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Flying circus of physics

Chap 2 (fluids) archived stories part B

Friday, February 06, 2009

For Chapter 2, here is part B of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

First, a list
2.44  Water and block puzzle
2.50  Pub trick --- reversing an egg in a tequila glass
2.50  Pub trick --- blowing out a candle
2.50  Bombardier beetles and the Coanda effect
2.53  Snorkeling by people and elephants
2.56  Flying in a lawn chair with helium balloons
2.56  Strapped to helium balloons
2.58  Walking on water (and corn starch)
2.58  A dancing slurry of water and corn starch
2.58  Pen ink is non-Newtonian, otherwise your shirt would be soaked
2.60  Bouncing and leaping liquid stream
2.64  Rogue waves
2.67  Pond resonance due to Chinese earthquake
2.69  Surfing
2.70  Bow-wave riding
2.73  Oil and waves
2.74  Tibetan singing bowls
2.75  Pub trick --- smooth pouring from a height
2.76  Pub trick --- beer bottle tapping
2.76  Gushing of beer and soda
2.76  Widgets and bubbles in a Guinness stout
2.76  Preventing gushing in a shaken soda or beer

Reference and difficulty dots
Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

Now the stories:

2.44  Water and block puzzle 

Jearl Walker
Aug 2008    Sola Saba, a student at Cleveland State University, recently brought me a puzzling problem. Suppose that a container of water is placed on a sensitive balance to measure weight, and then a block of lightweight wood (less dense than water) is submerged and attached to a thread that is tied to the bottom of the container. Thus the block is held fully below the water surface and a short distance above the bottom of the container. Next suppose that the thread slowly dissolves in the water and eventually breaks, allowing the block to float up to the water surface. Here is the puzzle: From the instant just before the string breaks to the instant just after the block has settled into its final floating position, what does the weight-measuring scale read? That is, does the reading increase, decrease, or remain the same, or does it undergo some series of changes?

Answer: Rather than slug our way through equations (though we should eventually do just that), let's just give a quick answer. Initially the scale supported both the water and the block, and the reading on the scale matched their weight. Once the block reached its final floating position, the scale again supported the water and block, and the reading again matched the weight. However, when the block was ascending and water was filling it its former location, the scale had less to support and its reading was less than the weight. You might think of the process this way: A block of lightweight wood went up and a block of heavier water went down. The net effect is a descent of mass --- a block of material effectively fell and during that falling, the scale did not fully support the material.

2.50 Pub trick --- reversing an egg in a tequila glass
Jearl Walker
Sep 2008  
Here is another in the series of tricks for the bar or pub. And again, the real trick is to explain the trick because anybody can do the trick but only a few know enough to explain it.

Place an egg (either fresh or hard-boiled) in a tequila glass (a bit wider than the standard shot glass), with either end down. The challenge is to invert the egg without touching it, the glass, or the supporting surface. Here is a link to show you how, but form an explanation while you which the video.

As you can see in the video, the technique is to blow hard straight down on the top of the egg, but doesn’t that seem exactly wrong? Won’t that create high pressure on the top, forcing the egg downward and thus pressing it more firmly into the glass?

Whenever I have been confronted with a fluid flow problem that I could not immediately explain, I have always joked, “Ah, the effect must be due to the Bernoulli principle.” That principle is really a statement about the conservation of energy in a flow of fluid that is constrained in something like a pipe. For an example of its application, suppose that a steady flow of water through a pipe encounters a section where the pipe diameter is smaller. As the water moves into the narrower pipe, its speed increases. The Bernoulli principle tells us that the kinetic energy (the energy associated with the speed and thus the motion) increases at the expense of the water pressure (the energy associated with the compression on the water). The total energy is conserved, that is, it stays constant and that is why the water pressure is lower in the narrower pipe.

The temptation with the pub trick is to say that the kinetic energy of the stream of air from your mouth came at the expense of the air pressure. Were that true, the lower air pressure in the stream on the top of the egg would cause the egg to jump upward. However, the kinetic energy of the stream came from the work your lungs did to expel the air from your mouth, not from the air pressure in the stream. Besides, once the air leaves your mouth it is in contact with the air in the room, which is at atmospheric air pressure.

So, the egg does not jump up because you have somehow lowered the air pressure above it. If you want to test my argument, go through your home blowing down hard on various objects to see if you can levitate them. When you get the cat, I am sure it will convince you (perhaps rather fiercely) that levitation is just not going to happen (unless, maybe, the cat leaps at your face, but that won’t count).

When you blow down on the egg, the air stream flows along the curved surface, clinging to the surface. This tendency of a stream (of air or a liquid) to cling to a surface, even a curved surface, is called the Coanda effect, after Romanian engineer Henri Coanda who discovered and then studied the effect.

Here’s a brief explanation of how it applies to the pub trick. If the airstream were to leave the surface of the egg, the region between the airstream and the surface would (momentarily) be left with a decreased number of air molecules and thus decreased air pressure. The stream would then have atmospheric air pressure on one side (the external side) and reduced air pressure on the other side (the side toward the egg), and the pressure difference would push the stream back onto the egg. Well, this just doesn’t happen until turbulence develops, and then the swirling can detach the airstream.

Such a breakup occurs when the stream reaches the rim of the tequila glass, but enough of the stream flows through the gaps between the egg and the rim to enter the space within the glass and below the egg. This inrush of air increases the air pressure below the egg. The egg then has high pressure below it and atmospheric pressure above it, and the pressure difference shoots the egg upward.

The flight is not stable and the egg can flip over completely or rotate only half way and then land straddling the glass rim. With some practice, you can control how hard you blow down on the egg to get either final resting place. Of course, it is always better to get a result and then explain to the onlookers that it was exactly what you were trying for.

Remember, anyone in the pub can do the trick. If you are there in the pub because you are lonely and want to attract the attention of someone who would make you less lonely, then being able to explain the trick in simple terms will lift you in that person’s eyes. See, physics is not only everywhere but it can also make you less lonely.

· Reba, I., “Applications of the Coanda effect,” Scientific American, 214, 84-92 (June 1966)

2.50  Pub trick --- blowing out a candle
Jearl Walker
May 2009 In this pub challenge, your face is at about table level and facing a wide bottle, while a small candle burns on the opposite side the bottle. You must blow out the candle (even though you cannot even see it). Of course, if you could blow onto the flame directly, you could eliminate the hot environment and thus stop the melting of the wax and the vaporization of the resulting liquid. With no vapor to burn, the candle would then have no flame. But here, a wide bottle is in the way of your puff.

This video shows how to meet the pub challenge, but keep in mind that anyone (such as the person in the video) can perform the trick but only if you understand physics can you explain the trick (and notice that no explanation appears in the video):

If the bottle is not too wide, you might be able to blow out the candle by simply blowing directly at your side of the bottle, at about the height of the flame above the table. Your airstream is deflected by the bottle to your left and right and much of it may be lost, but some of it will cling to the bottle surface, following the curve around the side and perhaps reach the far side of the bottle and thus the flame.

Fluid streams (whether gas or liquid) tend to cling to an outwardly curved surface like that of a bottle by a process known as the Coanda effect, named for Henri Coanda, the Romanian engineer who discovered it. When a fluid stream moves through air, it tends to entrain (grab and drag along) molecules from the surrounding air. Because the surrounding air then tends to lose molecules, the air pressure along the stream tends to decrease. However, the air pressure does not decrease because the ambient air just outside that region easily supplies fresh molecules to replace the entrained ones.

But if the stream is near a solid surface, the molecules removed from the region between the stream and the surface are not as easily replaced, and the air pressure in that region can actually decrease. There is then less air pressure on the surface side of the stream than on the outside of the stream, and the pressure difference pushes the stream up against the surface. It can be held there even if the surface curves. This is the effect that Henri Coanda discovered.

If bottle in the pub challenge is fairly narrow, the Coanda effect can bring enough of your airstream around to the back of the bottle to blow out the flame. However, for a wider bottle, you need the flanking bottles shown in the video to help funnel your airstream into the gap between the bottles. No Coanda effect is involved here --- the part of your airstream that flares off the main bottle simply hits a side bottle and bounces into the gap. Then the airstream reaching that the back of the bottle is stronger, strong enough to blow out the candle.

If you want another, seemingly bizarre example of the Coanda effect, read item 2.50 in The Flying Circus of Physics book, where I describe how bombardier beetles use the effect to aim a hot (100ºC), toxic stream toward attacking ants. The stream comes out the rear of a beetle, but the Coanda effect allows a beetle to aim the stream even at ants located in front of it. I just love it when animals figure out physics before we do. Video, watch the flap be pulled upward by the Coanda effect (note, the Bernoulli principle is not involved). Coanda effect with a spoon in a stream of water Coanda effect with a spoon in a stream of water Coanda saucer, photos and plans for making Video of a Coanda saucer Video of a large Coanda saucer Another video

2.50 Bombardier beetles and the Coanda effect
Jearl Walker
February 2013 When provoked by ants, bombardier beetles produce froth or spray that is hot (100°C) and toxic.

The more common type of bombardier beetle (brachinines) can direct its jet-like spray by rotating the tip of its abdomen like a gun turret. If an ant attacks, say, a front leg, the abdomen tip is aimed down and forward, targeting the leg. Once drenched, the ant quickly scampers off.

The paussines, a less common type of bombardier beetle, do not have such a mobile abdomen tip; rather their spray can be issued only toward the rear or to the side. Still, the beetle can deftly target an ant even if the ant is in front of the beetle or on a forward leg. It can do this by using the Coanda effect, named after Henri Coanda, the Romanian engineer who discovered the effect. Here are some examples of how well a bombardier beetle can spray a target:

Let me explain the Coanda effect with a water stream. Suppose the stream is reasonably near a solid surface. The stream entrains air; that is, it grabs adjacent air molecules, forcing them to move along with the stream. This action removes air molecules, and so other air molecules (farther from the stream) tend to flow in as replacements. However, the solid surface impedes this inflow the side of the stream nearest the surface. With insufficient molecules between the stream and the surface, the air pressure between them is reduced. The air on the other side of the stream is still at atmospheric pressure, and so the stream is pushed toward the surface, becoming attached to it. This attachment can persist even if the surface is curved away from the original direction of the stream.

The paussines possess flanges just forward of the gland opening from which the spray issues. To shoot the spray forward, the opening is controlled so that the spray hits a flange. There it can be deflected by as much as 50° as it moves around the curvature of the flange via the Coanda effect. When the spray leaves the flange, it flies through the air as a thin jet. The beetle can control the final direction of the jet by controlling where on the flange the spray hits as it is emitted from the gland.

Physics is everywhere, and even bombardier beetles know how to use.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
· Eisner, T., and D. J. Aneshansley, “Spray aiming in bombardier beetles: jet deflection by the Coanda effect,” Science, 215, No. 4528, 83-85 (1 January 1982)
· Eisner, T., and D. J. Aneshansley, “Spray aiming in the bombardier beetle: photographic evidence,” Proceedings of the National Academy of Sciences of the United States of America, 96, No. 17, 9705-9709 (August 1999)

2.53  Snorkeling by people and elephants
Jearl Walker
September 2012 In snorkeling, a swimmer breathes by means of a tube that extends above the water level. Why is the length of the tube restricted to about 20 centimeters? That is, what is the acute danger in using a longer tube, other than the difficulty in circulating air into and out of it? Using its trunk, an elephant can also snorkel. How can it survive its common snorkeling depth of about 2 meters?

Because the water pressure on a diver increases with depth, the blood pressure also increases. If a diver is swimming by holding the breath, the pressure in the lungs also increases. The match of the blood pressure and the lung’s air pressure allows the continued transfer of oxygen to the blood and the removal of carbon dioxide from the blood. However, if the diver began to breathe through a tube, the air pressure in the lungs would drop to atmospheric pressure. This decrease is small if the diver is not far below the water surface, but for greater depths the mismatch between the blood pressure and the lung’s air pressure could be fatal, a condition called lung squeeze. Then the small blood vessels at the lung surface rupture, and blood seeps into the lungs.

A mature elephant would seemingly undergo lung squeeze with each submerged swim because its lungs are about two meters below the water surface, which means the pressure difference between its blood pressure and the lung’s air pressure is large. However, its lungs are protected in a special way. The pleura is a membrane that encloses the lungs in any mammal. Unlike in the other mammals, the elephant’s pleura is filled with connective tissue that holds and protects the small blood vessels in the walls of the lungs. Thus, the vessels do not rupture during snorkeling.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Mackay, R. S., “To determine the greatest depth in water at which one can breathe through a tube,” American Journal of Physics, 16, 186-187 (1948)
··· Baz, A. M., “Optimum design of diving snorkels,” Medicine and Science in Sports and Exercise, 16, No. 4, 415-421 (1984)
·· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, John Wiley & Sons, 4th edition, 1993, pages 448-449; 5th edition, 1997, page 353
· West, J. B., “Why doesn’t the elephant have a pleural space?” News in Physiological Sciences, 17, 47-50 (2002)

2.56  Flying in a lawn chair with helium balloons
Jearl Walker
July 2007.  In The Flying Circus of Physics book, I describe how in 1982 Larry Walters ascended into the airflight routes over Los Angeles while sitting in a lawn chair to which he had attached many helium balloons. He was reported to airtraffic control by a pilot who spotted him while in flight. He gained his lift by the fact that helium is lighter than air. So, although a helium balloon is still pulled downward by the gravitational force, the surrounding air produces a larger buoyancy force that pushes the balloon upward. With enough balloons tied to a lawn chair, there was a net lift on Walters, chair, and balloons, and they all rapidly rose into the sky. Walters planned on controlling his flight by shooting out some of the balloons with a BB gun whenever he decided to descend. However, he dropped the gun, and the flight was then rather uncontrolled. He was very lucky to have survived.

This month Kent Couch of Bend, Oregon, repeated the stunt by strapping 105 large helium balloons to his lawn chair. He landed without mishap over 200 kilometers away, after popping enough of the balloons to (barely) eliminate his lift, so that he would settle down gently. Unfortunately, as soon as he jumped out of the chair and onto the ground, the wind whipped the chair, balloons, and his camcorder away into the air. So far, the camcorder has not been found and so you cannot his videos, but you can see some of the images of Couch, both in the air and on the ground, at the following news sites.
People have always wanted to fly. However, floating through clouds in a lawn chair is not the stuff of Greek legends.,22049,22055031-5012895,00.html Note that there are multiple images available.   Video currently on the BBC Lifting a car with helium balloons. The car breaks free and floats away. My gosh! But wait. Is this real or fake? Can you tell? Can you estimate how many balloons would be needed to lift a car body (with the engine removed)? Behind the scenes

Kent Crouch makes true his promise to fly from one state (Oregon) to another (Idaho, about 200 miles away) by means of a chair strapped to helium balloons. BBC video


· Faber, J., Great News Photos and the Stories behind Them, second revised edition, Dover, 1978, pages 76-77
· Patiky, M., "Balloon man vs. the Feds: Larry Walters fulfilled his impossible dream and found the FAA at his doorstep," Air Progress, 45, 25 + 57-63 (May 1983)


2.56  Strapped to helium balloons

Jearl Walker
April 2008  
  Every now and then someone gets the urge to be strapped to enough helium balloons that they can fly for a long distance. In The Flying Circus of Physics book I describe the flight of Larry Walters in 1982 and how he almost died when he dropped his BB gun and thus lost any way of decreasing the number of balloons in order to land. Last summer I wrote an item here at the FCP web site about Kent Couch who flew over 200 kilometers while strapped to 105 large helium balloons. (To find the story and all the links, go to the second year archive here at this site. Do you see the link at the top of the previous page?)

Well, the update today is most likely a tragic story. Hoping to raise money for a charitable cause, a Roman Catholic priest in southern Brazil strapped himself to hundreds of helium balloons commonly sold for parties. He intended to fly to another inland city but, once he was aloft, wind forced him out over the Atlantic. Here is the video link showing his launch.

I must admit that I am fascinated by the buoyancy of a large collection of seemingly innocent helium balloons. Being lifted away by a balloon is surely both the dream and nightmare of a young child when holding a helium balloon for the first time. When everything else tends to fall down, a balloon that tends to float upward is a thing of magic and perhaps the first lesson in the surprises that physics can bring. However, being strapped to a large collection of helium balloons, with no easy way of a safe descent and with no control over the direction of travel, is quite simply a nightmare. I fear that this latest story will end in tragedy.

2.58  Walking on water (and corn starch)
Jearl Walker
May 2007   One of the funniest videos I have ever seen on YouTube involves the non-newtonian nature of a slurry of common cornstarch and water. Cooks already know the effect: If the slurry is very watery, stirring it with a spoon is easy. But if the slurry is thicker, then it fights the spoon’s motion.

One measure of any fluid’s resistance to flow is the viscosity. Most fluids, such as water, have a certain value of viscosity for any given temperature; they are the newtonian fluids. But, as explained in the Flying Circus book, the viscosity of some fluids immediately changes when the fluid is stressed (put under pressure) by, say, a spoon. These fluids are non-newtonian (and far more fun than the simple newtonian fluids).

When a slurry of cornstarch that is sufficiently thick is suddenly put under pressure, its viscosity dramatically increases and the fluid is momentarily rigid. It is a non-newtonian fluid that is also shear-thickening, meaning that its viscosity increases under stress. You can hit it without making splash, and you can throw it at the wall, where it will hit like a handful of putty, without a splash. In an impact, the molecules in the cornstarch rearrange themselves so as to block any flow, so the fluid is rigid just then. However, at the end of the impact, the viscosity falls back to its normal value, and then the slurry flows.

Here is one more thing before I tell you where to watch the video. The basilisk lizard is peculiar in that it can run over water. As I explain in the book, in each footfall, the foot pushes a cavity into the water, and the lizard must then pull the foot out of the cavity before water can fill it. Thus, if the lizard runs fairly rapidly, each footfall is too brief for the lizard to sink into the water.

Ok, let’s put the two ideas together: (1) sudden impact makes a corn-starch slurry rigid and (2) pulling a foot up from a fluid before the fluid can flow into the cavity made by the foot allows an animal to run over water. The big question is: Can a person run over a corn-starch slurry?

Well, that is exactly what happens in the video on YouTube, which appears to be from a television show in Barcelona, Spain. We see a pool measuring about 3 meters by 1.5 meters that is filled with a corn-starch slurry to a depth of about 0.5 meter. The television personalities first demonstrate that the slurry is a fluid. Then, to my utter amazement, they run across the slurry for the length of the pool! They run just like a basilisk lizard, pulling up each foot just before the slurry begins to flow, right after the sudden impact has made the slurry underneath the foot momentarily rigid. I was laughing so hard that I was on the floor, looking up at the computer screen over the edge of my desk. You may not be able to walk on water, but you can run on a water and corn starch slurry!  Barcelona video on YouTube Click on Videos and then choose episode 4 to see my old video on non-newtonian fluids, where I jump onto a mixture of corn starch and water.

·  Merkt, F. S., R. D. Deegan, D. I. Goldman, E. C. Rericha, and H. L. Swinney, “Persistent holes in a fluid,” Physical Review Letters, 92, No. 18, article #184501 (7 May 2004)
·  Weiss, P., “Holey water: punctured fluid stays riddled,” Science News, 165, No. 20, 308 (15 May 2004)
·  Denn, M. M., “Fifty years of non-Newtonian fluid dynamics,” AIChE Journal, 50, No. 10, 2335-2345 (October 2004)
·  Habdas, P., E. R. Weeks, and D. G. Lynn, “Squishy materials,” Physics Teacher, 44, 276-279 (May 2006)

Want more references? Use the link at the top of this page.

2.58  A dancing slurry of water and corn starch
Jearl Walker
April 2012   As many science teachers and most cooks know, a fairly thick slurry of water and corn starch (called corn flour in some countries) has a peculiar viscosity. That is a measure of how resistive a fluid is to being stirred or poured. Water has a very low viscosity. Honey has a higher viscosity. And we could make a long list of the values for other fluids that you might find in, say, a kitchen or garage. The viscosity often depends on temperature. For example, if you chill honey, its viscosity will become so large that you will be frustrated in trying to pour it from its container.

A thick slurry of water and corn starch is different in that pressure (or better, stress) can immediately and dramatically increase the viscosity so much that the fluid is almost rigid. If you have watched my videos at the Flying Circus of Physics site on Facebook (it is a public site), you may have seen the one where I slap a bowl of water and corn starch. If the slurry is thick enough, it will not splash because during the impact, the viscosity is suddenly too large to allow the slurry to flow. Immediately afterwards, the viscosity drops back to its normal value and the slurry easily flows.

Here is a video that shows a corn starch slurry in a container mounted on an upright speaker cone which is driven into sinusoidal oscillations with a frequency of about 30 hertz (30 oscillations per second). (The video was recorded at 30 frames per second to eliminate the visible shaking of the cone.)

In certain places and at certain times, the slurry is propelled upward and is solid under the pressure. When it then begins to fall back down, it flows, but when it hits it again it is almost solid. The result is a mesmerizing, kinetic sculpture of oddly shaped spires dancing over the container.

Similar oscillations of corn starch slurries have been made in laboratory conditions, where the oscillation accelerations and frequencies were much greater. Researchers found that when they punched holes in an oscillating slurry (using a blast from an air hose), the holes would persist. The continuous hard oscillations kept the viscosity too high for the surrounding fluid to flow into a hole.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Trevena, D. H., “Elastic liquids,” Sources of Physics Teaching, Part 5, Taylor and Francis (London), 1970, pages 57-68
· Collyer, A. A., “Demonstrations with viscoelastic liquids,” Physics Education, 8, 111-116 (1973)
··· Collyer, A. A., “Viscoelastic fluids,” Physics Education, 9, 313-321 (1974)
· Walker, J., "Serious fun with Polyox, Silly Putty, Slime and other non-newtonian fluids," in “The Amateur Scientist,” Scientific American, 239, No. 5, 186-196 (November 1978)
·· Bell, D., “Non-Newtonian fluids,” Physics Education, 14, 432-436 (1979)
· Walker, J., “Easy ways to make holograms and view fluid flow, and more about funny fluids," in “The Amateur Scientist,” Scientific American, 242, No. 2, 158-170 (February 1980), see page 170
· Twin, J., and A. Vans, (letters) “Corny quicksand,” New Scientist, 139, 57 (25 September 1993)
· Merkt, F. S., R. D. Deegan, D. I. Goldman, E. C. Rericha, and H. L. Swinney, “Persistent holes in a fluid,” Physical Review Letters, 92, No. 18, article #184501 (7 May 2004)
· Weiss, P., “Holey water: punctured fluid stays riddled,” Science News, 165, No. 20, 308 (15 May 2004)
· Habdas, P., E. R. Weeks, and D. G. Lynn, “Squishy materials,” Physics Teacher, 44, 276-279 (May 2006)

2.58  Pen ink is non-Newtonian, otherwise your shirt would be soaked
Jearl Walker
December 2015  Here is short, cute video celebrating the ink flow from any common ballpoint pen.

Let me add a few words. You want the ink to flow when you write with the pen but not when the pen is lying on the desk or (worse) stored in your shirt pocket. For that reason, the ink is made to have a viscosity that varies with stress. In particular, when the pen is not being used and the ink is not under stress, the viscosity is large enough that the ink cannot flow through the very narrow opening between the ball and the sheath surrounding the ball. However, when you write with the pen and press the ball and sheath together, the increased stress on the ink decreases the viscosity enough that it can flow through the narrow opening. Any fluid whose viscosity changes with a change in the applied stress is said to be a non-Newtonian fluid. Water is Newtonian --- there is no change in its (low) viscosity when you stress it, such as with a hand slap. Pen ink is a shear-thinning fluid, because stress reduces its viscosity. Thank goodness, or we would all have ink-soaked shirts.


2.60 Bouncing and leaping liquid stream
Jearl Walker
November 2013   Pour a thin stream of hair shampoo or liquid hand soap onto a flat surface where the stream can form a mound that oozes outward. For certain pouring heights and certain liquids, why does the stream occasionally take a big leap sideways? I get very nice, frequent leaps with Ivory Hand Soap. Here is a figure from The Flying Circus of Physics book: 

And here is good video:

The traditional explanation of the leaping (included in The Flying Circus of Physics book) focuses on the viscosity behavior of the fluid. The type of shampoo that jumps is said to be viscoelastic because it is viscous (has internal friction opposing motion) and also elastic (it acts like a rubber membrane). The viscosity of the shampoo is fairly high when the shampoo moves slowly in the falling stream and in the mound. However, when the stream runs into the mound, the collision causes shearing; that is, it causes one viscous layer to move quickly across another viscous layer. The motion decreases the viscosity of that portion of the stream. Because the liquid is elastic, this sudden decrease in viscosity allows the colliding portion to bounce somewhat like a rubber ball, and so the stream forms a wide loop that extends (stretches) off to one side of the stream and mound. The loop is so fleeting that we see only the top section and the stream looks like it bounced off the mound.

However convincing this viscosity argument has been, a recent experimental investigation has laid it to rest. The stream leaps because when it hits the mound it is guided around and then back out in the air on an extremely thin (submicron) layer of air. Here is the situation as reported by S. Lee (Texas A&M University) and his associates:

This is a lovely explanation, 50 years after the first observation was made. I can still remember when I discovered that first paper by A. Kaye when I was writing the early versions of The Flying Circus of Physics in graduate school, that is, when I was searching for ideas through research journals instead of studying for my exams. Finally I know how the Kaye effect works.


· through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Kaye, A., “A bouncing liquid stream,” Nature, 197, No. 4871 (9 March 1963)
· Collyer, A. A., and P. J. Fisher, “The Kaye effect revisited,” Nature, 261, No. 5562, 682-683 (24 June 1976)
· Walker, J., "Serious fun with Polyox, Silly Putty, Slime and other non-newtonian fluids," in “The Amateur Scientist,” Scientific American, 239, No. 5, 186-196 (November 1978)
· Versluis, M., C. Blom, D. van der Meer, K. van der Weele, and D. Lohse, “Leaping shampoo and the stable Kaye effect,” Journal of Statistical Mechanics: Theory and Experiment, article # P07007 (July 2006)
· Thrasher, M., S. Jung, Y. K. Pang, C.-P. Chuu, and H. L. Swinney, “The bouncing jet: A Newtonian liquid rebounding off a free surface,” arXiv:0707.172v1 (2007)
· Thrasher, M., S. Jung, Y. K. Pang, and H. L. Swinney, “Bouncing of a jet off a Newtonian liquid surface,” Physics of Fluids, 19, article # 091110, (1 page) (2007)
· Castelvecchi, D., “Slick serpent,” Science News, 172, 54 (28 July 2007)

· Versluis, M., C. Blom, D. van der Meer, K. van der Weele, and D. Lohse, “Leaping shampoo,” Physics of Fluids, 19, article #091106 (1 page) (2007)
··· Thrasher, M., S. Jung, Y. K. Pang, C-P. Chuu, and H. L. Swinney, “Bouncing jet: a Newtonian liquid rebounding off a free surface,” Physical Review E, 76, article # 056319 (2007)
·· Binder, J. M., and A. J. Landig, “The Kaye effect,” European Journal of Physics, 30, S115-S132 (2009)
·· Lee, S., E. Q. Li, J. O. Marston, A. Bonito, and S. T. Thoroddsen, “Leaping shampoo glides on a lubricating air layer,” Physical Review E, 87, # 061001 (R) (2013)

2.64 Extreme and rogue waves
Jearl Walker
April 2014  Most ocean waves have heights within a certain range of values, which can be correlated with wind and storm conditions. However, larger waves sometimes occur.

If an extreme wave is described as having a frightening height, then a rogue wave would be described as having a terrifying height. It is preceded by a low point that is often characterized as a “hole in the water.” Large ships that were strong enough to withstand violent storms have been ripped apart as they slid bow downward into such a hole only to be wrenched upward by a wave standing some 30 meters above it. The height of the rogue wave that hit the U.S. Navy steamship Ramapo in 1933 was 34 meters, as measured by the officer on watch by triangulation of the crow’s nest against his view of the wave. (Doing physics in the face of death takes great physics courage.)

Both extreme and rogue waves have been spotted around the world, but the waters off the southeast coast of Africa produce more than their share of rogue waves, as verified by the many ships lost in the area. What causes extreme and rogue waves?

Here is the answer from the book The Flying Circus of Physics. For an ocean wave, you probably picture a sinusoidal wave (in the shape of a sine curve, with hills and valleys) moving over the ocean’s surface. If two waves traveling in the same direction were to overlap, you can imagine that the resultant wave (what you would see) is simply the addition of the two waves. If the waves were exactly aligned (in phase), the hills and valleys of the resultant wave would be higher and deeper than those on the individual waves. And if many waves, moving in different directions, overlapped, the resultant wave might be confusing to figure out, but simple addition of the individual waves should still give the height and depth of the resultant wave.

Such simple addition of waves is said to be a linear combination of the waves. Extreme waves seem to be a nonlinear combination; that is, the combination of individual waves somehow generates hills and valleys that are too high and too low. Perhaps as the hills grow, the wind over them enhances their growth so that the final hill height is greater than would be expected. Or perhaps in certain situations the buildup of a resultant wave past a critical point modifies the individual waves and creates an even larger resultant wave. In short, some feature enhances the resultant wave. The odds are against an extreme wave occurring, but occasionally such a wave slams into a cruise liner or some other ship, surprising captains who tend to think in terms of linear combinations.

Rogue waves (also called giant waves or freak waves) are even more difficult to explain but must also be due to a nonlinear combination of waves. However, their occurrence off the African southeast coast is surely due to the opposition of the Agulhas current and the wind-driven waves in the region. The strong Agulhas current flows toward the southwest in a meandering path; the wind-driven waves are typically toward the northeast. As the waves force the current to meander, they can be focused much like light waves can be focused by a lens. With the correct conditions, this focusing generates the hole in the water that is followed by a huge wave leaning toward the hole. Such a wave can kill, as reported in this next video:

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Shukla, P. K., I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Physical Review Letters, 97, article # 094501 (1 September 2006)
··· Gibson, R. S., and C. Swan, “The evolution of large ocean waves: the role of local and rapid spectral changes,” Proceedings of the Royal Society A, 463, 21-48 (2007)
··· Kharif, C., J-P. Giovanangeli, J. Touboul, L. Grare, and E. Pelinovsky, “Influence of wind on extreme wave events: experimental and numerical approaches,” Journal of Fluid Mechanics, 594, 209-247 (2008)
· Garrett, C., and J. Gemmrich, “Rogue waves,” Physics Today, 62, No. 6, 62-63 (June 2009)
··· Rozhkov, S. S., “Giant freak waves: Expect the unexpected,” EPL (Europhysics Letters), 85, article # 24001 (6 pages) (2009)
··· Gronlund, A., B. Eliasson, and M. Marklund, “Evolution of rogue waves in interacting wave systems,” EPL (Europhysics Letters), 86, article # 24001 (5 pages) (2009)
··· Ruban, V. P., “Two different kinds of rogue waves in weakly crossing sea states,” Physical Review E, 79, article # 065304(R) (2009)
··· Chalikov, D., “Freak waves: Their occurrence and probability,” Physics of Fluids, 21, article # 076602 (18 pages) (2009)
Want more references? Go here:
and search down for this item
2.64 Extreme and rogue waves

2.67  Pond resonance due to Chinese earthquake
Jearl Walker
June 2008
   The following link takes you to a video shot on the campus of Jiao Tong University in Shanghai, China, about five minutes after a devastating earthquake hit central China last month. An earthquake sends out seismic waves through the interior of Earth and also along the surface. When the surface waves reach a body of water, anything from a pond to a lake, they force the water to oscillate. Although the oscillations are usually negligible, if they have the right frequency, said to be a resonant frequency, they can build up a noticeable standing wave on the water, with appreciable sloshing. Such sloshing in body of water is said to be a seiche.

You inadvertently set up similar sloshing if you carry a large pan or bowl of water in your hands as you walk. Your gait oscillates the container with a broad range of frequencies, including the resonant frequency of the water in the container. The sloshing can be large, perhaps to the extent that you soak your clothing. (Here is a quick physics lesson for a first date. Just before your date arrives, never try to carry an open container of water across a room because the resulting wet pants may be difficult to explain when your date walks into the room.)

You can also set up a standing wave in a bathtub of water if you periodically push down on the water at one end and then adjust the frequency of your pushing until you set up a standing wave. If you work hard at pushing on the water, the standing wave can send water over the edge of the bathtub and onto the floor.

When the surface waves from the Chinese earthquake reached the university in Shanghai, some American students studying abroad happened to be near a pond where the waves created a seiche. Here is a link to their video of the pond but please do not be offended by their laughter because they did not know of the devastation that had occurred closer to the epicenter (above the origin of the earthquake) about 5 minutes earlier. The surface waves had reached them but not the terrible news.

·  Korgen, B. J., “Seiches,” American Scientist, 83, 330-341 (July-August 1995)
· · ·  Sobey, R., J., “Seiche modes of elongated natural basins,” Coastal Engineering Journal, 45, No. 3, 421-438 (2003)
· · Ichinose, G. A., J. G. Anderson, K. Satake, R. A. Schweickert, and M. M. Lahren, “The potential hazard from tsunami and seiche waves generated by large earthquakes within Lake Tahoe, California-Nevada,” Geophysical Research Letters, 27, No. 8, 1203-1206 (15 April 2000)

Want more references? Use the link at the top of this page.

2.69  Surfing
Jearl Walker
July 2014   What causes a surfer (on a surfboard) to move toward the beach or along a wave? Can you surf on top of the wave or on the backside? Here are two video examples: surfing on a wave 26 meters high, a record 21 meters high, beautiful

Here is what I wrote in The Flying Circus of Physics book:

In open water, far from shore, waves travel at identical speeds. However, near the shore, the speed of a wave decreases as the water depth decreases. Thus, when an ocean wave travels through progressively shallower water as it approaches a beach, the bottom of the wave tends to slow. The top of the wave does not slow and so it tends to outrun the bottom of the wave, causing the wave to lean forward. The height of the wave can also increase. If the wave simply collapses or surges, it spreads in the forward direction, becomes less high, and thus is useless for surfing. However, if the wave spills (the top outruns the bottom) or plunges (the top outruns the bottom so much that the top plunges over to hit the base of the wave front, forming a tube of water), then a surfer can ride the wave.

The ride involves an interplay of three forces on the surfer. (1) Buoyancy, which is perpendicular to the water surface, occurs because the surfboard is partially submerged. (2) Gravity, which is downward, attempts to slide the surfer along the wave face. (3) Drag, which is along the water surface, opposes the motion of the board through the water and is due to the water pressure in front of the board and the friction between the board and the water as they slide past each other.

By paddling to get up to speed, a kneeling surfer can move from the back face, over the crest, and to the front face. Once positioned, the surfer stands and waits for a free ride (no more paddling). By adjusting the orientation of the board in the water, the rider can adjust the drag and the board’s position on the front face. The three forces can cancel out (the surfer is in equilibrium) somewhere along the lower part of the front face. There, the buoyancy force is tilted in the wave’s direction of travel and thus tends to propel the surfer. Gravity tends to pull the surfer down the slope but the water drag tends to oppose that motion, so the surfer rides the wave. To move around on the wave face or to move along the length of the wave, the surfer changes the board’s orientation and thus the water drag. Generally, shifting the stance backward causes the rear of the board to dig more into the water, increasing drag and slowing the board, so that the rider climbs the front face. Shifting the stance forward causes the rider to speed up and move down the face.

Sample Problem

I also wrote about surfing in a Sample Problem in the 8th edition of my textbook Fundamentals of Physics Halliday, Resnick, and Walker. (The international version, in English, is known as Principles of Physics.) Here I have retyped that Sample Problem, complete with its calculations.
A surfer rides on the front side of a wave, at a point where a tangent to the wave has a slope of θ = 30.0o. Let there be an x axis up the slope and a y axis perpendicular and outer from the slope.

The combined mass of surfer and surfboard is m = 83.0 kg, and the board has a submerged volume of V = 2.50 × 10-2 m3. The surfer maintains his position on the wave as the wave moves at constant speed toward shore. What are the magnitude and direction (relative to the position direction of the x axis) of the drag force on the surfboard from the water? Let’s first apply Newton’s second law to the surfer and then see how the surfer can adjust the board to ride up or down the wave, avoiding a wipeout.

Key Ideas

The buoyancy force on the surfer has magnitude Fb equal to the weight of the seawater displaced by the submerged volume of the surfboard. The direction of the force is perpendicular to the surface at the surfer’s location.

By Newton’s second law, because the surfer moves at constant speed toward the shore, the vector sum of the buoyancy force Fb, the gravitational force Fg, and the drag force Fd must be 0.


The gravitational force Fg is downward and has a component mg sin θ down the slope and a component of mg cos θ perpendicular to the slope. A drag force Fd from the water acts on the surfboard because water is continuously forced up into the wave as the wave continues to move toward the shore. This push on the surfboard is upward and to the rear, at angle ϕ to the x axis. The buoyancy force Fb is perpendicular to the water surface; its magnitude depends on the mass mf of the water displaced by the surfboard, as given by Fb = mf g. From the definition of density ρ = m/V, we can write the mass in terms of the seawater density ρw and the submerged volume V of the surfboard: mf = ρwV. The seawater density is ρw = 1.024 × 103 kg/m3. Thus, the magnitude of the buoyant force is

Fb = mf g = ρwVg

= (1.024 × 103 kg/m3)(2.50 × 10-2 m3)(9.8 m/s2)

= 2.509 × 102 N.

So, Newton’s second law for the y axis,

Fdy + Fbmg cos θ = m(0),


Fdy + 2.509 × 102 N – (83 kg)(9.8 m/s2) cos 30.0o = 0,


Fdy = 453.5 N.

Similarly, Newton’s second law Fnet = ma for the x axis,

Fdxmg sin θ = m(0),


Fdx = 406.7 N.

Combining the two components of the drag force tells us that the force has magnitude

Fd = [ (406.7 N)2 + (453.5 N)2 ]0.5

= 609 N

and angle

ϕ = tan-1[(453.5 N) / (406.7 N)]

= 48.1o.

Wipeout avoided

If the surfer tilts the board slightly forward, the magnitude of the drag force decreases and angle ϕ changes. The result is that the net force is no longer zero and the surfer moves down the face of the wave. The descent is somewhat self-adjusting because as the surfer descends, the tilt angle θ of the wave surface decreases and thus so does the component of the gravitational force mg sin θ pulling the surfer down the slope. So, the surfer can adjust the board to re-establish equilibrium, now lower on the wave. Similarly, by tilting the board slightly backward, the surfer increases the drag and moves up the face of the wave. If the surfer is still on the lower part of the wave, then both θ and mg sin θ increase and again the surfer can control the forces and re-establish equilibrium. surfing big waves

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Hornung, H. G., and P. Killen, “A stationary oblique breaking wave for laboratory testing of surfboards,” Journal of Fluid Mechanics, 78, part 3, 459-480 (1976)
·· Hornung, H., “Physik fur die Konige von Hawaii,” Umschau in Wissenschaft und Technik, 81, No. 9, 267-271 (1981)
· Wolkomir, R., “The mechanics of waves---and the art of surfing,” Oceans, 21, 36-41 (June 1988)
··· Vanden-Broeck, J. M., and J. B. Keller, “Surfing on solitary waves,’ Journal of Fluid Mechanics, 198, 115-125 (1989)
· Anderson, I., “Let’s go surfin’. Imagine a beach where perfect waves break as regularly as the rhythm of a Beach Boys song,” New Scientist, 151, 26-27 (27 July 1996)
· Anderson, I., “Surf theories wiped out,” New Scientist, 155, 22, (6 September 1997)
··· Sugimoto, T., “How to ride a wave: mechanics of surfing,” SIAM Review, 40, No. 2, 341-343 (June 1998)
·· Edge, R., “Surf physics,” Physics Teacher, 39, 272-277 (May 2001)
··· Walker, J., Fundamentals of Physics, 8e, John Wiley & Sons, 2008 pp. 369-370x

2.70  Bow-wave riding
Jearl Walker
June 2013  Porpoises and dolphins often accompany boats and ships, moving stealthily alongside the vessel about a meter below water. They may be upright, rolled over on a side, or even showing off by revolving around the body axis. But they do not appear to swim—they just move along as if attached to the ship, perhaps for hours. For fun, they might leap up out of the water. Here are two examples, one with a boat and one with a partially submerged submarine.
The primary propulsion is due to the waves shed by the bow (or sometimes the stern). The porpoise or dolphin will position itself within the front of the wave, not too deep below the (slanted) surface. As the bow pushes on the water, forcing it forward, upward, and outward, the water pushes on the animal, propelling it forward. If the animal simply wants to ride the wave instead of play, it finds the depth where this forward force balances the drag from the water. Sometimes the animal can catch a free ride even if the bow wave is small, perhaps imperceptible to someone on the boat making the wave.
Want the references? Go to

and scroll down to item 2.70
2.73  Oil and waves
Jearl Walker
October 2006   A delightful paper by Joost Mertens of the History Department of the University of Maastricht, the Netherlands, explores how Benjamin Franklin first noticed the calming effect oil has on water waves. In 1757, while on voyage to England in a fleet of ships, Franklin noticed that the wakes behind two of the ships were much flatter than behind other ships. His captain offered that the cooks on those two ships must have just thrown over the greasy water from the day's cooking. The captain thought that the effect was obvious; Franklin thought that the explanation was unfounded.
    However, Franklin soon learned that the calming effect of oil or grease was well known to some groups of seamen. Indeed, many stories have been recorded about how seamen have purposely dumped various oily or greasy fluids on waters to calm them so that the ship could be brought safely through otherwise dangerous breakers. Eventually, through thought, experiment, and correspondence, Franklin realized that the oil "will not be held together by adhesion to the spot where it falls," but will spread out. (The oil actually forms a monolayer, one molecule thick, but Franklin did not have benefit of our modern concept of molecules.) "Now I imagine that the wind blowing over water thus covered with a film of oil, cannot easily catch upon it, so as to raise the first wrinkles, but slide over it, and leaves it smooth as it finds it." Watch the waves disappear after the sunflower oil is put onto the water.

· Lynch, D. K., and W. Livingston, Color and Light in Nature, 2nd edition, Cambridge University Press, 2001, pages 97-98
· Mertens, J., “Oil on troubled waters: Benjamin Franklin and the honor of Dutch seamen,” Physics Today, 59, No. 9, 36-41 (January 2006)
·  van Nierop, E. A., A. Ajdari, and H. A. Stone, “Reactive spreading and recoil of oil on water,” Physics of Fluids, 18, article # 038105 (4 pages) (2006)
· · · Behroozi, P., “The calming effect of oil on water,” American Journal of Physics, 75, No. 5, 407-414 (May 2007)

Want more references? Use the link at the top of this page.

2.74  Tibetan singing bowls
Jearl Walker
July 2011   Playing a Tibetan singing bowl is very much like producing sound by rubbing the rim of a wine glass. As a soft mallet is rubbed along the rim of the metal bowl, the repeated stick-an-slip action causes the bowl to oscillate in several of its resonant modes (repeated patterns of oscillation). Here is a wineglass set oscillating by the sound waves emitted by a speaker driven at a frequency near the resonant frequency of the wineglass:

When a singing bowl set oscillating by a mallet, several such resonant oscillations are set up and last a surprisingly long time. Here is an example in which several bowls are used to make a haunting music:

Recently Denis Terwagne (Departement de Physique of Universite de Liege) and John W. M. Bush (Department of Mathematics, Massachusetts Institute of Technology) examined the excitation of singing bowls containing water. To set up a single resonant oscillation, they excited the bowl by tuning the output of a speaker to a resonant frequency.

At resonance the water developed waves. By increasing the amplitude of the sound, the researchers could make the waves large enough in amplitude that water drops broke free. The really curious feature was that some of these drops floated, bounced, or even walked on the water. You can see such floating in one of the videos at

You may have notice something similar in a common setting as described in The Flying Circus of Physics: Floating drops can be produced when a common Styrofoam cup with coffee (or any other beverage) is rubbed across a tabletop so that the cup undergoes repeated sticking and slipping. If the staggered motion of the cup is fast enough, the ripples it produces on the liquid throw drops into the air. When those drops land, they might float on the liquid instead of immediately merging into it. When the stick-and-slip motion stops, the drops quickly merge.

I studied such drop levitation in one of my early articles for The Amateur Scientist department in Scientific American. (The article is reproduced here at the FCP web site---see the Article of the Month page). If the water surface is oscillated, either by oscillating the water container as I did or by setting up resonant oscillations of the container with sound waves as Terwagne and Bush did, a water drop can avoid coalescing with the water indefinitely. The drop rests on a thin layer of air. Without oscillations, the water would leak out from under the drop and then the drop would soon coalesce with the water surface. However, with oscillations, air is pumped is periodically pumped under the drop to replenish the air, maintaining the levitation.  

News item

Oscillations slow-motion of the waves on the water in a signing bowl. Edge waves can be seen along the rim, as well as radial waves.

Music striking large singing bowls to make music, long lasting resonance performance with an array of singing bowls, part 1 musical performance with singing bowls of various sizes

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
· Walker, J., "Drops of liquid can be made to float on the liquid. What enables them to do so?" in “The Amateur Scientist,” Scientific American, 238, No. 6, 151-158 (June 1978)
··· Terwagne, D., and J. W. M. Bush, “Tibetan singing bowls,” Nonlinearity, 24, R51-R66 (2011)

To read more about ways the levitation of water drops, see item 2.74 in The Flying Circus of Physics. To find a long list of journal references about such levitation, go to
and scroll down to item 2.74 Floating drops.



2.75  Pub trick --- smooth pouring from a height
Jearl Walker
April 2011 Ok, this month I am being sneaky.

Can you pour a beer (or any other freely flowing liquid) into a mug without splashing onto the surrounding table top? Well, sure, if you pour from a short height above the level in the mug or down the side of the mug. How about from a greater height and straight down, as might be the challenge in a pub, as in this video link?

Well, the problem with uncarbonated liquid is that the impact can cause significant splashing. If the liquid breaks up into individual drops, then each drop pushes out a hemispherical crater in the liquid surface in the mug and then forms a crown around the perimeter of the crater. That crown formation can throw liquid up and out of the mug, especially if the mug is almost full. As the crown subsides and rushes back into the crater, the rapid inflow throws water upward in a central jet. The jet may pinch off one or more drops as it reaches maximum height. If many such jets are being thrown upward, more liquid can be thrown out of the mug.

If the falling liquid hits the liquid in the mug as a stream, something similar happens but the crater and crown are more extreme and the central jet never gets to form until the very end. So, there is an even better chance for splashing out of the mug.

If the liquid is carbonated, then impact of either individual drops or a steady steam causes dissolved carbon dioxide to come out of solution and form foam. (With Guinness, nitrogen comes out of solution to form foam.) A longer fall can increase the rate at which the foam builds up in the mug, as you probably already know. The foam forms faster than the bubbles tend to burst, and the foam can overflow the mug. Since Guinness is notorious for its long-lasting bubbles, it must be poured slowly down the side of a tilted mug and in stages if foam overflow is to be avoided. (The reason for the long-lasting foam is that nitrogen gas diffuses much more slowly through the bubble walls than does carbon dioxide, which is used in every other type of beer that I know about. Thus the nitrogen bubbles are longer lasting than the carbon dioxide bubbles.)

So, what about the video? Can someone pour a beer from a height of half a meter or several meters without spilling the beer either through splashing or foam overflow. No, of course not. That breaks the laws of both physics and common experience. Well, I must admit, however, that if someone drinks enough beer, the laws of both physics and common experience may seem to be breakable.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Allen, R. F., “The mechanics of splashing,” Journal of Colloid and Interface Science, 124, No. 1, 309-316 (July 1988)
· Cai, Y. K., “Phenomena of a liquid drop falling to a liquid surface,” Experimetns in Fluids, 7, 388-394 (1989)
· Manzello, S. L., and J. C. Yang, “An experimental study of a water droplet impinging on a liquid surface,” Experiments in Fluids, 32, 580-589 (2002)
· Peck, B., and L. Sigurdson, “Impacting water drops,” in A Gallery of Fluid Motion, M. Samimy, K. S. Breuer, L. G. Leal, and P. H. Steen, editors, Cambridge University Press, 2003, page 74
· Stewart, S., “No use crying . . .,” in “The Last Word,” New Scientist, 197, No. 2640 (26 January 2008)
·· Deegan, R. D., P. Brunet, and J. Eggers, “Complexities of splashing,” Nonlinearity, 21, C1-C11 (2008)
· Calvert, J. R., and K. Nezhati, “Bubble size effects in foams,” International Journal of Heat and Fluid Flow, 8, 102-106 (1987)
· Flam, F., “Frothy physics: scrutinizing the laws of suds,” Science News, 136, 72-73 + 76 (29 July 1989)
··· Bhakta, A., and E. Ruckenstein, “Decay of standing foams: drainage, coalescence and collapse,” Advances in Colloid and Interface Science, 70, 1-124 (1997)
··· Bhakta, A., and E. Ruckenstein, “Drainage and coalescence in standing foams,” Journal of Colloid and Interface Science, 191, 184-201 (1997)
·· Peron, N., J. Meunier, A. Cagna, M. Valade, and R. Douillard, “Phase separation in molecular layers of macromolecules at the champagne-air interface,” Journal of Microscopy, 214, Part 1, 89-98 (April 2004)
·· Bamforth, C. W., “The relative significance of physics and chemistry for beer foam excellence: theory and practice,” Journal of the Institute of Brewing, 110, No. 4, 259-266 (2004)


2.76  Pub trick --- beer bottle tapping
Jearl Walker
January 2015  Here is a common prank: A friend has opened a bottle of beer (or any other carbonated drink). Tap a second bottle onto the mouth of the friend’s bottle. Within a few seconds, a foam of carbon dioxide bubbles gushes from the friend’s bottle. Here is a (noisy) example:

The questions is why. This is not like the situation where you shake a carbonated beverage while you seal off the opening with a finger and then remove your finger. With beer tapping, you barely tap the friend’s bottle. Why does that seemingly gentle gesture create such a dramatic result?

Most beers have a lot of carbon dioxide in solution under high pressure. When the bottle is opened, the pressure suddenly drops to atmospheric pressure, and then there is too much carbon dioxide in solution --- it is a supersaturated solution. So, the carbon dioxide begins to come out of solution by forming bubbles in any tiny crevice along the glass wall or bottom surface. Normally, the bubbles grow until they are large enough to break free and then float up to the top of the liquid. As they move upward, they grow larger as carbon dioxide diffuses (passes) into them from the liquid they pass. This is all rather gradual. However, if you shake up the contents, the bubbles break free more quickly and thus the bubble production is much more rapid, enough to allow gushing from the bottle. Some people enjoy spraying the contents of a shaken bottle over other party guests.

Something different happens with bottle tapping. The tap sends a pressure wave down through the fairly rigid glass wall to the bottom of the bottle. (The stunt does not work very well with the more flexible walls of a beer can.) When the wave reaches the bottom of the bottle, it cause the bottom surface to begin oscillating. The oscillation sends an expansion wave (the pressure in the liquid is slightly reduced) up through the liquid to the top surface. The wave then travels back down through the liquid as a compression wave (the pressure is slightly increased). The wave can then alternate between the two types and the two directions several time.

The waves travels through any existing bubbles that were on their way up. The expansion wave causes them to expand, but then the compression wave causes them to shrink. In fact, the shrinkage can eventually rupture each bubble into many smaller bubbles. These smaller ones may partially deplete the carbon dioxide from the surrounding liquid but as they float upward into fresh liquid with more carbon dioxide, they grow larger and larger. And the larger they become, the faster they are buoyed upward. Thus, they quickly form fast moving plumes, and as the plumes reach the top surface of the liquid, bubbles gush from the bottle, all because of a gentle tap.

Here comes a video demonstration and explanation:

Here is the marvelous slow-motion video posted by Javier Rodriguez-Rodriguez and Almudena Casado-Chacon of Carlos III University of Madrid, and Daniel Fuster of Universite Pierre et Marie Curie in Paris to accompany their paper in Physical Review Lettters (see below).

Here is a video with animation from Scientific American:

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
···Rodriguez-Rodriguez, J., A. Casado-Chacon, and D. Fuster, “Physics of beer tapping,” Physical Review Letters, 113, article #214501 (5 pages) (21 November 2014)

2.76  Gushing of beer and soda
Jearl Walker
January 2007    Here is puzzle to go with a new year’s celebration. Shake a can of carbonated beverage (soda or beer) and then pop the top open as you point the can toward a friend. (Don’t deny it---you’ve done this before, drenching someone with the beverage and then laughing as you claimed, “Gosh. I didn’t know. Somebody must have shaken the can before I picked it up.” Yeah, right.

   Why does the shaken beverage undergo gushing as it is called in the technical literature? (I am really pleased that I have a job in which I can read and write Flying Circus type of physics all day, but maybe, just maybe, having a job where you get to study beer gushing might be better. What do you think? Or is that what many college students already do?)

   As I explained in the book, bubbles in a carbonated drink can form in two ways. In a drinking glass, they nearly always form on microscopic bits of cellulose that was left on the glass interior the last time it was wiped with a paper or cloth towel. The interior of the cellulose tubes are ideal for allowing carbon dioxide molecules (the “carbonation” of a carbonated beverage) to come out of solution to start and then expand a bubble until the bubble is large enough to pinch off from the tube and escape upward.

   Bubbles can also form directly in the bulk liquid, but there is a hitch. A bubble must initially be larger than a critical size or otherwise it is squeezed out of existence immediately by the surface tension along its surface. The reason has to do with a competition taking place in each bubble that is formed in the bulk liquid: (1) Carbon dioxide passes through the bubble’s surface to join the gas inside the bubble, tending to expand the bubble. (2) The mutual attraction of the liquid molecules (primarily water) for one another produces a force that squeezes the bubble. That inward force is usually said to be due to the surface tension along the surface of the bubble. The force is greater for a smaller bubble than for a larger one because the surface is more tightly curved.

   If a bubble is larger than a certain critical size, the influx of gas molecules wins and the bubble continues to exist and grow. If the bubble is smaller than the critical size, surface tension immediately squeezes it out of existence. When you pour a carbonated beverage into a glass, the turbulence may create bubbles in the bulk liquid but they are almost all too small and quickly disappear. So the bubbles you see are ones from the cellulose fibers, not from the bulk liquid.

   Well, that is the traditional explanation of bubble formation but it fails to explain why a shaken can of beer gushes when opened. There are no cellulose fibers in a can and so the bubbles must form in the bulk liquid. But how?

   The shaking can mix the gas that was at the top of the can (above the liquid) down into the liquid but it can also create points of turbulence where the pressure is momentarily reduced, allowing dissolved gas to come out of solution and form bubbles. However, those bubbles should immediately disappear, not hang around for you to aim the can at a friend and pop the can open. Yet, the bubbles do last for tens of minutes. When you open the can, the pressure inside is suddenly reduced (it was about twice atmospheric pressure) and so the bubbles suddenly expand, shooting beverage out through the can’s opening. The traditional explanation for bubble formation says this cannot happen, but that is of little comfort to your friend.

   K. K. Sahu, Y. Hazama, and K. N. Ishihara of Kyoto University have produced an alternate explanation that is based on a series of experiments using ultrasound to “shake” the liquid inside cans of Asahi beer and Coca Cola. After an ultrasound application, a can would be opened and the extent of gushing measured. In line with common experience, they found that if the can is allowed to sit undisturbed for a while before it is opened, the contents will not gush. Surprisingly, Coke Cola required less time than the beer.

   Apparently, the shaking, whether by hand or via ultrasound, produces microbubbles that are smaller than the critical size and yet which do not immediately disappear. They don’t last very long in the Coca Cola (you have to squirt your friend right away) but they last tens of minutes in the beer (you can wait). Presumably something in the beer (some of the proteins), stabilizes the surface of a microbubble, allowing it to persist for a while. If the can is opened during this stage, the microbubbles suddenly expand and shoot the beer out through the opening.

   Here is something strange. Suppose that you shake a beer and then let it sit undisturbed just long enough (say, 10 or 15 minutes) that it would be safe to open. If you shake it just as hard a second time and then finally open it, there is very little gushing. The researchers suggest that the microbubbles produced in the first shaking were transformed somehow during the rest period, perhaps by splitting into even smaller bubbles. When the can is shaken the second time and then opened, gas cannot readily enter these smaller bubbles and so the expansion of the bubbles is insufficient to blow liquid out of the can. I’ll keep you posted if more is published on this explanation.

Here is a link on the book’s discussion of the fact that bubbles in a freshly poured glass of Guinness stout move down the side of the glass.

· · ·  Liger-Belair, G., C. Voisin, and P. Jeandet, “Modeling nonclassical heterogeneous bubble nucleation from cellulose fibers: application to bubbling in carbonated beverages,” Journal of Physical Chemistry B, 109, 14573-14580 (2005)
· Liger-Belair, G., A. Tufaile, P. Jeandet, and J.-C. Sartorelli, “Champagne experiences various rhythmical bubbling regimes in a flute,” Journal of Agricultural and Food Chemistry, 54, 6989-6994 (2006)
· · ·  Liger-Belair, G., M. Parmentier, and P. Jeandet, “Modeling the kinetics of bubble nucleation in champagne and carbonated beverages,” Journal of Physical Chemistry B, 110, 21145-21151 (2006)
· · ·  Uzel, S., M. A. Chappell, and S. J. Payne, “Modeling the cycles of growth and detachment of bubbles in carbonated beverages,” Journal of Physical Chemistry B, 110, 7579-7586 (2006)
· ·  Sahu, K. K., Y. Hazama, and K. N. IIshihara, “Gushing in canned beer: The effect of ultrasonic vibration,” Journal of Colloid and Interface Science, 302, 356-362 (2006)
· · Hackbarth, J. J., “Multivariate analyses of beer foam stand,” Journal of the Institute of Brewing, 112, No. 1, 17-24 (2006)

Want more references? Use the link at the top of this page.

2.76  Widgets and bubbles in a Guinness stout
Jearl Walker

June 2012    Here are the pub questions of the month: Why do cans and bottles of stout come with a widget, the little canister that you hear rattling around inside? Why are widgets used only with stouts? When a stout is poured into the usual pub glass and begins to settle, why do bubbles move downward instead of upward as they do in other types of beer? Two recent publications out of the University of Limerick have addressed these questions.


Most beers and soft drinks are carbonated; that is, they are liquids that have a fairly high amount of carbon dioxide in solution. The carbonation adds to the taste of the drink (it is a weak acid) and, in the case of beer, produces bubbles and foam to form the head on the beer. To get the foam, all you have to do is to open the container and pour the contents in a drinking glass. Initially the contents are under pressure so when you open the container, the pressure suddenly decreases to atmospheric pressure. As you pour the beer, the turbulence causes some of the carbon dioxide to come out of solution and form bubbles. However, most of the bubbles form once the beer is in the glass.

The bubbles cannot easily form in the bulk liquid because any initial bubble is so small — the large curvature of its surface means that the surface tension on the surface is large enough to collapse the bubble. Bubbles have a much better chance of starting (nucleating) in any micro-crevices in the glass wall. As more carbon dioxides moves (diffuses) to a bubble site, the bubble grows until the buoyancy on it causes it to break free of the crevice and float upward.

At least, that was the explanation for bubble production until recently when experiments by Liger-Belair of Universite de Reims in Reims, France, revealed that most bubbles nucleate in stray cellulose fibers that happen to be in the glass, probably left there when the glass was cleaned. The carbon dioxide diffuses into the hollow interior of a fiber, both through the walls and the ends. As the amount of gas increases, the bubble expands until it can move to one end of the fiber and then pinch off, floating upward. A train of bubbles, one after another, can rapidly escape in this way in any carbonated drink. It is especially rapid in champagne but is also rapid enough in beer to result in a thick head on the beer.

A Guinness stout is quite different because much of the carbon dioxide is replaced with nitrogen. Thus, a stout is less acidic than regular beer. Because the nitrogen bubbles are typically smaller than carbon dioxide bubbles, the stout is “creamy” to the taste, almost food-like. However, there is problem with stout. If you pour it into a glass, almost no bubbles form and thus the stout lacks a head. To get around this problem, cans of Guinness stout come with a widget, which is a pressure-sensitive device that releases carbon dioxide and nitrogen when the container is opened and the sudden drop in pressure ruptures the widget. When the stout is then poured, that released gas produces bubbles and a head.
So, the problem was solved with a widget but the question remained: Why don’t bubbles form in a poured stout in the same way that they form in a poured regular beer? In 2011, W. T. Lee, J. S. McKechnie, and M. G. Devereux of the University of Limerick in Limerick, Ireland found an answer.

The bubble-nucleation of Liqer-Belair works for a stout with carbon dioxide and nitrogen gasses, but the process is just too slow. The gas pressure in a gas pocket (cellulose fiber or micro-crevice) is now due to both gasses. The pressures of the carbon dioxide in the pocket and in the solution are equal. But that means the pressure of the carbon dioxide in solution is less than that total pressure in the gas pocket. Thus the carbon dioxide in the solution cannot easily enter the gas pocket to grow a bubble.

The nitrogen in the solution hardly helps because its diffusion through the liquid to a bubble site is very slow. Overall, the nucleation rate in a stout is about 15 times slower than in regular beer. Considering that the bubbles in the stout are smaller, forming a decent head takes way too much time. Thus, if you want bubbles and foam in a Guinness stout when you pour the stout into a glass, you need a widget to release the gas and stir up the liquid.

Descending bubbles

One of the enchanting puzzles about a Guinness stout is the descent of its bubbles during settling after the stout is poured. Some observers have claimed that the motion is an illusion. In my extensive history with Guinness, let me assure you that the motion is real—indeed you can follow the descent with a finger drawn down along the pint glass.

Obviously, if there is downward motion along the sides of the glass, there must be upward motion along the central axis of the glass. One plausible explanation has been that friction between the liquid and the glass wall retards the upward motion there. Because no wall friction acts along the central axis, the upward motion there dominates and then forces the downward motion along the wall.

The Limerick research team has now presented a much more convincing argument, complete with simple experiments. The shape of the pint glass sets up the circulation pattern. The pint glass is narrower toward the bottom than toward the top in order to provide an easy grip to the glass.

When the stout is poured into the glass, let’s assume that the bubble distribution is fairly uniform. The bubbles near the lower portion of the glass then move upward because of buoyancy, thereby decreasing the density of bubbles near the wall.

Each bubble produces a drag force on the liquid surrounding it. Because the density of bubbles near the wall is now small, the drag force there is also. Near the central axis, where the density is greater, the drag force is also. Thus, the liquid near the central axis is forced upward. To complete the circulation, the liquid descends along the wall, carrying bubbles downward.

To demonstrate this interplay of glass shape and bubble concentration and motion, the research team checked an “anti-pint” glass, which was wider lower down and narrower higher up. Again, if the bubble distribution is initially fairly uniform, bubbles would initially rise along the glass wall. Now, however, they crowded next to the wall because the wall tilts inward.

This greater density means that the drag force on the liquid near the wall is greater than near the central axis, and thus liquid and bubbles move upward along the wall, not downward as in the standard pint glass. Indeed, when tested, that is exactly what the bubbles did in the anti-pint glass.

When I pour a Guinness stout into my official Guinness pint glass, I can easily see the downward moving bubbles in the narrow, lower section but not above the wider section. If you happen to drink stouts, you have plenty of experimentation to do here. Use drinking glasses of various shapes: flaring outward (as in a large martini glass), flaring inward (this might be a bit difficult to find), and vertical (as in a vase for a single rose).

You will find that some stouts do not display descending-bubbles of a Guinness and foam fairly well without a widget. For example, Speedway Stout (San Diego, California) foams well. I suspect that these other stouts have lots of carbonation.
If you would like to watch my video demonstration of Guinness bubbles, go to my public Facebook site

and find the video titled “Guinness.”

There is one lingering question. If the explanation of descending bubbles is correct in focusing on the shape of the drinking glass, why doesn’t that shape send bubbles downward in a regular beer? Soon after I first posted this story, Dr. Lee sent me a Facebook message with the answer: The shape of the drinking glass should affect bubbles in a regular beer in the same way as it affects bubbles in a Guinness stout except for one difference: size. The bubbles of carbon dioxide in a regular beer are bigger than the nitroten bubbles in the stout and thus a much bigger buoyancy force acts on them. Thus, the carbon dioxide bubbles move upward in the common sense way. I now have many good reasons to look forward to another Guinness.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Lee, W. T., J. S. McKechnie, and M. G. Devereux, “Bubble nucleation in stout beers,” Physical Review E, 83, article # 051609 (4 pages) (2011)
··· Lee, W. T., and M. G. Devereux, “Foaming in stout beers,” American Journal of Physics, 79, No. 10, 991- (October 2011)
··· Benilov, E. S., C. P. Cummins, and W. T. Lee, “Why do bubbles in Guinness sink?” retrieved 23 May 2012
··· Liger-Belair, G., “The physics behind the fizz in champagne and sparkling wines,” European Physical Journal Special Topics, 201, 1-88 (2012)

For an extensive list of references, go to

and scroll down to item 2.76.

2.76  Pub trick --- preventing gushing in a shaken soda or beer
Jearl Walker
November 2012 Shake a sealed carbonated drink several times and then open it. Well, you’re not going to actually do that because you know what will happen: The fluid will spray through the opening, drenching you and everything around you. The spray is caused by a rapid, uncontrolled production of carbon dioxide bubbles when the pressure inside the container is reduced as the container is opened. The technical name for this bubble production and resulting spraying is gushing.

The pub challenge this month is this: What can you do to the shaken container to reduce or eliminate the gushing? Well, you could just wait several minutes if you have a soda or ten to 15 minutes if you have a beer. But is there anything else you can do so that you can safely open the container almost immediately?

Traditional answer
The long-standing answer is given in this video from television:

Before the container is shaken, a lot of carbon dioxide is in solution, with more in the region of free gas trapped just above the liquid. When the container is shaken, the liquid splashes around and that free gas mixes chaotically with the liquid, forming fleeting gas pockets. Some of the dissolved carbon dioxide then leaves the liquid and moves into those chance gas pockets, forming carbon dioxide bubbles.

There is then a competition: (1) More dissolved gas attempts to leave the liquid and move into each bubble, enlarging the bubble. (2) Surface tension along the surface of each bubble (due to the mutual attraction of liquid molecules for one another) attempts to collapse the bubble, to reduce the surface area. The traditional explanation then follows: Gas bubbles larger than a certain critical size have a curvature that is too large to be collapsed by the surface tension. But gas bubbles smaller than that critical size are too curved to resist the surface tension and so they are squeezed out of existence.

Bubbles have a far better chance of forming and growing if they cling to a tiny crevice or scratch on the container wall. Because the bubble surface then bridges the opposite sides of the crevice, the curvature is too small to succumb to the surface tension.

In the video, Steve Sprangler is certainly correct. If such bubbles form on crevices, they will contribute to the gushing. As soon as the container is opened, dissolved gas will rush into the bubbles and rapidly inflate them. They break free of the crevice and race to the top of the liquid with much vigor. More bubbles form in the crevices, race to the top, and add to the splashing. Indeed, as the pressure is reduced and gas flows out of the container, it carries some of the liquid. That is the spray that drenches you.

Updated explanation
That story has long been the explanation for the gushing of carbonated drinks. However, research in the last few years has pointed to another, more important cause of gushing. When the container is shaken, tiny bubbles form in the liquid but are not immediately collapsed by surface because their surfaces are coated with certain molecules (hydrophobins). This coating stabilizes the nanobubbles. If the container is opened, dissolved carbon dioxide flows into the bubbles so quickly that they bubbles rapidly expand, race to the top of the liquid. As in the traditional explanation, the rapid out flow of gas carries liquid, which forms the spray.

Researchers have identified how these stabilizing molecules work. (In fact, by adding or removing certain molecules, they can increase or decrease the extent of gushing in carbonated drinks.) Normally, the nanobubbles in soda last only a few minute and then the gushing potential disappears. Those in beer last much longer, and so shaken beer can be left on a table for up to 15 minutes as prank on whoever happens to open it.

When Strangler taps on the metal container, he might indeed be freeing any bubbles that had formed in crevices. Of course, we cannot see inside a metal can and thus cannot be sure that there actually any bubbles clinging to the wall. Even if there are clinging bubbles, the main source of the gushing is the nanobubbles produced by the shaking. The tapping reduces the chance of gushing because the acoustic wave it sends through the liquid collapses those nanobubbles. So, if you are ever afraid that someone has set you up for a prank with a shaken can of carbonated liquid, tap the can several times with a fingernail or fork edge to clear out the nanobubbles.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
·· Sahu, K. K., Y. Hazama, and K. N. Ishihara, “Gushing in canned beer: The effect of ultrasonic vibration,” Journal of Colloid and Interface Science, 302, 356-362 (2006)
·· Hackbarth, J. J., “Multivariate analyses of beer foam stand,” Journal of the Institute of Brewing, 112, No. 1, 17-24 (2006)
· Lutterschmid, G., M. Stubner, R. F. Vogel, and L. Niessen, “Induction of Gushing with Recombinant Class II Hydrophobin FcHyd5p from Fusarium culmorum and the Impact of Hop Compounds on its Gushing Potential,” Journal of the Institute of Brewing, 116, No. 4, 339-347 (2010)
· Deckers, S. M., Y. Lorgouilloux, K. Gebruers, G. Baggerman, H. Verachtert, H. Neven, C. Michiels, and J. Martens, “Dynamic light scattering (DLS) as a tool to detect CO(2)-hydrophobin structures and study the primary gushing potential of beer,” Journal of the American Society of Brewing Chemists, 69, No. 3, 144-149 (2011)
· Christian, M., J. Titze, and V. Ilberg, “Chemical structure of model substances related to their gushing-inducing and suppressing activity,”Journal of the American Society of Brewing Chemists, 69, No. 3, 170-179 (2011)
· Christian, M., J. Titze, V. Ilberg, and F. Jacob, “Novel perspectives in gushing analysis: A Review,” Journal of the Institute of Brewing, 117, No. 3, 295-313 (2011)

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