Liberally sprinkled with humor, these lessons will fascinate beginning physics students and other readers with chapters titled "On a Clear Day You Can't See Forever" and "Physics on a Manure Heap."
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CLOUDS IN A GLASS OF BEER
Simple Experiments in Atmospheric Physics
By Craig F. Bohren
Dover Publications, Inc.Copyright © 1987 Craig F. Bohren
All rights reserved.
Clouds in a Glass of Beer
Mix salt and sand, and it shall puzzle the wisest of men, with his mere natural appliances, to separate all the grains of sand from all the grains of salt; but a shower of rain will effect the same object in ten minutes. T. H. Huxley
In taverns of low repute the patrons may sometimes be observed to sprinkle salt into their beer. They do this not because they like salty beer but because they are amused by the resulting profusion of bubbles. Yet there is more than amusement in a glass of beer: it exemplifies a surprising number of physical phenomena, many of which occur in the atmosphere, particularly the formation and evolution of clouds. It would not be too much to say that a glass of beer is a cloud inside out.
BUBBLES IN BEER
Beer contains dissolved carbon dioxide (CO2), molecules of which at a pressure more than twice that of the atmosphere at sea level also occupy the space above the beer in a capped bottle. Although molecules continually flit back and forth between the beer and the gas, the rate at which they leave the beer is balanced by the rate at which they return: CO2 dissolved in the beer is in equilibrium with that in the neck. In equilibrium the amount of CO2 dissolved in a given amount of beer (at fixed temperature) is proportional to the pressure of the CO2 above it. When the bottle is uncapped, this gas escapes rapidly from the neck and its pressure drops greatly. Now the dissolved CO2 is no longer in equilibrium with that in the neck; the beer is supersaturated. In a sense it contains more CO2 than it ought to, but the excess does not escape explosively: it does so slowly, in the form of small bubbles.
Although many people know about bubbles in beer, the details of their formation sometimes escape notice. A few years ago (1982) an article appeared in Science (Vol. 215, p. 1082) entitled "Bubbles upon the River of Time," by M. Mitchell Waldrop. It was about the speculations of Richard Gott, an astrophysicist, that our universe is only one of perhaps an infinite number which formed like bubbles in a very hot dense space. What caught my eye was the following: "Gott's bubbles form just like bubbles in a glass of beer—randomly." This was too good to let pass, so I fired off a letter, which was duly published:
M. Mitchell Waldrop must not have spent much time in well-lit pubs. For if he had he would not have said about Gott's bubbles that they form just like bubbles in a glass of beer—randomly; they emanate from a small number of definite nucleation sites; cracks in the glass and bits of foreign matter. Moreover, strings of bubbles in which the bubble spacing increases regularly with height above these nucleation sites are easily observed in any glass of light (colored), gaseous American beer.
A bubble consists of gas surrounded by liquid, the two phases separated by a definite surface. It takes energy to form surfaces. For example, when you break a piece of chalk two new surfaces are created. This takes energy, not much, but still a finite amount. The chalk could break spontaneously, but this is highly unlikely. We would have to wait a long time for it to happen, longer than the age of the universe.
Because energy is required to create bubbles in beer they do not form spontaneously under normal conditions: nucleation sites, places where bubble embryos can grow in a supersaturated environment, are required. Such tiny invisible bubbles might inhabit microscopic cracks in the glass or in particles on its sides or in the beer.
Salt sprinkled into beer provides a great number of nucleation sites; each grain, which is pitted and cracked, has many such sites. This is shown in Figure 1.1, a photograph of salt grains descending in beer taken by E. Philip Krider at the University of Arizona's Institute of Atmospheric Physics. During a visit of mine to Tucson, Krider interrupted his lightning studies long enough to help me perform an experiment and to enjoy a discussion of the results—over a cold glass of beer, of course.
Although you might think that bubbles evolve from salt grains solely because the grains dissolve in beer, or because of a chemical reaction between beer and salt, this is demonstrably false: merely try insoluble particles. Fine aquarium sand (quartz) is quite suitable. Wash the sand thoroughly in acid, then water, to rid the grain surfaces of soluble impurities. When this clean sand is dropped into beer the resulting bubbles are in no apparent way different in number and size from those nucleated by salt grains, although sand does make the beer a bit gritty.
Clouds form when the relative humidity is sufficiently high that atmospheric water vapor, a gas, condenses into small liquid droplets (for more on cloud formation see the following chapter). A cloud is in many ways just the inverse of a bubbly glass of beer. The former is composed of liquid droplets suspended in a gas (air), whereas the latter is composed of gas droplets suspended in a liquid (beer). Cloud droplets fall (unless they are caught in updrafts), whereas bubbles rise. But both owe their existence to nucleation by agents external to themselves. Were it not for the presence of condensation nuclei, tiny particles in the atmosphere, clouds would not form under conditions that we have come to accept as normal. Without such particles in the atmosphere, or even ions (which also can serve as condensation nuclei), clouds could still form although it would require much higher relative humidities, perhaps 400 percent or higher. In this instance cloud droplets would form by homogeneous nucleation: enough water molecules get together by chance to form stable, long-lived clusters which can then act as nuclei for further condensation. The same is true in beer. If there were no nucleation sites—cracks and so forth—the amount of CO2 that could be dissolved in beer would be large, but eventually bubbles would form by homogeneous nucleation.
HOMOGENEOUS NUCLEATION IN A BEER BOTTLE
When a bottle of beer is opened, a cloud often forms in the neck (Fig. 1.2), although this may not be noticed by those who frequent poorly lit pubs or who are too eager to guzzle the bottle's contents. The cloud wasn't there when the bottle was capped. Why does it form when it is uncapped?
The space above beer in a capped bottle contains mostly carbon dioxide, but there are other gases and vapors as well. Among them is water vapor because beer is mostly water (some beers seem to be entirely water).
When the bottle is opened, gases and vapors in the neck expand rapidly into the surroundings, as a consequence of which the temperature in the neck drops precipitously. I have estimated that if the temperature is 5ºC (41 ºF) before opening, it drops to about —36ºC (—33ºF) immediately after opening. The water molecules in the neck become so sluggish that purely by chance several of them can get together long enough to form small embryos that will serve as sites for further condensation of water. This doesn't happen in the atmosphere because it almost always contains particles that may serve as sites for heterogeneous nucleation.
There undoubtedly were particles in the space above the beer at the time it was bottled. But this small, enclosed space becomes purged of them. The larger ones settle very quickly. The smaller ones settle much more slowly, but because of their small masses they diffuse rapidly to the sides of the bottle where they are captured. One way or another the particles are eventually removed. Yet clouds form in the necks of bottles that have been sitting for months, which is surely long enough for nearly all particles to have been removed.
If you carefully observe bubbles in beer you will notice that they are not all the same size. Nor are they evenly spaced. Figure 1.3 is a photograph of strings of bubbles rising from nucleation sites on the side of a glass of beer. Note that the spacing between the bubbles and their size increase more or less steadily with distance from the point of nucleation. This regular spacing suggests that the rate of bubble formation is nearly constant, which in turn implies that a bubble's velocity increases with its size because the spacing and size increase simultaneously. But why does a bubble rise in the first place? And what determines its speed? To answer this we must consider the forces acting on a bubble.
Gravity pulls a bubble downward with a force equal to its weight; buoyancy pushes it upward with a force equal to the weight of beer it displaces. Beer is so much heavier than carbon dioxide that a bubble's weight is negligible compared with the buoyant force on it. A bubble is therefore positively buoyant and rises when it breaks loose from its nucleation site, just like an untethered hot-air balloon. An upward buoyant force is not, however, the only force acting on a bubble: it also experiences drag.
Your hand, when thrust out the window of a moving car, is hurled backward by the force of wind resistance, or drag. The greater the speed the greater the drag. Bubbles, too, experience a drag force which increases with increasing speed, and this impedes their upward motion. Because the buoyant force, unlike the drag force, does not depend on a bubble's speed, the two forces acting on it must eventually come into balance, and when they do a bubble of fixed size moves upward at constant speed.
A bubble released from rest travels only a small fraction of its diameter before reaching a constant speed. Because of the large viscosity of beer (compared with that of CO2) and the low density of CO2 (compared with that of beer) the drag and buoyant forces acting on a bubble are nearly always instantaneously in balance. This is true even if the bubble grows suddenly. For a brief moment the two forces are unequal, but in the time it takes the bubble to travel a short distance the forces come into balance again. As dissolved carbon dioxide in the supersaturated beer diffuses into bubbles, these bubbles grow, and their speed increases. A string of bubbles is therefore nonuniform: the greater the distance from the nucleation site the larger the bubble and the larger its separation from adjacent bubbles.
CLOUD DROPLET BEHAVIOR
The same forces acting on bubbles also act on cloud droplets, although with different relative magnitudes. Because water is so much denser than air the upward buoyant force on a droplet is negligible compared with its weight. Also, the drag on a droplet is much less than that on a bubble with the same size and speed because air is much less viscous than beer. The terminal speed of a cloud droplet increases with its size, but it must fall a relatively greater distance—many times its diameter—before attaining this speed. Cloud droplets also grow by diffusion if they are in a supersaturated environment, and the larger they are the faster they fall. You might think that they grow this way until they are large enough and fast enough to become raindrops. But diffusion is a slow process, much too slow to account for the rapidity with which clouds can form and produce rain. So some other mechanism must transform cloud droplets into raindrops. One such mechanism, important in what are called warm clouds (those at temperatures above freezing), is collision and coalescence.
When two cloud droplets collide they sometimes coalesce into a single larger drop. Similarly, bubbles in beer also collide. You can observe this by tilting the glass so that different strings of bubbles intersect. But there the similarity ends. I have never observed them to coalesce, only to bounce.
CLOUD SEEDING AND BEYOND
The connection between beer and clouds sometimes extends into the realm of fantasy, nowhere more so than in a one-act play by E. M. Fournier d'Albe (Weather, July 1960, p. 243) entitled "Why not seed clouds with beer?" Two characters, meteorologists Fulano and Zutano, argue—in convivial surroundings—the merits of seeding clouds with beer. They conclude with the following "new recipe for seeding recalcitrant cumulous clouds":
Take a sufficient quantity of
good strong beer;
Add salt to taste, or until it
is slightly hygroscopic;
Add enough soap to give it a
really good froth;
Shake well, and administer in
the form of bubbles to promising
Then stand clear, and try to
evaluate the results.
One cannot help but wonder what would have been the reaction of John Aitken, the Scottish scientist who did so much in the last century to advance understanding of nucleation in the atmosphere, to all this talk of clouds and beer. It seems that a portion of his estate was left to establish a temperance public-house in his native Falkirk. Aitken would no doubt have preferred ginger ale in place of beer. But for several reasons I think that he would have had to grudgingly admit that, taste aside, beer really is superior to ginger ale for making the kinds of observations I have described.
I have by no means exhausted all the physics in a glass of beer. For example, I have said nothing about why bubbles migrate across the surface of the beer to the edge of the glass and accumulate there in rafts. And if you whip the beer into a froth the resulting head is, like a cloud, white, although the liquid from which the bubbles in the head were formed is yellow (for more on this see Chapter 15). And bubbles shrink as they near the surface, which has been observed by alert beer physicists. Investigation of these important matters is best left for a hot day in July.
GREAT MINDS THINK ALIKE: A POSTSCRIPT
Soon after the article on which this chapter is based first appeared in Weatherwise (October 1981), Jearl Walker published something remarkably similar in Scientific American (December 1981). Yet our articles were completely independent. I certainly did not know about his, and he learned of mine only after his had gone to press. Beer physics must have been in the air in the fall of 1981, and the two of us merely happened to be the lucky ones who plucked it out.CHAPTER 2
Genies in Jars, Clouds in Bottles, and a Bucket with a Hole in It
But presently there came forth from the jar a smoke which spired heavenwards into ether ... and which trailed along earth's surface till presently, having reached its full height, the thick vapor condensed, and became an Ifrit [genie, also spelled jinni].
The passage at the head of this chapter is from "The Fisherman and the Jinni," one of the tales from the Arabian Nights. When the fisherman in this tale uncorked the jar, its contents expanded rapidly into the surroundings, and the vapor it contained condensed into a genie. So also does water vapor in expanding air condense into cloud droplets.
A CLOUD IN A BOTTLE
I am unable, alas, to conjure a genie from a jar. But I can make a cloud in a bottle, and so can you. I use a large bottle, half of which is painted black so that the cloud will be more noticeable when illuminated by a bright light. The bottle should have a stopper with a hole in it. Put a little water in the bottle, just enough to cover its bottom, and blow hard into a length of tubing inserted through the hole in the stopper. Seal the end of the tubing with your finger, then release it suddenly. The result is likely to be disappointing (Fig. 2.1) because I have forgotten something: more particles are needed. Since the bottle is an enclosed space, many of the particles in it have either settled out or have diffused to the walls, especially if it has been stoppered for a long time (see the previous chapter). Particles are provided readily enough by a smoldering match. First decrease the pressure in the bottle by sucking out some of the air. Wave the match near the end of the tubing; as air rushes back into the bottle, it will carry with it some of the smoke. Now try once again to make a cloud. This time your efforts are more likely to be met with success (Fig. 2.2); if not, try adding more particles. To understand why the cloud forms and what the particles have to do with it, I must first discuss a few concepts and elucidate them with further demonstrations.
Excerpted from CLOUDS IN A GLASS OF BEER by Craig F. Bohren. Copyright © 1987 Craig F. Bohren. Excerpted by permission of Dover Publications, Inc..
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Table of Contents1. Clouds in a Glass of Beer
2. "Genies in Jars, Clouds in Bottles, and a Bucket with a Hole in It"
3. "Happy Ducks, Like Happy People, Perform Best with Cool Heads"
4. Sugar and Spice: The Dirty Wet-Bulb Temperature
5. Mixing Clouds
6. Conceptions and Misconceptions of Pressure
7. Dew Drops on a Bathroom Mirror
8. A Murder in Ceylon
9. The Freezing of Lakes
10. The Greenhouse Effect
11. Black Clouds
12. Once in a Blue Moon
13. The Green Flash
14. Multiple Scattering at the Breakfast Table
15. Multiple Scattering at the Beach
16. On a Clear Day You Can't See Forever
17. A Serendipitous Iridescent Cloud
18. Physics on a Manure Heap: More about Black Clouds
19. Polarization of Skylight
20. Colors of the Sea
21. Indoor Rainbows
22. Why Rainbows Are Not Impossible in Winter
Selected Bibliography and Suggestions for Further Reading