THE FIZZ IN BEER AND CARBONATED soft drinks arises from carbon dioxide that remains dissolved in the liquid because the drink was bottled or canned under pressure. Without the dissolved carbon dioxide the taste and smell of the beverage would be quite different. When the container is opened, the internal pressure is released and the carbon dioxide comes slowly out of solution as a gas.

When a beer bottle is opened, the sudden change of pressure in the gas just above the beer creates a mild turbulence and cavitation (the formation of partial vacuums) at the surface. As a result bubbles of carbon dioxide form and burst. The pressure change also gives rise to a slight mist just above the open top of the bottle. The mist has two components: large droplets thrown upward by the cavitation and smaller droplets condensing out of the escaping gas (air, water vapor and carbon dioxide).

The condensation is more apparent to me if the beer bottle is only slightly cooled. Then the pressure in the vapor just above the liquid is higher than it would be if the bottle were cold. As I open the bottle this pocket of gas suddenly expands into the atmosphere just above the neck. Such an expansion of gas requires energy because the pocket must push its way into the atmosphere. The gas must do work: it applies a pressure that moves an interface (between the gas and the atmosphere).

Since the expansion is quite fast, there is no time for the energy to be transported from the beer, the bottle or the atmosphere. The gas is driven by the kinetic energy of its own molecules. They have a random motion whose energy is measured indirectly as the temperature of the gas. When the molecules lose energy, they move slower and the temperature of the gas decreases. The decrease in temperature causes the water vapor to condense into droplets, forming the mist that gathers momentarily over the mouth of the freshly opened bottle of beer.

When beer is poured into a glass, the turbulence and cavitation are much greater. Air is trapped in the liquid, forming bubbles. In the regions where the turbulence lowers the pressure of the beer the dissolved molecules of carbon dioxide collect to form a bubble, which grows as it gathers more carbon dioxide. Since the bubbles are much lighter than the beer, they rise to the surface, where they form the thick raft called the head.

A despicable prank people sometimes play is to surreptitiously shake a closed container of beer or some other carbonated beverage and then hand it to someone else. When the other person opens the container, the contents erupt vigorously and often spray all over him. The shaking generates such severe turbulence in the liquid that small pockets of gas come out of solution in the regions where the turbulence momentarily reduces the local pressure.

When an unshaken bottle of beer is opened, the carbon dioxide has only one major place to come out of solution: the top surface of the beer. A shaken container of beer is different. It develops hundreds or thousands of tiny bubbles, each one providing a surface where additional carbon dioxide can come out of solution. When the container is opened, the transformation from dissolved to undissolved carbon dioxide is so rapid that liquid is expelled.

In a still glass of beer the carbon dioxide comes out of solution far slower. Bubbles of the gas form, break off from the wall of the glass and drift to the surface, where they eventually burst. All the bubbles develop on the walls or the bottom but only at imperfections in the surface of the glass or where a mote of dust has lodged. In the absence of cavitation the bubbles need condensation nuclei. It is not the condensation nucleus itself, however, that gives rise to the bubble but rather the air or carbon dioxide that is adsorbed on the surface of the nucleus.

Imagine a small crevice on the inside of a glass. Air can lodge in the crevice as the glass is filled with beer. The pocket of air provides a surface on which the molecules of carbon dioxide can come out of solution. A bubble of carbon dioxide begins to grow, eventually becoming large enough to break off and float to the surface. Probably enough air and carbon dioxide remain in the crevice to encourage the formation of another bubble.

A mote of dust serves the same purpose if air is adsorbed on its surface. You can promote the formation of bubbles in beer or a soft drink by adding any solid surface onto which air is adsorbed. Perhaps you have noticed that ice dropped into a soft drink increases the production rate of bubbles and the consequent fizzing. Tiny bubbles of air are trapped in the surface of the ice. When the surface melts, the pockets of air are exposed and can serve as nuclei for bringing the dissolved carbon dioxide out of solution.

A bubble that forms on the air in a crevice in a glass filled with beer is never spherical. As more carbon dioxide enters the bubble it gets bigger and extends upward. Its shape also changes. As the bubble expands, its top surface remains roughly hemispherical but the lower section narrows into a cylinder. The cylinder is unstable; with further growth of the bubble and narrowing of the cylinder the cylinder collapses, releasing the bubble.

Two forces work on the bubble forming on the air in a crevice. Since the gas is lighter than the beer, buoyancy pulls the growing bubble upward, away from the crevice. The force countering the buoyancy, at least initially, is the surface tension at the boundary between the beer and the gas. This force develops because of the mutual attraction between the molecules in the liquid at the surface, putting the surface effectively in tension. The force of the surface tension at any given point on the curved boundary is perpendicular to the boundary. When the bubble is just forming, these force vectors point toward the central region of the bubble, that is, downward.

As the bubble grows, the buoyancy increases and eventually overwhelms the surface tension. The opposing forces do not engage in a simple tug-of-war in opposite directions. Buoyancy pulls the enlarging bubble farther from the crevice. The bottom section of the bubble then begins to form a cylinder with concave sides. Once the bubble has been pulled sufficiently far upward the cylinder collapses from surface tension, pinching off the upper section of the bubble. Then surface tension shapes the bubble into a somewhat more spherical configuration.

Why do bubbles not form before a container is opened and stop forming in an open container after an hour or so? When the container is closed, the relatively high pressure in the liquid (exerted by the pressure of the gas at the top) creates a high pressure in the gas adsorbed at the nucleating sites. At such a site carbon dioxide molecules are constantly entering and leaving a tiny gas pocket. Since the beer is in equilibrium, as many molecules enter each second as leave. With a high pressure in the gas pocket additional molecules cannot enter to make the bubble expand.

After the container has been opened the pressure in the gas decreases, additional molecules enter and the bubble grows. Although the growth is periodically interrupted as bubbles break away, it continues until the supply of carbon dioxide molecules has been greatly reduced. Once again as many molecules enter the gas pocket as leave it, and the bubbles do not grow.

As a released bubble ascends it increases in size. The main reason is that it moves into areas of progressively less hydrostatic pressure, so that it is able to expand. A diver who has spent some time at depth suffers from this phenomenon if he comes up too fast. Under pressure the nitrogen in air has gone into solution in his blood. When the pressure is released, bubbles form in the body fluids, resulting in the symptoms known as the bends. A slower ascent allows the nitrogen to be reabsorbed into the blood and eliminated in the lungs.

When a bubble in beer reaches the surface, it may linger for several minutes before bursting. The bubble is far from spherical. The hydrostatic pressure just below the bubble (call it point A) must equal the pressure at the same level in the beer at a distance from the bubble (point B), otherwise beer would flow from one point to the other. At B the hydrostatic pressure results from the atmospheric pressure and the weight of the beer above that point. The same atmospheric pressure acts on A, but the weight of the liquid above the point is minimal because only a thin film of liquid is there. How can the pressure be equal at A and B?

The additional pressure at A is provided by the surface tension of the arched dome over the bubble. The curvature of the dome contributes a downward force. The surface tension at the concave bottom of the bubble contributes an upward force. The bottom is not as curved as the top, however, and so the upward force is smaller. On the whole the shape of a floating bubble generates a net downward force, which increases the pressure just below the bubble to the equilibrium value.

If a bubble arrives at the surface near a wall of the container, it moves to the wall and adheres to it. If another bubble is nearby, the two bubbles move toward each other. The attraction between two bubbles or a bubble and a wall is due to unequal pressures in the surfaces surrounding a bubble. Between two nearby bubbles the liquid surface is curved, not flat as it is in other directions. The curve is concave, which means that the force of the surface tension pulls upward. As a result the pressure just inside the beer at the curved surface is decreased. On the other sides of the bubbles the pressure is not reduced since the surface is flat. The bubbles are pushed together by the unequal pressures.

When a bubble is near a wall, the surface of the liquid between the bubble and the wall is more curved than that on the opposite side of the bubble. Again the curvature creates a surface tension that reduces the pressure in the liquid surface. The bubble is pushed to the wall.

If two identical bubbles touch, their common wall, which is called a lamella, is flat because of the identical gas pressures on the two sides of the wall. If the bubbles are not the same size, the lamella becomes curved so as to give rise to equal pressures on the two sides. Between two such bubbles the pressure initially differs because of different surface tensions in the bubbles. The larger bubble, with a greater radius of curvature, has a lower internal pressure because the surface tension of its wall is less. When a large bubble touches a small one, their common wall must bulge into the larger bubble. The changes in surface tension resulting from this bulge equalize the pressure in the two bubbles. (Complete equalization is not possible in a foam consisting of bubbles of many different sizes.)

In an idealized foam with bubbles of identical size the bubbles would be organized in groups of three in contact with one another. The lamellae of the bubbles intersect symmetrically at a point called a Plateau border (after Joseph A. F. Plateau, who studied soap bubbles in the l9th century). This organization is the stablest against shocks.

Even if a beer foam had identical bubbles and such a stable organization, it would still collapse within minutes. One reason is that gravity drains liquid from between the lamellae, thinning them until they are only from 20 to 200 nanometers thick. Then they stabilize for a while until a chance shock from the surrounding foam thins them to about five nanometers, at which point they burst.

Drainage is also promoted by a curious interplay of surface tensions within the lamellae. Between two bubbles the surfaces of a lamella are relatively flat and hence low in surface tension. Where three lamellae join in a Plateau border, however, the surfaces are curved, the surface tensions they contribute are larger and the pressure inside the intersection differs from the pressure in the flat region. Since the surfaces facing the intersection are convex, the forces of their surface tensions pull away from the intersection, thereby reducing the pressure there. The pressure inside the lamellae is therefore less at a Plateau border than it is elsewhere. The pressure difference sucks liquid from the relatively flat lamellae into a Plateau border, thinning the lamellae.

A gradual decrease in the number of bubbles in a foam also results from the diffusion of their gas across the thin bubble walls. When a small bubble touches a larger one and the two cannot equalize pressures at their common wall, the higher pressure in the small bubble forces some of its gas to dissolve into the wall. The gas diffuses across the wall and enters the larger bubble. In this way larger bubbles consume smaller ones.

Much of the strength of the foam comes from the surface viscosity of the surfaces in the lamellae. Surface viscosity is distinct from bulk viscosity, which is the viscosity of the liquid between the surfaces. The surfaces have such a large viscosity that they may be almost rigid, at least until the stress and shearing on them reach some critical value. Then they yield and the bubble bursts.

In some foams electric forces help to strengthen the bubbles. A layer of.. charged molecules can lie on each of the two surfaces of the lamella between two adjacent bubbles. As the lamella thins on draining, the layers of charge move closer to each other. Their mutual repulsion prevents or delays the collapse of the lamella.

Although such a double layer of electric charge is important for some types of foam, I do not know if it plays a vital role in stabilizing beer foam. The primary stabilizing factors in beer are still not well understood. Proteins apparently help. Aged hops also seem to be important. Other ingredients, such as salts of cobalt, iron, nickel and zinc, are added either to prolong the life of the head on the beer or to enhance the clinging of small bubbles to the glass above the head when the glass is tilted.

I have long been an observer of beer bubbles (for scientific reasons, naturally), but recently Craig Cook, a student at Cleveland State University, showed me a phenomenon that was new to me. It is seen in Pilsner beer glasses, which are prized by beer drinkers more sophisticated than I. A Pilsner glass is fairly wide at the top and tapers to almost a dimple at the bottom. The tapered end is buried in a thick cylinder of glass for ease of holding. A Pilsner glass is unique in that the main output of bubbles is in the narrowly tapered bottom.

A steady stream of bubbles, none of them initially more than about .5 millimeter in diameter, rises from the bottom. Fewer bubbles form on the sides of the glass.

The sides of the glass appear to be quite smooth, whereas the bottom seems to be roughened with tiny hills and crevices. If the glass is clean and dry before the beer is added, the crevices hold trapped air pockets that nucleate bubbles of carbon dioxide. The bubbles quickly tear away from the crevices, beginning to ascend while they are still small. The rapid production of the tiny bubbles forms a stream that rises to the center of the top surface of the beer.

When bubbles form on the sides of the glass, they are typically much larger than the ones rising from the bottom. One reason for the difference is that the bubbles at the bottom are under greater hydrostatic pressure and so must be smaller. I believe another reason can be found in the degree of roughness. At the bottom there are many adjacent sites for nucleating bubbles. No one of them can form a base wide enough to generate a large bubble. The size of the bubbles is also limited by the turbulence generated as nearby bubbles break away from their nucleating sites.

I could find no bubbles originating away from the walls, presumably because of a lack of nucleating air pockets. When I dipped a knife into a glass of beer, bubbles immediately began t form on it. After a while the activity lessened. To see whether the decrease was due to a loss of dissolved carbon dioxide in the beer or to a loss of air pockets on the knife, I lowered the knife farther into the beer. Many new bubble appeared on the freshly submerged par of the blade. The number of nucleatin pockets of air on the knife seems to diminish after several minutes of bubble formation.

I observed the same kind of result with the glass. Bubbles were produced at the highest rate in an originally clean, dry glass. The rate decreased with each new container of beer poured into the glass. Pouring still created a foam and many bubbles, but the yield of bubbles several minutes after pouring was less. Apparently the continued use of the glass lessens the number of nucleating air pockets on its walls.

I did several more experiments with a knife dipped in beer. When the knife was tilted, layers of bubbles formed on the underside because they could not escape easily. When I tilted the knife the other way, layers of bubbles began to break away from the knife, clearly demonstrating that the release of one bubble can force the release of others.

The temperature of the knife did not seem to matter, but its cleanliness did. I coated the lower end of a knife with corn oil and then dipped the knife into the beer past the oiled region. The crop of bubbles in the oiled area was much smaller than it was in the unoiled area because the oil covered the air pockets adsorbed onto the metal.

Donald Deneck of New York once showed me how one drinks from a "yard of beer," a container that stands from two to three feet high and has a hemispherical bottom and a long, tapered neck that is narrowest in the middle. When the beer in the neck has been consumed, further drinking from such a container is tricky. To make the beer pour one must tilt the glass so that the hemispherical end is higher than one's mouth, but if the container is tilted too much, a large bubble of air enters the neck, slides to the now-raised bottom and displaces enough beer to douse the drinker.

Deneck's technique is to first tilt the container so that the bottom is only slightly higher than his mouth. Then he gently taps on the side of the neck to send a few small air bubbles or part of the foam up the neck to the hemispherical bottom. These bubbles displace a drinkable amount of beer. By gradually adjusting the tilt of the container and tapping its neck Deneck manages to get his full ration of beer.

I have had many letters about my discussion in May of phosphenes, the luminous figures one can see without benefit of light. Several readers described the phosphene displays that warn of and accompany a migraine headache. Carol McAlpine of Stroudsburg, Pa., wrote that when a migraine is beginning, she sees the network of blood vessels in the retina for an instant after shutting her eyes. Sometimes the network reappears in apparent rhythm with her pulse. After the migraine takes hold she sees "bursts of cloud billows in violet, blue and gray green, which float in all directions, constantly changing shape." As the headache subsides the display changes to an array of dots of the kind I described in connection with the monocular viewing of phosphenes.

Paul Tobias of Los Angeles sent me a report that he and J. P. Meehan have made on phosphene displays instigated by rapid acceleration. Blindfolded volunteers, strapped in a centrifuge, were spun in a circle at an increasing speed. When the effective acceleration reached a certain threshold, the subjects saw an array of blue spots and stars. At an effective acceleration of about 3.6 g (3.6 times the acceleration of gravity) the array also developed what they described as golden worms. When the effective acceleration reached 4.5 g, the worms formed a brilliant orange gold geometric pattern. Some subjects saw a pulsation in the pattern.

After the centrifuge stopped the subject remained blindfolded for a short time in order to study the afterimage of the phosphenes. The afterimage, which lasted for as long as 90 seconds, was a doughnut or something like a full solar eclipse with a dark background.

These displays appeared only when the effective force on a subject was along the body axis. When the effective force was from the chest to the back, no displays were seen. Tobias and Meehan concluded that the phosphenes depend on the rate at which the acceleration is varied. When the acceleration is along the body axis and is varied fast enough, it probably reduces the blood pressure in the retina and distends the eye. Both effects contribute to the creation of phosphenes.

Astronauts and pilots might see such phosphenes during moments of rapid acceleration if the effective force is along the body axis. I think anyone on a rapidly rotating ride at an amusement park might see the displays. Some rides develop an acceleration of more than 3 g. A rider with enough presence of mind during these rapid maneuvers might see phosphenes. I must admit that I am too busy fearing for my life.

Bibliography

GAS IN LIQUIDS. J. T. Davies and E. K. Rideal in Interfacial Phenomena. Academic Press, 1963.

FOAMS. J. J. Bikerman. Springer-Verlag, 1973.

SO WHAT'S A BUBBLE? Jeffrey C. May in SciQuest, Vol. 52, No. 8, pages 16-20; October, 1979.

CLOUD PHYSICS IN A GLASS OF BEER. Craig F. Bohren and Gail M. Brown in Weatherwise, Vol. 34, No. 5, pages 221-223; October, 1981.

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