quantum mechanical effect. Blobs

Since it is the repulsion between protons which makes big nuclei unstable, it might be thought possible to make nuclei without them, using only the neutral particles - neutrons. One of the reasons why not is that neutrons are unstable, decaying into protons. They only survive in nuclei because their energy is effectively reduced in that environment.

But there is another island of stability, which does indeed comprise only neutrons. In a neutron star the force of gravity generated by a huge number of particles crushes everything together into an enormously dense mass. The electric charges are sent packing in the form of electrons - in effect the protons have decayed into neutrons. Surface tension plays no part here - the surface is a negligible part of the whole. Neutron stars are like no other object. Nature seldom repeats herself exactly.

If the symmetry is broken, drops are no longer spherical. The sticky blobs on a spider web have circular, but not spherical, symmetry because the threads are cylinders (Spider Webs). They also have mirror symmetry because the threads have no preferred direction. For water drops resting on a horizontal surface, gravity breaks the up-down symmetry, although the drops are circular in plan. The pressure in the drop increases slightly with the depth, and so the total radius of curvature decreases from top to bottom.

The next picture shows an approximate simulation for a range of drop sizes, for the case where liquid has no affinity at all for the solid surface. The tiniest drops are almost spherical, but the larger ones are a little less curved at the top.

If the density of the liquid increases, or the surface tension decreases, or we look at larger drops, the drops will be flatter for a given radius or volume . The second, third and fourth pictures above show examples. The scales are decreasing in order to accommodate the greater widths. Eventually the drops do not become higher - they just become wider and flatter.

This is an example of the way that large and small things are not comparable. Small insects can ride on the surface tension of a pond, but large ones cannot. Nobody will ever make a boat that floats by surface tension. Some insects, such as spring-tails and pond-skaters, can live on top of the surface of water. The surface is dimpled by their weight until it provides an upward force equal to the weight. Some insect larvae which live below the surface can push breathing apparatus through the surface, and cling there while they take in air. The breathing tubes often have feathery tips to increase the area.

The reason that surface tension affects only small objects is that it is confined to a layer only a few molecules thick. Its energy is proportional to the surface area. But other effects are often related to the volume. Multiplying the length of a shape by ten increases the area a hundred-fold, but the volume a thousand-fold.

The spider Argyroneta aquatica makes a net under the water, under which it traps air to make a home in which it can live. The net needs only to be fine enough for surface tension to stop the air from getting through any holes. The curvature of a bubble or a drop is proportional to the pressure difference between the inside or the outside. If the hole is small enough, there won't be enough pressure to make the small radius needed for a bubble to get through the hole. This is also how an umbrella or a tent works - the holes are too small to let the water through. Of course, the material must not be wetted by the water.

If we had a deep container with a bottom made of umbrella material, and we started to fill it, the pressure would eventually force the water through. Why not try it with an inverted umbrella, pouring the water in slowly and carefully.