We could illustrate this by considering a flat sheet of water; for example, an open trough of water which is exposed to the atmosphere. It is but natural to assume that in such a situation there would be an exchange of molecules across the air-water interface. The molecules of water are constantly moving about. A small proportion of molecules, which move more rapidly than others, escape from the liquid by overcoming the internal molecular forces which bind them together. The situation is much the same as that of a missile which, given sufficient speed, escapes from the earth’s gravitational attraction. In a similar fashion, a number of molecules of vapour penetrate the water surface and are captured by the liquid. Eventually, a state of equilibrium is set up when the number of molecules escaping from the liquid equals the number of vapour molecules entering it. When this happens the shape of the interface is stable and the vapour pressure acquires a steady value.
Let us consider now a spherical water drop surrounded by an environment of vapour. In this situation the shape of water vapour interface is curved instead of being flat; consequently, it has a larger area than a flat interface. In view of its larger area, a larger number of molecules are transported across it when a state of equilibrium is reached. Another way of stating this would be to assert that the vapour pressure required to maintain a spherical drop in equilibrium is larger than the saturation vapour pressure over a flat surface. In other words, a certain amount of supersaturation is necessary to maintain a spherical drop in equilibrium.
This interesting observation is due to Lord Kelvin, who derived a mathematical relation between the excess of vapour pressure and the curvature of the interface. From Lord Kelvin’s results, we are able to reason that if water vapour was directly converted to liquid droplets – of the size of water molecules – an exceedingly high degree of super-saturation would be necessary. The excess vapour pressures required to maintain such minute droplets in equilibrium would be quite unrealistic. On the other hand, if condensation occurred on a nucleus, the water-air-interface will have a much larger radius of curvature. Consequently, much smaller degree of supersaturation would be sufficient to initiate the formation of liquid drops.
From this reasoning we see that the presence of nuclei is essential for the process of condensation. As the sizes of nuclei are much larger than the dimensions of a water molecule, a drop once formed by condensation on a nucleus required a considerably lesser degree of supersaturation. There is, therefore, a reasonably good chance for the drop to survive in the atmosphere. On the other hand, a drop which does not form on a nucleus would need an extremely high degree of supersaturation. It would almost certainly evaporate as soon as it was formed.
It is worthwhile to recall that this fact was well demonstrated in a laboratory experiment by C T R Wilson, the scientist to whose ingenuity we owe the Expansion Cloud Chamber. Wilson was able to show that if we could purify the air sufficiently by removing from it all traces of nuclei, then it was possible to prevent condensation even with very high degrees of supersaturation. Despite relative humidities of the order of 400 per cent, little or no condensation was observed in the absence of nuclei.
It is important to note that the curvature of a liquid vapour interface is one of the several factors that determine the saturation vapour pressure needed to maintain a droplet in equilibrium. It is possible to show, for example, that the degree of supersaturation that is required is considerably smaller for nuclei that are hygroscopic. Hygroscopic substances are those that absorb moisture. In India, hygroscopic nuclei are present in plenty in the form of suspended salt particles or minute drops of acid contained in gases from industrial factories.
When hygroscopic nuclei are present in the air, it is possible for clouds to form with little or no supersaturation. There is evidence to indicate that condensation has taken place even when the relative humidity of the air was below 100 per cent.
A number of experiments have been carried out in recent years to measure the size and concentration of condensation nuclei. These experiments reveal that even on days of fairly good visibility, the number of nuclei in the atmosphere is exceptionally large. The concentration of small condensation nuclei is of the order of a million per litre of air.
The diameter of an air molecule is about a ten millionth part of a millimeter. The average diameter of a small condensation nucleus is about thousand times larger than an air molecule, that is, about ten thousandth part of a millimeter. In dealing with such small sizes physicists usually use a unit called the micron. A micron is a millionth part of a metre (10-6 m).
The origin of hygroscopic nuclei in the atmosphere is an intriguing problem. From the little experimental evidence that we have, it appears that such nuclei are largely particles of sea salt. Considering the fact that the earth is largely ocean-covered, it seems natural to assume that most hygroscopic nuclei have an oceanic origin. Meteorologists have believed that very large numbers of salt particles are injected into the atmosphere by the breaking of waves. When waves strike the coastal regions of a large land mass they release a large volume of spray. Millions of minute salt particles are injected into the free atmosphere in this manner, and they provide nature with a store-house of condensation nuclei. But can we be sure that an adequate number of nuclei are indeed generated by this process?
Many years ago Sir George Simpson argued that the average rainfall of the earth was about 100 cm per year. This represents 100 cubic cm of water over each square centimeter of the earth’s surface. Let us assume that this volume of water is obtained by a combination of cloud drops, each having a radius of 10 microns, and let each drop contain a salt particle as its nucleus. With a little arithmetic it is possible to show that the number of nuclei returned to earth should be of the order of 2.5 X 1010 per year over each square centimeter. This works out to be about 1000 nuclei per second over each square centimeter. The rate at which nuclei are generated by breaking waves should be at least of this order. It was felt that such a high rate of nuclei production was impossible. But, more recently, laboratory experiments by Professor B.J. Mason in England suggest that the bursting of minute bubbles from the sea surface might well produce 1000 nuclei per square cm per second, which is the figure required.