POUR A THIN STREAM OF HONEY onto a small pool of honey and you will probably see that the fluid forms a coil on the surface of the pool. Syrup glue, oil and liquid chocolate are among the other viscous fluids that behave this way. As an alternative to coiling you may see the fluid fold back and forth in a ribbonlike pattern or wrap around in some other pattern.

The first study of these phenomena was made in the late 1950's by George Barnes, who is now at the University of Nevada at Reno, and two of his students, James MacKenzie and Richard Woodcock. They worked with a heavy oil (No. 140 transmission oil) that they poured into a dish. When the stream was circular in cross section, it coiled on reaching the pool. When it was fairly flat because it had been poured over an edge, it resembled a folded ribbon. If the stream fell onto a surface that was not horizontal, it formed a figure eight or a petal-like figure.

The frequency of coiling depended on the height from which the stream fell, being larger with a greater fall. This relation was linear for long distances but more complicated for short ones. A certain minimum fall was necessary. If the fall was less than the minimum, the fluid entered the pool without coiling. When the fall was more than the minimum, the stream reached the surface at a rate of speed higher than the rate at which the pool could absorb it, and so it began to form a coil.

When the stream fell quite far, the coiling generated a cone of oil that rose slightly above the surface of the pool. A stream that coiled quickly usually resulted in a relatively high cone, although the height was never more than a centimeter. A cavity formed at the top of a tall cone as the stream coiled there.

Barnes observed that a given particle of oil in a falling stream does not spiral around the central axis of the stream but instead is confined to a vertical plane. As the particle approaches the region of coiling it moves to the side and off the central axis before continuing on to the surface of the pool. Barnes tried to follow the motion of individual particles of fluid by inserting particles of aluminum into the stream, but the motion of the particles was too swift to monitor.

Barnes then directed the light of a stroboscope at the stream. When he matched the frequency of the flashing to the coiling frequency of the stream, each flash illuminated the stream at the same phase of coiling. To Barnes the coil appeared to be stationary. If the frequency of the stroboscope was slightly out of synchrony with the coiling rate, the coil appeared to turn slowly. Barnes could monitor a rapidly turning coil by effectively slowing it in this way.

The next investigation of liquid coils was made by Geoffrey Ingram Taylor, one of this century's leading investigators of fluid dynamics. He attributed the coiling to mechanical stress in the viscous stream as it approached a pool of fluid at fairly high speed. The fluid in a stream increases in speed as it falls because of the acceleration of gravity. The stream also becomes narrower. Both effects figure in Taylor's explanation of coiling.

To make sense of the narrowing one must compare the speed of the fluid as it passes through two cross-sectional slices of the stream, one near the bottom and the other near the top. The volume of fluid passing through a slice each second must be the same, but the speed is greater through the bottom slice than it is through the top one. Because the same volume of fluid must pass through each slice each second and also because the stream is moving faster through the bot- tom slice the bottom slice must have a smaller diameter.

If the stream is moving faster than the fluid can enter the pool, the stream begins to slow down and to widen a short distance above the pool. Each particle of fluid passing through the narrowest section of the stream must slow down. The force responsible for the slowing is stress in the part of the stream just below the narrowest section. Stress is the force per unit area of a cross section through the stream. It is greatest at the narrowest section because the area is smallest there. If the stream is sufficiently narrow, the stress causes the stream to buckle to one side.

The deflected stream also further buckles in a direction that will initiate a circular motion around the central axis of the stream. Coiling begins. More fluid enters the buckled region, waiting its turn to enter the pool, and the stream moves in a circle around the central axis.

The coiling frequency depends on how narrow the stream becomes. A narrow stream buckles only slightly to the side, so that the radius of the coil it makes is small. Since the speed of the fluid particles in such a thin stream is relatively high, the fluid coils around the central axis with a high frequency.

In a stream with a somewhat wider narrow region the buckle is farther to the side, creating a coil with a larger radius. The frequency of coiling is lower because the speed of the fluid particles in a wider stream is lower. The size of the narrowest portion of the stream depends on the size of the stream as it leaves the container and the distance through which it falls. If one examines streams flowing from an aperture of a fixed size, only the height matters.

Suppose the container of fluid is initially just above the pool and is then raised. At first the distance of fall is too short to give rise to coiling. When coiling begins, the stream is still fairly wide even at its narrowest point. The coils have a large radius and the coiling frequency is low. As the container is raised more the thinnest section of the stream narrows, the radius of the coils decreases and the coiling frequency increases. Eventually the container is so high that the stream breaks up into drops.

Taylor made his studies primarily with streams of glycerin. When the glycerin fell through air, its acceleration was the normal acceleration of gravity: g. To vary the acceleration Taylor made a. stream fall through a less viscous fluid. The acceleration of the stream was the n less than g because the surrounding fluid provided an upward buoyancy. The acceleration of the stream was calculated from a comparison of the specific gravity of the stream and that of the surrounding fluid. The specific gravity of glycerin is about 1.255, of fresh water 1. The difference is .255, and so the acceleration of a glycerin stream falling through fresh water is .255g.

Such a stream does not increase in speed as rapidly as it would in air. Suppose an experiment is designed to compare the coiling in the two cases. Glycerin will be poured through the same aperture and from the same height. When it falls through air, it coils at a certain frequency. When it falls through water, the c oiling frequency is lower because just above the pool of glycerin the stream moves slower than it does in air.

Taylor also made a stream of glycerin fall through two layers of fluid, each layer less dense than the glycerin. The stream coiled as it passed from the first layer into the second. The first layer had the smaller specific gravity, as was ;- shown by the fact that it floated on the second layer. Thus the acceleration of a.- the stream was larger in the first layer than it was in the second. If the change in acceleration at the boundary between layers was sufficiently large, the stream was stressed as it crossed the boundary. If the stream was sufficiently thin at that point, it buckled and coiled as it descended through the bottom layer.

Once a stream begins to coil, its downward speed changes. The ratio of the two speeds depends on the diameter of both the stream and the coil. The ratio is equal to the diameter of the stream divided by the product of pi and the diameter of the coil.

In my investigations of the coiling of viscous liquids I set up a ring stand to hold a paper cup inside an aquarium. Below the cup was a small plastic platform onto which a fluid stream fell from a hole in the bottom of the cup. The platform was convenient when I photographed the coiling stream because the draining of the fluid off the platform ensured that the coils would always be at the same height above the bottom of the aquarium.

I made the hole in the cup with the point of a pencil; I tried to make the hole smooth on the inside of the cup so that small flaps of paper would not alter the flow of the fluid. The diameter of the hole was about four millimeters. The cup, which I set snugly in a ring clamped to the stand, could be raised or lowered by adjustments of the clamps.

I started with Karo dark corn syrup. The stream of syrup fell through air and onto a shallow pool of syrup on the platform. The height of the fall was the distance between the platform and the top surface of the syrup in the cup. (Because of the fluid pressure on the syrup at the bottom of the cup a particle of syrup going through the hole has the same speed it would have had if it had fallen :from the top surface of the syrup.)

When the height of the fall was between seven and 13 centimeters, the stream coiled as it hit the pool. With a shorter fall there was no coiling. With a longer fall the syrup emerged from the cup in spurts. Each spurt displayed some coiling or a more complex twisting, but there was no sustained coiling and no cone. When the fall was fairly long, the stream was quite thin just above the E platform and quickly built up a cone that extended about a centimeter above the platform. At the top of the cone the coiling of the stream was too fast for my eye to follow. The coiling could be in either direction, but once it started it would not reverse.

When the fall was shorter, the stream was relatively thick just above the pool. No cone developed and the rate of coiling was slow. The horizontal extent of the coiling also depended on the height of the fall. In a long fall the stream extended to the sides only a few millimeters; in a short fall it extended about a centimeter.

I partially filled the aquarium with tap water and repeated the-experiments. The syrup fell through the air and then through the water. The fall was relatively long, so that the coiling was fairly fast, although the rate was lower than it was when the syrup fell only through the air from the same height. The cone in the pool of syrup was considerably less well defined than it was in the preceding demonstration because the coiling was more erratic.

I increased the specific gravity of the water by stirring in salt. The acceleration of the stream through the salt water was less than it was through the tap water. After leaving the salt water undisturbed for a long time I repeated the experiments. The coiling frequency was somewhat less than it was in the tap water. Again the coiling and the formation of the cone were not well defined.

With strong back lighting on the impact area I saw the circulation of the salt water created by the coiling. Vortexes shed by the coiling made the salt water first swirl away from the cone and then move upward and back to the falling stream of syrup.

With a considerable distance between the cup and the surface of the water the syrup fell from the cup in bursts. The lower end of each burst was a fat glob of syrup, followed by a thinner stream that eventually broke away from the hole. When the stream entered the water, it formed quite complex shapes. The glob hit the bottom first and sent a shock through the thin stream, which stretched, twisted and turned, even occasionally bouncing from the pool of syrup. In a short time the stream slowed and merged with the pool.

In another experiment l poured a layer of transmission oil over the salt water. When corn syrup was poured into the aquarium, it passed through air and then through the transmission oil, entraining some of the oil. When it descended into the salt water, it had a much greater diameter because of the added oil. The stream coiled very slowly at the bottom.

Since the transmission oil was lighter than the salt water, the downward acceleration of the stream was less than it was when the syrup fell only through salt water. At times the acceleration appeared to be zero or even negative (upward). Whenever air bubbles were trapped in the stream, I could follow the motion of components of the fluid. Usually the bubbles moved downward, but sometimes adjacent parts of the stream moved in opposite directions. Occasionally the stream stopped coiling and broke, whereupon the lower end rose back to the layer of transmission oil.

I tried to create an inverted rope coil. After filling the aquarium with tap water I submerged a plastic squeeze bottle containing viscous motor oil. Because the oil was less dense than the water it rose when I squeezed it out of the bottle. I supposed that when a layer of oil had formed on top of the water, the rising stream of oil would coil as it reached the oil layer. The driving force would be the upward buoyancy on the stream. Little or no coiling occurred, presumably because the rising stream gained speed too slowly. When it reached the oil layer, it was still moving slowly enough to merge with the layer without the stress that causes buckling. If the tank of water had been deeper so that the stream was moving faster when it reached the oil layer, the demonstration might have worked.

A drop of oil that emerged from the squeeze bottle rose to the oil layer and remained there for about 10 seconds. The reason for the delay was that after the drop reached the oil layer a thin layer of water remained between the two. The water layer had to be squeezed out before the drop could merge with the layer of oil. The flow of the water was hampered by the viscosity of the oil on the surface of the drop and the oil layer. Eventually the water escaped and the drop disappeared into the oil layer.

I did manage to achieve an inverted coiling with rubber cement. I submerged a small container of the cement and caused a thin stream to move upward to the surface of the water. As soon as a small area of cement was on the water surface the rising stream of cement began to coil. By adjusting the depth of the container I could control the rate of the coiling. (This demonstration makes a big mess. I ended up with rubber cement all over my hand and arm.)

I set up an experiment in which a stream of corn syrup fell through a layer of dilute ammonia (window cleaner dyed blue) and then through a layer of glycerin. The fluids were in a large beaker because filling the aquarium was getting too expensive. When I adjusted the height properly, a thin stream of syrup broke up into large, beautiful coils as it passed into the glycerin. The coils were not smooth and the planes of the successive coils were not parallel.

I left the demonstration in place for several days. When I returned, four distinct layers could be seen in the beaker. At the top was the blue fluid (from which the ammonia had evaporated). Next came a gray layer, then a layer of fairly clear glycerin and finally a layer of glycerin with a tint of syrup (or perhaps a dye from the syrup). I repeated my earlier experiment and then decided to lower the paper cup of syrup into the top layer of dyed fluid. The coiling of the stream entering the glycerin decreased in frequency because the stream was now thicker.

When I lowered the cup farther into the fluid, the pressure from the fluid in the beaker prevented any syrup from leaving the cup. I raised the cup above the fluid again. While the cup had been partially submerged some of the blue fluid had entered it, decreasing the viscosity of the syrup. The stream now coiled twice, once on top of the blue layer and again as it entered the region clear glycerin. The first coiling was id and produced a small cone. The second coiling was much slower and made no cone.

Most of the fluids I investigated were of the kind termed Newtonian. The viscosity of a Newtonian fluid can be altered only by changing the temperature of the fluid. If the temperature is increased, the viscosity is decreased. To see the effect of temperature I warmed corn syrup and let it fall through air. With less viscosity the stream merged more readily with the pool. With less stress the stream buckled less. After several trials the syrup was so warm and the viscosity so low that the stream did not buckle at all and the coiling disappeared.

Two toy products made from highly viscous fluids are Slime and Silly Putty. They are so viscous that many people consider them to be solids. To see whether a descending stream of Silly Putty would coil I formed a thin roll of the stuff and hung part of it over the edge of a low table. The hanging strand descended slowly to the floor. When the lower end touched the floor, the stream began to coil into large, graceful loops. Then I put a quantity of Slime into a paper cup in the usual arrangement for generating a falling stream. The Slime emerged from the hole in the cup and then descended gradually to a tabletop, where it too began to coil.

Both of these fluids are of the kind termed non-Newtonian. In such a fluid the viscosity depends not only on temperature but also on the stress on the fluid. The viscosity of Slime and silly Putty is higher when stress is applied, but the stresses in the gradual flows I created probably did not much increase the viscosity. The effect of stress in a non-Newtonian fluid is more apparent in a mixture of cornstarch and water. When enough cornstarch is added to water to make a rather thick fluid, the fluid is noticeably non-Newtonian. (I discussed the strange behavior of the mixture in this department for November, 1978.)

I prepared a thick mixture of cornstarch and water and poured it into the paper cup to create a thin falling stream that landed in a beaker. When the height of the fall was adjusted appropriately, the stream reached the pool in the beaker at a rate of speed too high for it to merge with the pool. The stress in the lower part of the stream increased the value of the viscosity over the value higher up, and the stream merged slower than a comparable Newtonian fluid would have. It did not coil in a circle but instead oscillated from side to side. Occasionally the plane of oscillation changed orientation.

I do not know what determines the orientation of the plane, nor can I explain why circular coils do not develop. My guess is that stress buckles the stream to the side but also increases the viscosity too much for the mixture to buckle in such a way that it follows a circular path around the central axis. Oscillating to and fro like a folded ribbon must be the alternative.

I poured into a beaker a thick mixture of cornstarch and water, followed by a layer of corn oil about one centimeter deep. The paper cup delivered a stream of corn syrup. When the syrup entered :the corn oil, it broke up into attractive coils. The coils did not, however, descend along a straight line. Instead the succession of coils itself coiled as it approached the cornstarch. The small coils arose from the stream's transition from air to corn oil. The coiling of the coils probably resulted from the impact of the smaller coils on the layer of cornstarch.

My results with ketchup, another non-Newtonian fluid, came as something of, a surprise. The falling stream of ketchup - coiled only when the height was between two and five centimeters. The coiling built up a large mound that blended slowly into the pool of ketchup. When I raised the height of the cup, I expected to see a higher rate of coiling and then a stream that disintegrated before it reached the pool. Instead I found that the coiling was replaced by a crater in the mound. The stream was still continuous.

Ketchup is a type of non-Newtonian fluid in which the viscosity decreases when the fluid is stressed. When the stream fell a considerable distance, its speed near the pool was high. The stress from the impact of the stream on the pool apparently decreased the viscosity of the ketchup in the lower section of the stream and the surrounding mound, with the result that the stream was able to dig out a crater. As the ketchup flowed away from the impact site its viscosity increased and the flow slowed, maintaining the surrounding mound.

I also investigated how a pool in motion might affect the coiling of a viscous fluid. I figured that if the pool were turning, the coiling of a stream would be altered. I mounted a pie pan on an inexpensive record player, fastening the pan to the turntable with tape, and then positioned a paper cup above the center of the turntable. When syrup flowed into the pan from the cup, I turned on the player. With a few tries I made the pan turn in the opposite direction from the coiling of the syrup. I had little control over the speed of the turntable, and so I adjusted the height of the cup to vary the frequency of the coiling. When the frequency matched the rotational frequency of the pan, the coiling stopped. The stream was still buckled just above the pool of syrup, but the shape of the stream was stationary. The result demonstrates Barnes's point that the fluid particles in the stream do not themselves spiral around the central axis of the stream.

Among many other examples of coiling and ribboning of viscous streams, probably the most interesting arises in the preparation of an egg foam for, say, a cake. An egg foam is made from a mixture of egg yolks and sugar, beaten in order to lighten the mixture with air bubbles. The sugar absorbs water from the yolks, making the mixture syrupy and increasing its viscosity. If the mixture is not beaten enough, the yolks are not sufficiently denatured (their proteins are not fully unraveled) or dispersed through the mixture. The product is then a cake tasting like cooked egg. If the mixture is overbeaten, the yolks are denatured too much and the air bubbles are too large. The cake will then feel like cotton candy.

A good cook ascertains when the mixture is properly beaten by doing a simple test. The beater is lifted occasionally from the mixture so that a stream of the fluid flows back into the bowl. When the stream either coils or folds to and fro like a folded ribbon, the beating is complete.

In April I discussed the hydraulic jump, a shock wave in which a fluid switches from supercritical flow to subcritical flow. Wallace B. Riley of San Francisco wrote to me about how a circuit board is soldered with a hydraulic jump of molten solder. Transistors, integrated circuits and other electronic devices are mounted on the top of the board with their leads stuck through holes to the bottom, where interconnecting metallic pathways have been etched. Initially the leads are crimped to hold them in place.

To solder the lead to the interconnecting paths the boards are passed over a 4' wave soldering machine" that consists of a tilted channel down which molten solder flows. Near the bottom of the channel is an obstruction creating a stationary hydraulic jump of solder. The jump extends a bit farther from the channel than the rest of the descending solder. As a circuit board is carried down the channel by a conveyor, it is preheated by the thermal radiation from the hot solder. When it travels over the jump, the bottom of the board is bathed with solder. After the board leaves the channel the solder falls away from all but the leads and the interconnecting metallic paths and cools. The leads and the pathways are then permanently soldered together.

Bibliography

LIQUID ROPE-COIL EFFECT. George Barnes and Richard Woodcock in American Journal of Physics, Vol. 26, No. 4, pages 205-209; April, 1958.

HEIGHT OF FALL VERSUS FREQUENCY IN LIQUID ROPE-COIL EFFECT. George Barnes and James MacKenzie in American Journal of Physics, Vol. 27, No. 2, pages 112-115; February, 1959

INSTABILITY OF JETS, THREADS, AND SHEETS OF VISCOUS FLUID. Geoffrey Ingram Taylor in Scientific Papers of Sir Geoffrey Ingram Taylor, edited by G. K. Batchelor. Cambridge University Press, 1971.

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