Bubbles are really not as simple as they appear
This article was prompted by a brief account in J. R. Partington's book on gunpowder of the history of soap, which he presented in connection with the production of saltpetre, which used similar chemical compounds (alkalis), because of its peculiar interest, and mentioned that the history of soap had not been adequately treated. This led me to think about (soap-) bubbles, but when I looked for information on bubbles in my usual references, I found nothing. Not even Minnaert said anything about them, but there is an excellent book by C. V. Boys on surface tension and bubbles. For more information on surface tension, see Surface Tension. This article is certainly not a complete account of either soap or bubbles, and contains only what comes to mind on a first attempt.
Soap is an example of a detergent, or surface-active agent, or surfactant. In everyday life we use it to wash dishes, clean clothes, or keep our bodies presentable to nose and eye. Soaps have many other uses. For example, they are used in greases to make compositions that will not run, are lubricants in their own right, and produce foams that can be used for mineral separation. With humans being as dirty and smelly as they are, it is surprising that soap, as we know it, did not come into general use in the middle ages. Humans make a poor contrast with cats, who keep themselves generally spotless and odorless without assistance. To clean their fur, cats roll in clay dust or other suitable powder, then lick the powder off. All contaminants come off with the dust.
In ancient times, those people who usually washed (the Romans) rubbed oil on their skins, then scraped it off, following this with immersion in hot water. Hair was probably originally cleaned by dusting it thoroughly with talc (the massive mineral talc or steatite is also called soapstone, probably from its soap-like softness and appearance), then rinsing off the talc. Urine also appears to have been used, or lemon juice if you had it. Cleaning hair with oil would leave one looking distinctly greasy. A soap was made specifically for washing hair, that also tinted the hair, usually red. This was borrowed from the Celts and Germans, who most desired the red hair, and not any associated personal fastidiousness.
Some plants can be used to help in washing clothes (such as the yucca, or "soapweed"), and these were commonly used before soap was available. The removal of oil from wool, called "fulling" since it also involved softening and felting the wool, used fuller's earth, usually diatomaceous earth, which adsorbed the oil and was then washed out, again demonstrating the cat's principle. A lye of wood ashes was popular for washing clothes, and probably for greasy dishes as well.
Soap was made in Marseilles from the 9th century, and in Venice from the 14th, but only in small amounts. Information on when the use of soap became general is not available. Galen mentions its use as a medicine, but also that it is better than lye or soda for washing. The Greek for soap is sapwn, from which all the modern words for it come. I have heard nothing about the use of soap in India or China.
Until quite recently, all soap was a soluble sodium or potassium salt of a long-chain hydrocarbon (fatty) acid, for example H3C(CH2)16COO-Na+, which is sodium stearate, containing 18 carbon atoms in a straight chain. To make soap, fats or oils from which the fatty acids come are boiled with strong NaOH or KOH. The reaction is H2COSt-HCOSt-H2OSt + 3NaOH → 3StNa + H2OH-CHOH-CH2OH, where St is the stearate radical. The first substance is a typical fat, an ester of glycerol (glycerine), a tribasic alcohol, in which each OH is replaced by OSt. Boiling with the alkali regenerates the glycerol while freeing the St- ions that are the actual soap. The soap is precipitated from the solution by adding salt, NaCl, which raises the Na concentration so much that the solubility product of the soap is exceeded. Sodium stearate is a hard soap that is not very soluble in cold water. If KOH is used instead, a soft soap is produced that is easier to use. Soap is basically a soluble fat.
When the American midwest was being cleared in the early 19th century, one means of ekeing out a living was to boil the ashes of trees that had been felled and burnt in large pots over a fire, concentrating the extracted lye, and selling it as potash. This potash was used mainly for making soap, and for purifying saltpeter for gunpowder. The fat used came mostly from pigs, some from cattle (tallow), but the latter was valuable for making cheap candles. Fine soaps were made from olive oil or other high-quality fats. More recently, cottonseed oil, coconut oil, and palm oil have been used. The associated fatty acids have the formulas H3C(CH2)nCOOH. If n = 10, this is lauric acid; if n = 14, it is palmitic acid; and if n = 16, it is stearic acid. Natural fatty acids usually have even numbers of carbon atoms. Oleic acid, occurring in oils such as olive, is an unsaturated acid, H3C(CH2)7CH=CH(CH2)7COOH with a double bond between the 9th and 10th carbon atoms. Note that all of these feature long chains that easily can become entangled with similar molecules.
The calcium, magnesium and iron salts of these soap anions are quite insoluble. If they are present in the water, calcium stearate or similar precipitates out and forms a gummy deposit, which makes up the familar "bathtub ring." Water containing these cations is called "hard." They may be largely eliminated by adding sodium carbonate ("washing soda") to the water before the soap, or for gentleness to the hands, sodium phosphate, which is less alkaline. Borax is a still better addition. Since the soap is not very soluble in cold water, it is also necessary to use hot, or even boiling, water. With these precautions, soap will do a very good job.
In the 1940's, a search was made for a soap anion that would not precipitate with the usual cations of hard water, and would at the same time be more soluble. Sodium cetyl sulphate, H3C(CH2)15CH2OSO2ONa, meets these requirements. The hydrocarbon end is like that of familar soaps, but the charged end is a sulphate radical. These new soaps were called detergents to distinguish them, but one can see that it is pretty much still the same thing. Tide was an early example of a detergent. It did not have to be used with washing soda, and worked in cool water. Instead of sulphates, other detergents were sulphonates, and might even contain benzene rings, as in sodium alkylphenylsulphonate, RArSO2ONa, where R, the "alkyl," is a long-chain hydrocarbon and Ar is an "aryl" or aromatic group. Dreft was an example of such a detergent, and was even gentler than the sulphates. There are many different compositions, but the idea is clear.
A problem with the new sulphates and sulphonates, especially those with aromatic groups, was that they were not biodegradable. When washed down the sink, they remained in the water and were not removed by sewage treatment. Streams and rivers began to foam, which was found highly objectionable. Before the whole country was covered by suds, biodegradable detergents were created, which replaced the earlier "hard" detergents in the early 1960's. Many current products proudly say they contain no phosphates (phosphorus is a plant nutrient that can cause "blooms"), but it seems that detergents never did. Phosphates were added to make the detergent work better. Borax is an excellent and unobjectionable washing aid, and is again available in supermarkets. Sodium carbonate and ammonia are also excellent (the latter eliminates the "films" left by glass cleaners), but sodium carbonate is definitely strongly alkaline and should not be used with bare hands. If you can tolerate phosphates, trisodium phosphate (TSP) is a superior washing agent all by itself. Why alkaline solutions are effective at removing grease deserves further explanation.
All soaps have a charged end that attracts water molecules strongly, and a hydrocarbon end that attracts molecules similar to itself which are not soluble in water. In other words, hydrophilic molecules bind to one end, and hydrophobic molecules, such as those of grease, oil and dirt in general, to the other end. Oil and dirt become covered with a hydrophilic film that is easily washed away by water. Note that water is essential to this process, and thorough rinsing is necessary.
The bubble is a familiar thing that would seem so simple as scarcely to need explanation. It is an approximately spherical volume of slightly compressed air surrounded by a thin film of water. The difficulty is that thin films of water spontaneously and almost instantaneously collapse into droplets, so that bubbles should be impossible. In fact, if you agitate pure water vigorously, you do indeed get no bubbles at all. When even a tiny amount of soap is added, however, bubbles are easily formed, and even a foam or suds of a multitude of bubbles can be formed, which is remarkably persistent.
When a soap molecule migrates to the surface of water, it finds itself in a low-free-energy environment with its charged end held tightly by water molecules while its hydrocarbon end bristling outwards. The presence of these soap molecules changes the surface tension; indeeed, usually reducing it. For soap in water, the surface tension is reduced to about 38% of its value in pure water. J. Willard Gibbs showed that when the surface of a soap-water film is disturbed, the concentration of soap changes in just such a way that the change in surface tension acts to stabilize the surface. This happens in different amounts with different substances and concentrations, of course. In favorable cases a water film becomes quite stable and permanent, so that bubbles will persist. Indeed, the ability to make a foam (suds) is often taken as an indicator of the effectiveness of a washing solution. Some materials may be effective detergents, however, without being able to make stable films, and these are used where foam would be a nuisance. Neither a strengthening of surface tension, nor the formation of an actual surface film, is responsible for soap bubbles.
Boys remarks that beautiful bubbles of a mercury film in water can be produced by violent agitation. They are not very stable, but do exist, and indicate that surface action to stabilize them is important even here. The attraction of impurities to the surface of mercury is well-known.
As explained by Boys, a plane film can easily be studied when it is suspended on a wire frame. This film consists of two surfaces, with water between. If the film is held vertical, the water will drain under the force of gravity from top to bottom, but only very slowly, since the film is thin and viscous forces are dominant. This demonstrates Gibbs's explanation very well. If the surface tension were not affected but constant, a small element of film would have equal forces acting at top and bottom, and so would fall with the acceleration of gravity, which is certainly not observed. Therefore, the total surface force in the upper parts of the film is enough greater than that in the lower parts to overcome the weight of the film. This is a very small difference, but it is essential to the stability of the film.
Of course, the water does drain out by gravity, thinning the film. To slow this action, glycerol is usually added to the bubble mixture to increase its viscosity. A recommended bubble mixture is 19 ml of sodium oleate (soap) in 750 ml of water, made up to 1000 ml with glycerol. For a good bubble mixture, the water should be clean distilled or at least deionzed water.
Light is reflected from each side of the film. These two contributions interfere in the familar manner to give the colours of thin films by removing certain colours by destructive interference, just as seen in oil films and in the oxide films on tempered steel. When the film thickness becomes less than about 1 μm the colours begin to appear, at first green and magenta, then the brighter colours of lower orders, including reds, blues and one good yellow or straw colour. At about 0.1 μm there is a white, but for thinner films the colour approaches black (film invisible) as the light from front and back cancel. Recall that there is a difference of π in the phase of the reflected light between rare-to-dense and dense-to-rare reflection, just as in the case of Newton's Rings (which, in white light, show the same colours). These colours not only make soap bubbles attractive, they also serve to indicate the thickness of the films. As a soap bubble thins as the water drains and evaporates, the colours appear first on the upper parts, and a drop of water grows at the bottom. A black film is very tender, and soon after this appears, the bubble bursts as the two sides of the film cannot be held apart.
A formula for the pressure in a bubble can easily be derived from statics. The tension in the film, (2πr)(2γ), where γ is the surface tension, must equal the total force πr2p, where p is the difference in pressure on the two sides. Therefore, p = 4γ/r. For a sodium oleate solution, Rayleigh found γ = 25 dyne/cm. In the case of a nonspherical surface with principal radii of curvature r and r' (these are the maximum and minimum radii, which will be at right angles), p = 2γ(1/r + 1/r'). For a 1 cm radius bubble, p = 100 dy/cm2. If the film is 1 μm thick, the bubble will weigh about 1.2 dyne, or 1.3 mg. It is no wonder that such a light object can float on the slightest breeze. Bubbles can have positive buoyancy if filled with a light gas. Even methane, M = 16, will give a 1 cm radius bubble a lift of 3 mg, enough to float it. If a small bubble and a large one are connected, the small bubble will blow into the large one, so that large bubbles grow at the expense of small ones, something that is easily observed in foams.
A cylindrical bubble can be made by pulling on the ends of an originally spherical bubble and adjusting the pressure within it until the sides are cylindrical. The pressure inside a cylindrical bubble of radius r will be p = 2γr (since r' = ∞), the same as inside a spherical bubble of twice the radius. As long as the length of the cylindrical bubble is less than 2πr it is stable against small displacements. However, a longer bubble will break into two spherical bubbles, on on each support. Since the surface tension acts like a surface film, a jet of water is subject to the same instability, and breaks into droplets. Boys explains and illustrates these matters very well. Among other things, he shows how collisions between droplets cause the scattering of a water jet.
A cylindrical bubble with no ends, so that the pressures on the two sides of the film are equal, assumes the shape of a catenoid of revolution. The curvature of a catenary is equal to the reciprocal of the distance from an axis. This distance will be the radius of curvature of the film in a horizontal plane, and also the radius of curvature in the vertical plane, so that the net curvature will be zero. A film on a spiral frame with a central axis is a particularly attractive surface of zero curvature.
Soap films will intersect along lines with three films making equal angles of 120° with each other, adjusting themselves so that this occurs. If four films happen to intersect at a line, they will move so that only three meet on any line. If two bubbles intersect, they meet along a circle. The centres of curvature of the two bubbles and of the surface separating them lie on a straight line, and obey the relation 1/r + 1/r' = 1/r", where r is the radius of the larger bubble, r" the radius of the smaller, and r' the radius of the common film. Relations like this are also familiar from optics and from electric circuits, as well as from projective geometry.
When two bubbles collide, they often remain separate and bounce off one another. This demonstrates that only the hydrocarbon tails of the surface soap molecules come into contact, which does not break the film, not the strongly attracting water molecules. There is also a thin air film that must be squeezed out. Such air films often protect a water droplet from a hydrophilic surface, and it rolls like a ball bearing.
We haven't discussed the bubbles that appear in an effervescent drink or in a boiling liquid, which have only one surface layer and which break when reaching the surface, or form an actual bubble there. These are the bubbles of the "bubble chamber" in which ionizing radiation triggers the evolution of gas in a supersaturated solution. When you move a glass of beer suddenly, the drops seem to have negative mass, like the holes in a semiconductor. Lava lamps contain a bubble of coloured material that is immiscible with its surroundings, and slightly heavier (more dense) than the surrounding liquid when cool. It sinks to the bottom, where it is heated by the illuminating lamp, making it become lighter, whereupon it languidly makes its way upwards. Bubbles and froths are used in the separation of minerals. The surface-active agents are specially tailored to attract the minerals of interest, either the ores or the gangue. The froth, carrying the mineral of interest, is then easily separated by skimming it off.
In English, the word "bubble" seems to be onomatopoeic, from the sound made by the lips when making bubbles. In German, "eine Blase" is also associated with blowing, as was the word in ancient Greek, fusa, which came from fusaw, "to blow." In Latin, the word was "bulla," mentioned by Ovid, which gave the French "une bulle." These seem derived rather from "to boil" than "to blow." "Bulla" was used for the spherical seals of papal documents, and by extension to their contents. In Spanish, a soap bubble is "una pompa de jabón" although the general word for a bubble is "barbuja."
J. R. Partington, A History of Greek Fire and Gunpowder (Cambridge: Heffer & Sons, 1960). pp. 306-309.
E. F. Degering, ed., Organic Chemistry (New York: Barnes & Noble College Outline Series, 1951). Chapter XXX, pp. 280-284. Or see any similar reference text.
C. V. Boys, Soap Bubbles; Their Colours and the Forces that Mould Them (New York: Dover, 1959).
Composed by J. B. Calvert
Created 20 March 2004