MIXING A BROWN POWDER (Nestea) and an orange one (Tang) in order to prepare a drink called Russian tea, Geoffrey Bate of the Verbatim Corporation in Sunnyvale, Calif., noticed something strange. Although he shook the powders vigorously, they would not mix uniformly. Islands of orange persisted in the pool of brown. Why so? One answer that comes to mind is that an electrostatic separation arises because the grains of powder acquire a charge when they are shaken. Another answer is that the grains of one powder may be slightly smaller than the grains of the other so that they tend to settle differently.

Bate took the matter up with A. D. Moore of the University of Michigan, who among other things is an expert on electrostatics. He said that any electric charge created by the shaking would be too weak to separate such large aggregations of powder. Moreover, an electrostatic separation would be unlikely to form neat piles. Moore concluded that the separation must arise because of a difference in the mechanical properties of the grains.

Putting the powders in a clear beaker, which enabled me to see what was happening at the bottom surface as well as the top one, I did a bit of exploring. With about half a centimeter of Nestea in the beaker I began adding teaspoons of Tang. The Tang remained on top of the Nestea until I gently shook the beaker. With each shake a certain amount of Tang sank into the Nestea. If there was only a little Tang, it soon disappeared. When the amount of Tang began to build up, each shake sank some of the freshly added powder and also exposed islands of what I had put in earlier.

Through the bottom of the beaker I could see the size of the orange area increase as I shook in more Tang. Apparently the powder was migrating to the bottom of the beaker. If I shook the beaker vigorously or even just tilted it a bit, pockets of the sunken Tang were exposed on the top surface. Since the grains of Tang were noticeably smaller than the grains of Nestea, it seemed evident that shaking made individual grains of Tang gradually fall between grains of Nestea.

As a further test I poured everything into a mortar and ground the mixture to a more uniform grain size with a pestle. Returning the powders to the beaker and shaking it, I found no islands of color. The powders mixed evenly because the grains were fairly uniform in size.

To make sure that the islands in the original mixture did not result from some peculiarity in my method of shaking I rigged an audio oscillator to drive a loudspeaker that would shake the powders in a consistent way. The signal from the oscillator was fed through an amplifier and then to the speaker, which was on a table and pointed upward. To the top of the speaker I firmly taped the bottom half of a metal container made to hold motion-picture film. I poured in a small pile of Nestea and over it a layer of Tang. With the oscillator generating a sinusoidal signal at a frequency of 64 hertz I gradually increased the amplitude of the amplifier until the powder began to move. The Tang almost immediately sank into the Nestea.

Grains isolated from the main pile vibrated vigorously and gradually moved to the rim of the container, where the

vibration set up by the speaker was at a minimum. This motion was easy to understand. The vertical oscillations of the container tossed the grains upward and slightly to the side. Eventually the center of the plate, where the oscillation was at its most vigorous, had tossed away all its grains. They naturally collected in the area where the oscillation was weakest.

When the entire plate was vibrating only feebly, the pile of powder barely moved. With a somewhat stronger vibration it began to migrate as a body toward the rim. At the maximum vibration the pile disintegrated into individual grains that migrated to the rim.

The tendency of the pile to migrate intact when the vibration was of medium intensity surprised me until I realized the weight of the pile reduced the vibration in that area. Instead of being shaken into individual grains the pile was lifted as a whole. The-greater strength of the vibration near the center of the container gradually moved the pile toward the rim.

My arrangement for making the powders vibrate is based on a classic demonstration first given by Ernst F. F. Chladni in 1787. He showed that when a flat plate vibrates, grains of sand sprinkled on it gradually collect at nodes, that is, places with little or no vibration. The patterns, which are now called Chladni patterns, reveal the vibrational characteristics of the plate by marking the nodes. The absence of sand (or powder) shows the antinodes, where the vibration is strongest.

When Chladni replaced his sand with a finer material such as lycopodium powder, he discovered that vibration moved the powder to the antinodes. If he put both sand and lycopodium powder on the plate and set up vibrations, the sand went one way and the powder went the other. Why do large grains shift to the nodes and smaller ones to the antinodes? The classic explanation is that gentle currents of air above the vibrating plate catch the fine powder once it is airborne and gradually carry it to the antinodes. I shall return to this point.

When I went on to see how Nestea and Tang compared with sand on my vibrating-plate apparatus, I encountered several oddities. The first appeared when I poured a pile of Tang on the plate in order to examine how it was affected by changes in the amplitude of vibration. As I turned up the amplitude the pile suddenly pulled in at the base and rose at the top. Individual grains came loose from the top and rolled down the sides. It looked to me as though they reentered the pile at the bottom.

I was astounded. An inert pile of orange powder had become animated. The Tang was circulating, apparently moving along the bottom of the pile toward the center, then rising to the top and finally rolling down the sides to begin the circuit again.

To follow the internal circulation I added a bit of purple Tang as a tracer. Piling the purple powder at the center of the plate and covering the pile with a larger amount of orange powder, I turned up the vibrational amplitude past the point at which internal circulation could be expected. Soon purple grains began to emerge from the top of the pile, near the center; they rolled down the sides of the pile and slowly disappeared into the base.

Trying lycopodium powder on my apparatus (baking powder would do), I again found a threshold above which the pile began to shrink at the base and rise at the center. The internal circulation looked livelier than it had with Tang. I tested the circulation by burying a few grains of purple Tang near the top of the pile. Again they worked their way to the top of the pile and fell down the sides. If I made a pile of lycopodium powder vibrate mildly, patterns appeared on top of it. Complex waves formed there and moved down the pile. They appeared to be moving slower than the individual grains that rolled down the sides. Sometimes I could make out what happened as a ridge went down the sides. Falling powder built up the ridge until it was too heavy for the powder lower down the slope to support it. Then the lower powder slid down en masse for a short distance, like an avalanche, and the ridge was reinstated there. This sequence continued until the ridge reached the base of the pile.

Occasionally I was able to create stationary patterns on the pile. Lines running from the top to the base appeared to be

formed of powder constantly sliding down. Between them were depressed areas where little movement of powder was visible. Sometimes individual waves traveled up the sides of the pile. This remarkable motion depended on careful adjustment of the vibrational amplitude. A slight increase beyond that level of vibration sent waves of small avalanches down the sides.

I touched the top of a circulating pile of lycopodium powder lightly with the edge of a spoon. Little vibration could be felt, which suggested that the pile was loosely structured close to the top. With a pile of Tang I felt considerably more vibration. The pile was much firmer to the touch but was still loosely structured near the top.

Working again with Tang on top of Nestea, I found that vibration made the former sink into the latter, but I also saw that the internal circulation soon caused grains of Nestea to emerge from the top of the pile. The larger grains usually shook erratically and then fell a slight distance down the sides, where the process was repeated. The large grains that reached the base became separated from the pile; only the finer ones could reenter. Since the grains of Nestea were typically larger than the grains of Tang, a slight segregation of the powders developed at the base of the pile.

I tried blowing gently down on the powder, thinking it would spread out uniformly toward the rim of the container. Instead I saw a bare region in the center and then bands of color: orange and then a separate brown ring that seemed to be slightly higher. Apparently the particles of Nestea were being bounced higher than the particles of Tang, and my breath carried them farther from the center.

With powder spread fairly uniformly in the container I stepped up the level of vibration, largely just to see the grains dance. To my surprise I reached a threshold where small mounds of fine powder rose and began migrating on the plate like amoebas, often fusing when I they met and occasionally fissioning. At a slightly lower level of vibration they dropped in place; only the larger grains kept bouncing.

I tried the same thing with lycopodium powder and found that many mounds developed. Apparently this is the response of fine powder to intense vibration. The mounds were soft to the touch of a spoon, indicating that they were not solid.

One surprise was still to come. Wanting to see if a barrier on the bottom of the container would alter the flow of powder, I made a hill with modeling clay. I had to clean the metal thoroughly to make sure that the clay would stick to it when the vibrations began. The hill was about one and a half centimeters high and roughly symmetrical; it stood at the center of the plate.

I distributed lycopodium powder around the hill and turned up the vibration to the amplitude that made the powder begin to shake. As before the layers of powder shrank at the base and rose in height. They also began climbing the hill. By increasing the vibrational level more I could make the powder climb to the top of the hill. I could hardly believe my eyes.

Soon so much powder had reached the top that it fell down one side and pooled at the base. It then circulated around the base and eventually began to climb again. Sometimes a notably wide stream climbed on one side and descended on another in a continuous flow. Powder routinely climbed slopes of 45 degrees and occasionally went up even steeper ones.

Is this phenomenon caused by currents of air set up by the vibrating plate and clay? Apparently not. I held the edge of a table knife above a moving stream to block any air current. The knife had no effect unless it actually touched the vibrating particles in the stream.

The powder climbs well at oscillation frequencies below 100 hertz; 60 or thereabouts is best. As I increased the amplitude

of the vibration I could see the pile of powder at the base of the hill lift up. A dark line seemed to be visible between the powder and the clay, but it was an illusion resulting from the fact that both powder and clay were oscillating in and out of that region. At the upper end of a climbing stream powder was being thrown upward on the slope until enough had accumulated to start a downward avalanche.

Perhaps the powder climbed the hill only because the vibrations tended to move it toward the center of the plate. To check this possibility I reshaped the clay into two hills adjacent to the center of the container. Powder placed in the valley between them moved away from the center and up each hill.

Next I made a ring of clay surrounding a valley at the center of the plate. I put a mixture of Nestea, Tang and lycopodium powder in the valley. When I increased the vibration until the lycopodium began to move, it mounted the ridge while the other powders stayed in the valley. I had supposed that if the lycopodium could climb hills, the other powders could too at a sufficient amplitude of vibration.

I believe the key difference in the climbing properties of the powders is that lycopodium powder is notably cohesive. The mechanism of climbing appears to be that an upward movement of the, vibrating clay throws a few grains at a given spot slightly up the incline. More precisely, the clay surface moves upward, pushing against the layer of powder lying on it and expanding the powder into a less dense concentration. In this condition the layer of powder closest to the surface can slip upward along the bottom of the layer to which it would normally cohere. When the clay descends in the second phase of a vibrational cycle, the rest of the pool of powder falls back on it. The action is repeated with each cycle, a fresh slippage layer being tossed up the slope by each upward vibration. Eventually some of the material tossed upward slides back down over the top of the stream, reaches the lower end and is carried back under the stream. Even in a stream that is.. standing on a slope too steep to climb, material is always circulating up the slope along the bottom of the stream and down along the top.

The climbing of a slope depends critically on the adhesion to the surface of the grains that are tossed uphill. Cohesion is another important factor. As additional powder is tossed up to a section of the slope already holding grains from an earlier toss some of the fresh powder remains in place because it adheres to the clay and coheres with other grains. Tang and Nestea do not climb because they do not have enough adhesion and cohesion. If I ground one of them into a finer powder, it did climb slopes.

I could make a large grain climb a hill of lycopodium powder. At a mild level of vibration a grain of purple Tang moved up the slope in a series of hops. After each hop it returned to the lycopodium, making a small crater that held it until the next hop.

This last set of observations provided the key that enabled me to understand why individual grains in an oscillating pile move toward the center rather than in some other direction. The entire pile is tossed upward simultaneously and uniformly by a vibrating plate. The density of concentration of the grains decreases, becoming least at the surface and greatest at the bottom.

In the bottom illustration at the left a broken line marks the imaginary contour of grains at a particular concentration. Above the boundary the concentration is lower, below the boundary it is higher. Consider a grain just above the boundary. In an upward movement of the plate the grain is tossed slightly up the slope of the boundary. In the next part of the cycle the grain and the pile come down again. One might expect the grain to slide down the boundary at least as far as it had moved up, but friction with other grains moderates the slide. The grain therefore achieves a net motion up the boundary with each toss.

Each grain in the pile can be regarded as lying on such a boundary. In each upward vibration a grain is moved up the boundary because the concentration of grains is lower above the boundary than it is below it. The net movement of the material in the pile is therefore toward the center and the top.

After I had worked out this explanation I discovered that Michael Faraday, who is best known for his studies of electromagnetism, had published in 1831 a similar set of observations with a different explanation. He noticed that lycopodium powder sprinkled on a vibrating plate gathered into small humps showing an internal circulation. His explanation focused on the flow of air set up by the motion of the plate.

According to this view, an upward vibration lifts the pile and allows air to flow under the base of it, bringing in fresh powder from the perimeter. The amount of material in the pile therefore grows. If air flows under the lifted pile, however, it surely must flow out again as the pile comes down. The model also fails to explain the movement that I observed with tracers (upward in the pile out at the top and then down a side).

Why is a vibrational frequency of about 60 hertz optimal for internal circulation? The answer is found in work done by R. A. Bagnold, a British petroleum engineer, on the movement of grains. If the plate vibrates too frequently, the lifted pile never gets fully back down before the next vibration. Instead it remains more or less stationary in the air while the plate beats on its bottom surface. On the other hand, the vibrational frequency must be high enough to set the grains in motion.

In April I described certain entoptic phenomena, meaning things that are seen even though they originate within the eye. I said the "floaters" included among the phenomena are due entirely to blood cells released by the retina. Several people who are professionals concerned with vision have written to say that although floaters occasionally originate with blood cells, they are more often bits of the vitreous humor that have come loose and are floating in the watery layer in front of the fovea.

Bibliography

SOUND. Arthur T. Jones. D. Van Nostrand Company, Inc., 1937.

THE SHEARING AND DILATATION OF DRY SAND AND "SINGING" MECHANISM. R. A. Bagnold in Proceedings of the Royal Society of London, Vol. A295, pages 219-232; 1966.

CHLADNI'S LAW FOR VIBRATING PLATES. Thomas D. Rossing in American Journal of Physics, Vol. 50, pages 271-274; 1982.

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