VICOSITY is the measurable resistance of a fluid to flow. The viscosity of water is fairly low; that of honey and syrup is considerably higher. With most common fluids the viscosity can be altered only by changing the temperature of the fluid. Viscosity is reduced by raising the temperature and increased by lowering it. Such fluids are called Newtonian.

In another class of fluids, called non-Newtonian, the viscosity can be altered by other means, primarily by shearing the fluid as it is stirred, poured or spread. Many household fluids are in this class, and their usefulness depends in large measure on their non-Newtonian character. The behavior of three general types of non-Newtonian fluid is my topic for this month.

In the first type of fluid the viscosity is suddenly changed by the application of a shearing force but immediately retains its normal value when the force is removed. If the shearing causes the viscosity to increase, the fluid is said to be shear-thickening. Common examples include starch solutions, quicksand, wet sand on the beach, some printer's inks and some paints. If the shearing causes the viscosity to decrease, the fluid is called shear-thinning. Mayonnaise and some paints and inks display this behavior. The advantage of shear-thinning is perhaps most apparent in ink. You want the ink in your ball-point pen to flow freely (by being sheared) as you write, but you do not want it to flow when the pen is in your pocket.

The higher the rate is at which a shear-thickening fluid is sheared, the greater the viscosity will be, until finally the fluid may offer tremendous resistance to being moved. This type of behavior was first examined in detail by Osborne Reynolds beginning in 1885, when he explained fluids such as a wet sand mixture that dilates (expands) when it is sheared. Although most shear-thickening fluids appear to be dilatant, the connection is not conclusive. It does, however, provide a simple model to explain the general nature of shear-thickening fluids.

Some years ago Richard E. Berg of the University of Maryland showed me a simple demonstration of Reynolds' model for dilatant fluids. He had me squeeze a 500-milliliter plastic bottle fitted with a stopper and a clear tube at the top. He had partly filled the bottle with sand (you could also use marbles, but the effect is more difficult to see) and then had added water until the water level was in the tube at the top. When I gently squeezed the flexible sides of the bottle, the mixture inside offered considerable resistance. When I suddenly squeezed hard, the resistance was so great that I could not make the bottle collapse significantly. The water level also changed when I squeezed the bottle, but the initial change was not what one would intuitively expect: the water level went down rather than up, dropping several inches in the tube.

Reynolds had explained these features (for sand) by pointing out that at first the grains are packed as closely as they can be, too close to enable the surface tension of the water to pull water into all the space between grains. Berg makes certain of this close packing by tapping the bottle several times. A yielding of the mixture when it is squeezed necessarily means that some of the grains move over one another and so are typically farther away from their neighbors than they were initially. The total volume occupied by the grains therefore increases, leaving enough room between them for water to flow between the grains. Although the sides of the bottle are pushed slightly inward, this flow of water between grains decreases the water level in the container.

Reynolds' model also explained the increase in resistance to squeezing. At the moment of a sudden squeeze and the corresponding dilation the amount of water between the grains is not enough to lubricate the grains that would otherwise slide. Hence a sudden shearing produces additional friction between the grains and an increase in the apparent viscosity of the suspension. The faster the shearing is applied, the faster the grains try to move over one another and out of their closely packed state and the less sufficient the lubrication is. The mixture resists squeezing even more Low shearing rates, on the other hand, allow water to move into the additional space between the grains to keep the friction low.

A similar example can be seen at the seashore. Walk across a stretch of sand that is wet but not so wet that the grains are floating. Your footsteps will look dry and relatively white for a short time, provided you have kept your foot in place briefly. If you leave your foot in place longer, the effect is lost.

In a brief step your weight shears the sand under your foot. Since that sand was already closely packed, it can be moved only if it goes into a less closely packed arrangement. That in turn means it occupies more volume: it expands upward under your step, leaving the water level a small distance below the surface. The surface then looks dry. Eventually the water climbs up through the raised grains and on reaching the surface makes the sand look wet again.

You can easily set up this demonstration in a sandbox. To see the sand be come dry under stress you could lay thick glass plate on the sand and then carefully press down on the plate. I suggest you use a plumber's plunger to push on the glass so that you will not be cut if the glass breaks.

Quicksand is another shear-thickening fluid. A suspension of sand in water is quick when the water is under pressure from a small influx of water below the surface, such as from a natural spring. If the additional water pressure at any depth is equal to or slightly greater than the pressure of the sand at that depth, the sand grains are slightly separated and well lubricated. A heavy object placed on the top will sink to the bottom because of the low friction from the suspension.

If the suspension is rapidly sheared, the viscosity increases because the grains are initially in almost their closest packing and the shearing dilates the body of sand somewhat. As before, a sudden dilation leaves those grains less lubricated and therefore offering more resistance to the shearing. If the object is already submerged, as your leg might be in quicksand, the dilatancy would also press the quicksand more tightly about the object, making its motion even more difficult. Quicksand is not as dangerous when the influx pressure of water is high, because the grains are then well separated and the sand is not dilatant. It may even be washed away by the water current. Sand does not become quick without an influx of water, because any extra water separates out on top of a bed of closely packed sand, creating a situation similar to the ones encountered on the beach and in the demonstration with a bottle.

You can make your own quicksand Fill a large container with sand and set up a garden hose so that it delivers water to the bottom of the container. By appropriately adjusting the water pressure from the hose you can lift the grains slightly to make the sand quick. If the water pressure is too low, a fairly heavy object placed on top of the sand will stay there. When the pressure is sufficient to make the sand quick, the object will slide through the sand to the bottom.

Most people do not know the best way to escape from quicksand. When they are caught in it, they respond by struggling. The more they struggle, however, the more they shear the quicksand and the greater are its dilatancy and apparent viscosity. If you ever step into quicksand, try to move as slowly as you can to free yourself. (Of course, you do not want to move too slowly or this entire argument will become academic.) If you have sunk up to your knees, you should lie down backward on the surface (so as to float), spread your arms and then slowly free your legs. Once they are on the surface, roll or crawl to shore, keeping your weight spread over as much of the surface as possible. If you crawl, you should push back quickly with your hands and feet, so that the shear thickening provides you with a firmer fluid.

The easiest example of a shear-thickening fluid that you can whip up in the kitchen is a simple mixture of water and cornstarch (or any common starch). Add water to the starch until the mixture is somewhat thick. When you pour this mixture or scoop it up with your hand and allow it to run back into the bowl, you will notice that it flows fairly easily and with an apparently low viscosity. Now punch your fist down into the mixture. If the viscosity remained at its previous low value, the mixture would splash all over you. The sudden shearing of the fluid, however, so greatly increases the viscosity that there is virtually no splashing, even if you hit the mixture as hard as you can. There is also little splashing if you hurl some of the fluid at the floor. This mixture is obviously great fun for the children.

If the container is fairly small, you can lift it briefly by inserting a rod into the mixture and then quickly lifting the rod. The rapid shearing increases the viscosity during the lift so that the mixture adheres to the rod.

Theories other than the one involving dilatancy have been advanced to explain shear-thickening fluids composed of suspended particles. One of the theories has the particles rubbing against one another and thereby acquiring electric charge. The increase in the viscosity is then due to the electrical attraction between individual particles.

Some shear-thickening fluids are suspensions or solutions of long-chain molecules (polymers) that are kinked and coiled. When the fluid is put under shear, the molecules are stretched and aligned perpendicular to the direction of flow, thereby increasing the apparent viscosity by inhibiting the flow. The alignment occurs almost immediately, and it disappears almost immediately when the shearing is removed.

More information on the several models of shear-thickening fluids and other non-Newtonian fluids can be found in a series of articles by A. A. Collyer of the Sheffield City Polytechnic in Britain. His publications, which are listed in the bibliography of this issue [bottom], are the source of many of my demonstrations.

Examples of shear-thinning fluids are not as easy to find. Collyer points out that you can make such a fluid by mixing distilled water and polyethylene oxide (often called Polyox, a registered trademark of the Union Carbide Corporation) in a .01 percent solution. ("Percent" refers to the weight of the solute with respect to the weight of the entire solution.) For the demonstrations I shall describe Polyox WSR-301 is best. It is composed of polymers with thousands of CH links and with a very large molecular mass (about four million atomic-mass units). Polyox dissolves slowly in water. Collyer recommends building alternating layers of the Polyox powder and water. For three or four days keep the container covered and occasionally stir the mixture, but do not stir it vigorously or you might rupture the long-chain molecules. (The Union Carbide Corporation has generously given me a supply of Polyox WSR-301. For a small sample of the powder send a mailing label and $2 to cover postage and handling to me at the physics department, Cleveland State University, Cleveland, Ohio 44115.)

The faster a shear-thinning fluid is sheared, the lower its viscosity becomes. Eventually the shearing rate is fast enough so that the viscosity levels off at a low value. As soon as the shearing is removed the viscosity regains its former value. When the fluid is poured, portions of it appear lumpy compared with other portions, apparently because the shearing is nonuniform through the moving fluid and hence the viscosity is nonuniform too.

One explanation for shear-thinning is that under shearing the asymmetric particles or the long molecules in the fluid become aligned parallel to the streamlines and offer less resistance to the flow, the least viscosity resulting when all the particles or molecules are aligned. The degree of alignment depends on the shearing rate, and so therefore does the viscosity of the fluid.

Another class of non-Newtonian fluids is quite similar to the class of shear-thinning and shear-thickening ones except that the viscosity depends not only on the rate of shearing but also on how long the shearing has been applied. Once the shearing is removed measurable amount of time is needed for the viscosity to regain its initial value. These fluids are therefore time-dependent.

If the viscosity decreases with shearing, the fluid is said to be thixotropic; if the viscosity increases, the fluid is negatively thixotropic. Examples of the latter are few, but thixotropic fluids include margarine, some paints (such as one-coat paints), shaving cream and catsup. Margarine, for example, has a fairly high viscosity that is decreased when it is sheared across toast. If it did not behave this way, it would be more difficult to spread.

No one theory explains the change in viscosity of all thixotropic fluids. If the fluid consists of asymmetric molecules or particles, the viscosity may be decreased when they become aligned parallel to the streamlines of the sheared fluid. This model would differ from the one for shear-thinning fluids only because the bonds between molecules or particles would take longer to break or because the strength of the bonds would vary through the fluid.

For suspensions of particles of such substances as clay other theories are favored. The initial structure before shearing could be considered a gel in which the suspended particles are held in place by an ordered structure, by electrical forces between particles or by water lying between the particles. Under shearing the gel is transformed to a sol (a less solid colloidal fluid) as one of these structures is destroyed. If the thixotropic fluid is composed of polymers, one again considers alignment along the streamlines as being responsible for the change in viscosity. In addition the shearing may uncoil, disentangle and stretch the polymers to decrease the viscosity. Negative thixotropic fluids might be explained with a model in which the number of intermolecular bonds increases in the course of the motion. Therefore the viscosity would increase as the fluid began to gel.

Catsup can give you experience with a thixotropic fluid. If it is stirred or mixed for a few minutes, its viscosity decreases; eventually the substance becomes runny. You may have noticed this effect if you have poured catsup from a bottle just after someone has shaken it vigorously.

I tested the thixotropic nature of catsup with a simple arrangement, filling a beaker with it, allowing the fluid to stand for five minutes and then dropping small steel balls into it and timing their fall to the bottom. Since I could not see through the catsup, I put the beaker on a plastic sheet laid on a ring stand. By looking up through the plastic I could see the balls when they reached the bottom. I allowed five minutes between each fall.

After timing five falls I changed the arrangement by stirring the catsup for one minute just before each fall. The average time with no stirring was 27 seconds; with stirring it was 13 seconds. The stirring did decrease the viscosity of the catsup and the viscosity of undisturbed fluid was not regained until several minutes after the stirring had been stopped.

The third general class of non-Newtonian fluids I shall discuss includes fluids that are elastic in addition to being fairly viscous. Examples are silicone putty, STP Oil Treatment, some condensed soups, some motor oils and the thick portion of egg white. In general the elasticity is due to the coiling of the polymers in the fluid. Shearing and stress can compress or extend these long-chain molecules, which then behave somewhat like springs.

Silicone putty, which is such a viscoelastic fluid, is derived from dimethyl silicone oil. (A laboratory procedure for its preparation was published in Journal of Chemical Education, Vol. 50, 1973, page 434. One type of silicone putty is sold as Silly Putty.) This substance has three interesting ranges of stress and shearing. If you shear it slowly, the putty flows like a highly viscous fluid. For example, if you suspend it from a rod, it will slowly droop downward. A somewhat faster shearing, however, causes the putty to behave like a rubber ball. Roll a ball of the putty and bounce it on the floor; its elastic recovery is fairly high. With even faster shearing the putty has almost no elasticity. If you suddenly pull on a piece, it fractures much as a metal rod does when it is stretched under tremendous strain.

By stuffing a quantity of silicone putty into a tube and pushing it through the tube you can display another interesting feature of certain elastic liquids. When the putty emerges at the other end of the tube, it expands in what is called die swell. This expansion is a nuisance in the manufacture of synthetic fibers, which also exhibit die swell when they are being spun from an orifice, because the orifice must be designed to allow for die swell in order to give the fiber the desired size and shape. Die swell can also be demonstrated with a Polyox solution of about 1 percent concentration.

The swelling appears to be a sudden recoiling against the shearing and stress of the fluid when it is being forced through the tube and the exit opening. In the tube the long-chain molecules are contracted because of the forcing. When they emerge from the tube, they suddenly expand to relieve the internal stress. If you leave the putty in the tube for a while before pushing it on through the opening, it does not expand as much. Apparently under those circumstances the stress is relieved in some other way.

Elastic recoil can also be seen in stirred solutions of Polyox and in certain condensed soups. For the Polyox, Collyer recommends a 2.5 percent solution. I tried a diluted solution of Campbell's tomato soup, following a suggestion by Peter Murphy of Centre College in Kentucky, who first pointed out the effect to me. Add one can of water to one can of condensed soup. Smoothly stir the solution with a spoon and then remove the spoon. Just as the swirling is about to die out, the direction of swirling reverses. The reversal is a recoil against the stresses and shearing that the swirling has set up in the elastic fluid.

Some elastic fluids can siphon themselves out of a beaker once you initiate a falling stream. For this demonstration Collyer recommends a Polyox solution of .8 percent. The fluid is elastic enough so that once you have a long length of it hanging from the lip of an elevated beaker, the falling length will pull more of the fluid from the beaker up to the lip and then over the side. You can reverse the direction of flow by decreasing the length of the hanging fluid. For example, allow the falling fluid to collect in another beaker and then slowly raise the second beaker to decrease the length of the fluid falling between the two.

You can see a similar climbing tendency if you suck Polyox from a beaker into a hypodermic syringe. First dip the syringe into the fluid surface and then, as you slowly pull back on the plunger, lift the syringe. The fluid continues to be drawn into the syringe even when you have raised the needle from five to 10 centimeters above the Polyox surface in the beaker. The fluid moves along that surface, reaches the thin stream to the syringe, climbs it and enters the syringe.

A stream of a 2.5 percent Polyox solution can be cut with a pair of scissors. Coat the scissors with Vaseline to eliminate sticking and then cut the stream a few centimeters below the lip of the beaker from which it is being poured. Once the cut is made, the top portion of the stream recoils upward and back into the beaker.

This effect can also be demonstrated conveniently with Slime, a new toy from the Mattel Corporation. It is a green viscoelastic fluid that displays die swell, self-siphoning, the ability to be cut and elastic recoil. It is somewhat like Silly Putty in that it has three distinct types of response to shearing and stressing. Slow shearing enables it to flow like a highly viscous fluid. After somewhat faster shearing it recoils like a rubber surface. Fast shearing causes it to fracture.

You can demonstrate two of these responses by dropping a steel ball onto the surface of Slime. The ball penetrates the surface slightly, causing the surface to oscillate as a rubber surface would. Then the ball slowly sinks into the surface and to the bottom of the Slime. Slime, which is available in most toy stores, is probably a polymer solution much like a Polyox solution. (A similar fluid called Super Liquid is available from the Edmund Scientific Company, 7875 Edscorp Building, Barrington, N.J. 08007.) The fluid is an almost irresistible toy for children and adults alike, partly because the feel and behavior of a viscoelastic fluid are so different from the feel and behavior one associates with an ordinary fluid.

To me one of the strangest effects of some of the elastic fluids is their behavior when they are stirred with a central rotating rod. Centrifugal force would cause a normal fluid stirred in that manner to form a concave surface with its lowest point in the center of the container. When an appropriate elastic fluid is stirred in this way, it does just the opposite: it moves to the center and climbs the rod in what is called the Weissenberg effect (after K. Weissenberg, who studied the phenomenon in the 1940's). Several fluids display this behavior: gelatin, some condensed milks, certain types of honey such as heather honey, STP Oil Treatment, some types of oils, Polyox and the thick portion of egg white. For Polyox, Collyer recommends a 2.5 percent solution.

The demonstration with gelatin was described in this department in January, 1965. After the gelatin was mixed with hot water at about 130 degrees Fahrenheit, it was Newtonian until it had cooled to 86 degrees. From then until the gel point of 82 degrees was reached the mixture's climbing tendency increased as the temperature decreased.

Why does a viscoelastic fluid behave so strangely? When it is sheared in one direction, its structure causes additional forces to arise perpendicularly. In the Weissenberg effect the shearing set up by the turning rod creates a force radially inward toward the rod, pushing the fluid to and then up the rod. The greater the shearing rate is, the stronger the radially inward force is and the higher the fluid climbs. You can consider the surface as being a system of concentric elastic bands. When the bands turn at different speeds because of the fluid's viscosity, they create shearing forces between themselves, which in turn create the radial forces that attempt to make the elastic bands contract toward the center.

The same results are obtained if the rod does not rotate but the container does. Again shearing around the central rod forces fluid inward. If the rod is replaced by a hollow tube, the fluid will climb up through the tube; the faster the container is rotated, the higher the fluid climbs. A row of tubes placed across the diameter of the fluid surface clearly shows the climbing tendency: the climbing heights increase from the tube at the rim to the tube at the center. This effect is best seen if the tubes are under partial vacuum. In certain circumstances the central object can be a flat disk held by a central rod from the top. If the disk is first lowered to the surface of the rotating fluid and then slowly lifted, it can draw the fluid up under itself.

Writing in Journal of Fluid Mechanics, Gordon S. Beavers and Daniel D. Joseph of the University of Minnesota recently reported obtaining the Weissenberg effect in STP Oil Treatment in a novel way. Several centimeters of the liquid were floated on a deeper layer of water, and a central rotating rod stirred both layers. The STP fluid is viscoelastic and normally displays the Weissenberg effect, but in addition to climbing up the rod into the air it also climbed down the rod into the water. Since gravity aids in pulling the STP fluid downward, the downward bulge around the rod was more pronounced than the upward bulge. If the water were replaced by a fluid with a density closer to that of STP, the downward bulge would turn out to be even larger.

If you would like to produce the Weissenberg effect, you might use a mixing bowl mounted on a turntable. You could also mount a small container on an inverted hand drill as was described in this department in the 1965 article on the Weissenberg effect in gelatin. If you prefer a central rotating rod, you could use a rod clamped into a power drill, but you should be careful not to shatter the container or splash liquid into the motor of the drill. Such a mishap could cause serious injury or even death.

I worked with a common kitchen mixer that had a variable speed control. With a hacksaw I removed the blades from a beater so that only the central rod remained. I smoothed the rod with a file. After stripping the other beater in a similar way, I glued a flat disk to the end of the beater so that I could try the disk demonstration. To control the speed better I plugged the mixer into a variable voltage control so that I could easily change the voltage to the mixer, but because this procedure might damage some mixers I would not recommend it in general.

I had little luck with Borden Eagle Brand condensed milk (which showed a small climb), Carnation evaporated milk (no climb) and partly diluted Campbell's condensed tomato soup (small climb). Egg white, however, gave a noticeable climb at the highest speed of the mixer. (Separating the egg white from the yolk is easy with an egg separator commonly sold in kitchen-supply stores.) STP worked well, climbing both up and down in the arrangement reported by Beavers and Joseph. At the highest speed of my mixer the climb into the air was about a centimeter.

In studying the Weissenberg effect you might like to try other common fluids such as different grades of motor oil and different types of elastic fluids such as honey. Different fluids could also be substituted for STP and oil in the climbing demonstration. You might correlate the depth of the downward climbing with the difference in the density of the two fluids. A third fluid (instead of air) could be added on top. In any of the Weissenberg demonstrations it would be interesting to plot the climbing height against the rotational speed and concentration of the fluid.

In 1963 A. Kaye, who is now with the Institute of Science and Technology in Manchester, noticed that when a viscoelastic solution of polyisobutylene in dekalin is poured from a height of 25 centimeters into a dish of the fluid, a thin stream occasionally leaps upward from the point of impact. This effect, now named after Kaye, operates as follows. The falling stream first creates a small heap of fluid at the point of impact. Soon a thin stream develops and flows outward from the heap in a low trajectory, eventually collapsing. Why the fluid leaps in this way was not initially understood.

Recently Collyer and P. J. Fisher pointed out that the leaping stream is actually a loop of the fluid. After examining high-speed motion pictures of the leap in order to slow down the motion they were able to propose an explanation for the Kaye effect. Because the fluid in the initial heap is moving slowly its viscosity is fairly high and the heap is therefore quite rigid. As the fluid in the stream falls its shearing rate is low and its viscosity is high. On impact, however, the shearing rate suddenly increases and the elastic fluid thins enough by shearing so that it can bounce upward from the rigid surface of the heap.

Collyer recommends mixing the polyisobutylene into the dekalin by chopping the polyisobutylene into small pieces before adding it to the liquid. Afterward the mixture must be left covered for about three weeks to complete the mixing. Collyer has written me that the Kaye effect can be demonstrated more conveniently with some types of hair shampoo, although the leaping may not be as pronounced. I tried Prell Concentrate (both in the concentrated form and in a diluted version) and Gold Circle baby shampoo. The Prell gave no effect but the Gold Circle gave occasional leaps of two or three centimeters.

The leaps last about a second, so that you must watch for them carefully or make high-speed photographs of them. To generate the leaps you should adjust the height of the shampoo container so that the stream pouring out of it is fairly narrow. Within a certain critical range of fall the stream will leap for you.

Bibliography

DEMONSTRATIONS WITH VISCOELASTIC LIQUIDS. A. A. Collyer in Physics Education, Vol. 8, No. 2, pages 111-116; March, 1973.

TIME INDEPENDENT FLUIDS. A. A. Collyer in Physics Education, Vol. 8, No. 5, pages 333-338; July, 1973.

TIME DEPENDENT FLUTDS. A. A. Collyer in Physics Education, Vol. 9, No. 1, pages 38-44; January, 1974.

VISCOELASTIC FLUIDS. A. A. Collyer in Physics Education, Vol. 9, No. 5, pages 313-321; July, 1974.

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