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Photo of Sidney Nagel Photo of Heinrich Jaeger Sidney Nagel and Heinrich Jaeger as seen on
Life's Little Questions: Sand to Nuts

Click on Sidney or Heinrich's photo to read a brief bio.

q In answering a question from Dr. Arnie Diamond you said, regarding a container with angled sides, "Thus, the 'Brazil nut effect' can be reversed and larger particles can be moved to the bottom of the container rather than to the top!" I don't believe that is correct.

I believe the factors are: a) amplitudes of vibration b) frequencies of vibration c) waveforms of vibration, sinusoidal, square, whatever d) directions of vibration e) particle sizes f) elasticities of particles and containers In actuality the larger particles can move "to" the bottom only in the sense of "toward" they are really moving "to" a point of random distribution throughout the mixture. Any comments?

A (From Heinrich Jaeger) You are of course right that granular materials respond in very complex ways to vibrations and that, at least in principle, all sorts of details about the type of vibration used could matter. However, it turns out that there are circumstances such as convective flow where only a few parameters appear to be crucial. For example, we found that for convection the applied acceleration (= amplitude times frequency squared) is one of those crucial parameters, rather than amplitude, frequency and waveform separately (I should add that this holds only in the regime where the frequency is smaller than the internal relaxation rate of the material, typically below 100Hz). Furthermore, for convection the waveform does not seem to matter: we found that the behavior did not depend on whether we used vibrations produced by a continuously oscillating shaker, or well-separated individual pulses of the same acceleration.

You point out that the direction of vibration should affect the behavior and that is very much the case. In my response to Dr. Arnie Diamond, I was talking exclusively about vertical vibrations (as shown in the SAF piece). We have also looked into what happens under horizontal vibrations (and Prof. Robert Behringer's group at Duke University has studied simultaneous vertical and horizontal vibrations). While horizontal vibrations still produce convection patterns, the underlying mechanisms are different from those for vertical shaking. Particle size has some influence, but I believe that for convection at least, it is rather inconsequential: during convective flow, large regions of particles move together with the same speed. Having said that, there are regions in the flow field where there are velocity gradients, i.e., neighboring particles move with different velocities. Those gradients lead to shear and shear also can induce particle size and/or shape separation. This would be a mechanism different from the "convection plus trapping" mechanism we find for vertically vibrated systems to be the most dominant for the "Brazil nut effect". The other important aspect with respect to particle size is that for very small particles, say below 0.1mm in size, air trapped in the interstices has a pronounced effect. That's why we typically use larger grains and also evacuate the system to reduce "bubbling" and other effects that stem from the interaction between particles and air flow.

Finally, you mention the elasticity of particles or the container walls. First of all, I assume that you refer to "in-elasticity", i.e., the amount of energy lost in each collision (elastic containers, such as drum heads or membranes lead to completely different patterns, so-called Chladni figures). Again, convection is very robust to changes in this parameter: different kinds of particles lead to the same qualitative behavior. However, friction with the container walls competes with particle-particle friction, and in continuously vibrated systems this interplay can affect the sense of rotation for the convection cells (clockwise vs. counter-clockwise). Specifically with regard to the slanted wall system, it turns out that the angle at which the flow reverses does not depend on the vibration amplitude or frequency (nor on acceleration), but rather appears to be sensitive to the amount of wall friction. For more details I refer you some of our publications on this topic:
J. B. Knight, H. M. Jaeger, and S. Nagel, "Vibration-Induced Size Separation in Granular Media: The Convection Connection," Physical Review Letters, vol. 70, pp. 3728-3731, 1993.

E. E. Ehrichs, H. M. Jaeger, G. S. Karczmar, J. B. Knight, V. Y. Kuperman, and S. R. Nagel, "Granular Convection Observed by Magnetic Resonance Imaging," Science, vol. 267, pp. 1632-1634, 1995.

J. B. Knight, E. E. Ehrichs, V. Y. Kuperman, J. K. Flint, H. M. Jaeger, and S. R. Nagel, "Experimental Study of Granular Convection," Physical Review E, vol. 54, pp. 5726-5738, 1996.

J. B. Knight, "External boundaries and internal shear bands in granular convection," Physical Review E, vol. 55, pp. 6016-6023, 1997.

J. B. Knight, H. M. Jaeger, and S. R. Nagel, "Magnetic Resonance Imaging of Granular Convection," in Advances in Fluidization and Fluid-Particle Systems, vol. 93, AIChE Symposium Series 317, D. King, H. Arastoopour, J. C. Chen, A. W. Weimer, and W.-C. Yang, Eds. New York: American Institute of Chemical Engineers, 1997, pp. 109-112.

There is also a paper by Grossman with extensive simulations on these systems:
E. L. Grossman, "Effects of container geometry on granular convection," Physical Review E, vol. 56, pp. 3290-3300, 1997.

q I enjoyed your segment with Alan Alda and it reminded me of a few thinks I've puzzled over for a long time. I have silver gray hair but when I wash it and as long as it stays wet, it turns nearly black. I assume it has something to do with light transmission but where does the color come from? ML

A (From Heinrich Jaeger) I am intrigued by your observation. I tried it with my hair but could not reproduce a convincing result (maybe it works only with silver grey hair). You may be on the right track, but this is so far off my field of expertise that I really would not want to guess at the reason for the color change.

q I've heard that there is a major problem with burying tires in a land fill because they will eventually rise to the surface. Is this related to your size convection experiments? Thanks for your work.

A (From Heinrich Jaeger) This is the first time I hear about tires rising to the surface in landfills. Without more information I really have no clue about what makes them do that.

q My name is Mike, and I am in the fifth grade. I saw your show. I decided to do my science project on: why does a coffee stain have a ring around it? I have four weeks. I hope you can answer a few questions: I saw your answer that, if you completely cover the drop of coffee except for a small hole in the middle, a ring will not occur, and this shows that the ring is caused by evaporation at the edge. Can you think of other demonstrations that would show that the ring is caused by evaporation at the edge and water flowing to where the coffee evaporated at the edge? Also, what do you think: if the drop of coffee is covered completely except for a small hole at one point on the edge, would a partial ring form at that point? Mike

A (From Sid Nagel) You have suggested a very good experiment! Certainly you should try that. When we did similar experiments we found that, as you suggested, there was a pronounced ring at the drop's edge directly under where we had left a hole in the cover. (Remember that you must have the cover very close to the surface of the drop everywhere else. If you don't there will be evaporation from those points as well.) Another thing that you can do is make drops of different shapes. The stains left can be beautiful with subtle shadings around the perimeter that depend on the local curvature of the contact line. Thus, in a region where the drop has a point there will be a very dark stain. In the same drop, where the curvature is concave (or inward like a cove in a seashore) the stain will be much lighter. This effect can be used to make unusual graphics: If you write the words "COFFEE STAINS" in coffee on a hard surface such as a stiff sheet of plastic (a transparency sheet for example) when it dries it will leave the letters outlined in the stain but with a darkening at the ends of the letters (where the curvature is greatest). You will then have what I call the "coffee stain font"!

q I saw your explanation why the large object floats to the top of a sand pile. I always believed the reason was that at any moment, "holes" are formed by the configuration of the particles. Any particle can fall but only particles that are small enough to fall into any particular random hole that is formed could fall. Since larger objects will always have a lower probability of falling into any random hole, the holes will almost always be filled by the smaller particles. Is there evidence that this theory is incorrect? Dr. Arnie Diamond

A (from Heinrich Jaeger) Your explanation for size separation might work in situations in which there is no granular convection, for example for containers with completely frictionless side walls or deep below the surface of tall containers (where convection is strongly suppressed). On the other hand, when friction with the side walls or other mechanisms set up a convection roll pattern inside the vibrated container, we found that the convective motion immediately takes over as the dominant mechanism for size separation.

You can easily see the crucial role of convection for size separation in the experiments. First of all, by just looking at the overall flow pattern in plexiglass containers like the one filmed for the Scientific American Frontiers show and following the motion of individual particles, the convection rolls can be traced out (we have also used magnetic resonance imaging to trace the flow deep inside of containers). Another indicator is the speed with which larger objects move to the top: convection leads to the same speed for all objects regardless of size and furthermore it leads to a characteristic increase of this speed as the surface of the granular material is approached. Finally, there is a most striking consequence of convection as driving mechanism for size separation: the direction of the flow in a convection roll depends on how far the container walls are angled outward in a V-like fashion. Once the sidewalls are flared out about 10-15 degrees with respect to the vertical, the flow direction will reverse and now particles will move up the sidewalls and down the center. Thus, the "Brazil nut effect" can be reversed and larger particles can be moved to the bottom of the container rather than to the top!

You can find more details on how the sidewall angle affects the convective flow and also on how convection rolls can be established even without sidewall friction in the following paper:
J. B. Knight, "External boundaries and internal shear bands in granular convection," Physical Review E, vol. 55, pp. 6016-6023, 1997.

q Hi, my name is Jessie and I want to get more information on why your research is useful in everyday life. I am using this for my Science Fair project. This is for 6th grade. Thank you. Jessie

A (From Sidney Nagel) The storage and manipulation of granular materials is very important for many aspects of your daily life. For example, if you have a cat or a dog you may be feeding them dry food from a dispenser. This is a large container with a hole at the bottom through which the food flows onto a small tray. If the food were liquid rather than granular, it would all flow out onto the floor. With the granular material, only a little bit flows out at a time so that it just keeps the tray filled. This is because of the way in which granular material flows against a wall. Another example of the properties of these materials that you have seen over and over again is what happens in a grocery store when you try to fill a container with candy, coffee beans or grain. If you overfill the container you often do not need to empty it out but only need to tap it a few times and the material will settle inside it and become more dense so that you can then close the top.

Granular materials also have a very wide range of industrial applications. For example in the pharmaceutical industry, powders must be mixed up to form pills. If the mixing is not complete, then some pills will have a different content than others. This could have a disastrous effect on the patient taking the pills. Factories that are built to handle granular materials are notoriously inefficient as compared to those that deal with liquids. The reason for this is that the granular material does not flow properly from one side of the factory to the other.

q I thought that sand was cubic, not round like in the computer simulation. Is that true? tec_dice

A (From Sidney Nagel) Sand comes in many different shapes and sizes. It depends on how and of what material it was made and how it was treated to get to the beach or the dune. Some sand is very rough indeed whereas other sand is quite spherical. Despite these differences, many of the behaviors that we saw in the show are the same.

There are some beautiful pictures of different kinds of sand, showing their different shapes, in the book: Sand by Raymond Siever published by Scientific American Library (New York, 1988).

q The segment on sand and nuts was very interesting to me because I work with violin varnish. The coffee effect seems to also occur with violin varnish. Color touch-up is done by dissolving the color in the varnish and the applying multiple layers until the area matches the original finish. This becomes a maddening process for many reasons. One thing I have observed is that the varnish tends to do what the coffee does thereby creating a dark ring around the touch up area. Is this, in fact, the same phenomenon? Are there any studies being done to look for ways to minimize the ring around the edge of the drying coffee spill. Have your studies been published in a place that the general public can read your findings? Are there other sources of information available that relate to this topic? James

A (From Sidney Nagel) Ring formation is very ubiquitous and hard to get rid of. One clue to our understanding of how the rings formed came from our observation that we could prevent the ring from forming by covering the drop almost entirely except for a small hole in the center. Under these conditions we did not see a ring at the edge. What happened was that the evaporation of the liquid was forced to occur near the center of the drop. Since no evaporation occurred near the edge there was no replenishing flow from the inside to replace the lost material. With no flows there was no extra material transported to the edge. If you can find a way to cover your varnish except in the middle of the spot this might help. However the varnish will take a much longer time to dry.

q At the edge of the spilled liquid, I believe you said flow stopped at the boundary because of imperfections on the underlying surface. Doesn't surface tension of the liquid have something to do with the flow stopping? Thanks. Bernie

A (From Sidney Nagel) Surface tension is very important for determining the angle at which the liquid surface meets the substrate. For an absolutely clean and smooth substrate, this angle will be determined by a balance of forces, some of which try to extend the drop while others try to make it shrink. The balance is achieved when the liquid has the correct angle. When the surface is rough, this same competition still goes on but on a much more microscopic scale. The balance of the forces can be maintained as the drop shrinks by moving the contact line (where the liquid meets the substrate surface) by only tiny amounts. The angle that is maintained is not the one measured between the liquid and the average substrate but is rather the angle that is measured much more locally at the point of contact. Thus a small movement of the contact line can change the (observed, macroscopic) angle considerably as the point of contact moves over small rough portions of the substrate.

q Why does a cork or a beach ball float? Are the water molecules acting like the poppy seeds in your demonstration? Jim

A (From Sidney Nagel) A beach ball or cork floats because it is lighter than the liquid surrounding it. Similarly a balloon filled with helium gas will rise in air. If the beach ball were heavier than water (for example, if it were filled with a heavy liquid instead of air) it would sink and not float at the surface. The behavior of our granular material is different because the larger particles that rise can be much more dense than the surrounding particles. Thus in the first demonstration shown on Scientific American Frontiers, the steel ball was much heavier than the orange sand around it. It came to the top because of the convection rolls (that is, the large scale flows) that we showed in the poppy seed demonstration.

q Saw your segment Sand to Nuts on SAF - excellent. We are a 30 year old sand collectors society based in CT. We have at present 140 members in 17 countries and many of our members are teachers and professors in various sciences. Many of us work with sand in some way and I found your demos very good. Can you please tell me if any of your demo aids is available for sale? I do a lot of programs with grade schoolers and would love to buy or be able to make some of these materials. If you care to know more about our society, please write to International Sand Collectors Society at Again, great job. Nick D'Errico, Director ISCS

A A: (From Sidney Nagel) We have been aware of your society and would be delighted to learn more about it. As you could see from the show, our demonstrations were very easy to put together and we have not commercialized them. Some we found in toy stores (such as the game "Mikado" with which Alan Alda was playing to show how forces propagate within a granular material.) Others were made by us very cheaply. The bottle that showed the dilatancy (i.e., expansion) of sand whenever it is forced to move, was made from an ordinary laboratory squeeze bottle which we filled three-quarters full with sand and then filled with water so that it just covered the top of the sand. If you don't have a laboratory squeeze bottle you can use a transparent soda pop bottle. You only have to have a small hole in the top (or leave the top loose) to let the air out as you squeeze the bottle. The demonstration showing that the big particles will move to the top due to vertical shaking, was made with a plastic tube approximately one foot long and three quarters inch wide. We filled it three-quarters full with sand (using colored sand from a toy store makes it look more elegant!) and put one large steel ball inside it. If no steel ball is available an ordinary marble will do equally well. We then covered the ends with a thin sheet of plastic and taped it closed with electrical tape (not nearly so elegant). Many other such demonstrations can be made equally easily to show other fascinating behavior of these materials.

(Webmaster's note: Some of the supplies seen on the show are available from Jenike & Johanson.)

q I'm wondering whether your work with particle motion and deposits left by fluids is published somewhere? I'd like more information on this topic to aide my research -- any references would be appreciated. Dave

A (From Sidney Nagel) We have published one paper on this topic and two more have been submitted for publication. The reference for the one already published is:
"Capillary flow as the cause of ring stains from dried liquid drops," R. D. Deegan O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Nature, Volume 389, Pages 827-829 (1997).

A fuller version we hope will be published:
"Contact Line Deposits in an Evaporating Drop," R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Phys. Rev. E (submitted).

An extension of this work was carried out by Robert Deegan who looked at the deposits left on mica where the surface is atomically flat. He found a great array of unusual and beautiful patterns left by the deposits.
Robert D. Deegan, "Deposition at Pinned and Depinned Contact Lines: PatternFormation and Applications," (1998)

q I am working on a pavement design using unbounded aggregate materials. Your demonstration dealing with sand and nuts may have some relevance to my work. Do you have published papers dealing with this experiment? And where might I find them? Thank you. Stephen

A (From Sidney Nagel) We have written a few papers on the convection patterns in a shaken container filled with granular materials. Here are some references:
"Vibration-Induced Size Separation in Granular Media: the Convection Connection," J. B. Knight, H. M. Jaeger and S. R. Nagel, Phys. Rev. Lett. 70, 3728-3731 (1993).

"Granular Convection Observed by Magnetic Resonance Imaging," E. E. Ehrichs, H. M. Jaeger, G. S. Karczmar, J. B. Knight, V. Yu. Kuperman and S. R. Nagel, Science 267, 1632-1634 (1995).

"Experimental Study of Granular Convection," J. B. Knight, E. E. Ehrichs, V. Yu Kuperman, J. K. Flint, H. M. Jaeger, and S. R. Nagel, Phys. Rev. E 54, 5726-5738 (1996).

We have also studied a related issue of how the material becomes denser due to vibrations. The references for that are:
"Density Relaxation in a Vibrated Granular Material," J. B. Knight, C. G. Fandrich, C. N. Lau, H. M. Jaeger and S. R. Nagel, Phys. Rev. E 51, 3957-3963 (1995).

"Reversibility and Irreversibility in the Packing of Vibrated Granular Material," E. R. Nowak, J. B. Knight, M. Povinelli, H. M. Jaeger, and S. R. Nagel, Powder Technology, 94, 79-83, (1997).

"Density Fluctuations in Vibrated Granular Materials," E. R. Nowak, J. B. Knight, E. Ben-Naim, H. M. Jaeger, and S. R. Nagel, Phys. Rev. E 57, 1971-1982 (1998).

q I run a university research laboratory and investigate the physical mechanisms responsible for radar scattering from the ocean surface. I have collected radar images of the Chesapeake Bay outflow plume -- a layer of buoyant, low salinity estuarine water that sits atop the saltier waters of the continental shelf. At the time of maximum ebb tide, my radar images look similar to your "coffee stains", exhibiting sharp frontal boundaries at the interface between the estuarine water and the ambient shelf water. The hydrodynamic picture has current convergence existing at the surface, due to the buoyant flow overtaking the ambient flow, and strong vertical shear beneath the surface, possibly due to a return flow of ambient waters back toward the bay; these effects may conspire to create a region of active wave breaking at the boundary as well as an agitated sea surface in the plume waters near the boundary. My horizontally polarized imaging radar is primarily sensitive to steep and breaking waves and sees a very bright radar echo in a region ~10m wide at the interface as well as a region of enhanced echo extending for several km into the plume side of the boundary. Subjectively, my images look much like your coffee stains! Would you please restate the mechanism by which your stains are formed and comment whether you think a similar process is at work in the outflow plume? (Some hydrodynamicist collaborators at NRL suspect the bright line at the interface is caused by swell propagating in from the sea and steepening to the point of breaking on encountering the plume current; the source of the enhanced echo in the plume adjacent to the interface is an open question at present.) David

A (From Sidney Nagel) The explanation of the coffee ring stain effect was published in: "Capillary flow as the cause of ring stains from dried liquid drops," R. D. Deegan O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Nature, Volume 389, Pages 827-829 (1997).

Since there are figures in that publication it might be a bit clearer than what I can say here in just text so if what I say below is not clear then that might be a good place to look.

The stain is created because the contact line of the drop (where the liquid drop meets the substrate surface) is pinned on the substrate and cannot move even though the liquid is leaving the drop due to evaporation. But liquid will removed from the drop near the contact line because evaporation takes place there at least as rapidly as it does anywhere else on the surface of the drop. If any liquid is removed from the edge of the drop near the contact line, it must be replenished by a flow from the inside of the drop since the contact line cannot move. It is this replenishing flow which brings all of the solute (dissolved coffee particles) to the edge where they are stranded and left as a stain once all the liquid has evaporated.

This effect depends crucially on two processes: evaporation must take place and the contact line must be pinned and unable to move. If one liquid is on top of another liquid, it would be more difficult to keep the contact line stationary in time. However it is not impossible for that to happen. However, it is difficult for me to see how evaporation can play a prominent role in the plume formation that you describe. However, the hydrodynamic flows that occur within the drop due to the outward flow of liquid may have some common features with your problem.

q Regarding the orderly array of spherical particles under the microscope (in a water current); This effect was documented by Kubitschek ("The Array Method of Sizing Monodisperse Particles" in Ultrafine Particles, ed. W.E. Kuhm, Wiley, p.438-454,1963) and has been used for a lot of different applications from particle sizing to actually trapping light photons. Personally, I have done a lot of work with 'array sizing' and am quite used to watching small particles moving around under the microscope. Duke Scientific Corp. produces spherical particles from 20nm to 2mm, and I've measured most of them! Just for your info, looking at coffee in a UV/Vis spectrophotometer is also fun. Ellen

A (From Sidney Nagel) Certainly the uses for colloids and other particles is enormous and the applications are growing at a very rapid rate. The ones you mention are just a few of ways that such materials can be harnessed for exciting applications. Learning how to fabricate and control these particles is one of today's scientific challenges.

q I am working on a project involving the manufacture of toothbrushes. The brush filaments are feed in a walled lane (fiber box) with pressure at the back and filaments (26-400 strands) removed from the front of this pressured column by a method called "picking". We see jamming patterns, etc. in the filament much like the flow of sand. I am convinced I am dealing with a granular flow phenomena. I have an MS in Mechanical Engineering so am able to read and understand complex stress/strain equations, etc. I did find a text discussing Theory of Elasticity application to the extrusion of metals that did explain some of the shear lines we see in the bed as material is removed from the front. Could you point me to some books or other references? Larry

A (From Sidney Nagel) The physics of "jamming" has recently gotten a lot of attention and presently there are attempts to see if many different types of jammed systems (that is, granular materials, traffic, foams, etc.) can be thought of as all being different aspects of the same phenomenon. There was a program on this at the Institute for Theoretical Physics at Santa Barbara in the Autumn of 1997. The talks themselves can be found on the Web. In addition there have been a few papers that I can point you to. However, as you will quickly see this field is still in its infancy and much more work needs to be done in order to gain a better understanding of it. At least some of the important issues are now being addressed.

A very brief review of what important issues are involved in jamming that came out of the Santa Barbara conference and program can be found in:
"Jam Session, Santa Barbara, 1997," S. R. Nagel, Europhysics News 29 #2, 58-59 (March/April 1998).

There is also a News and Views comment in Nature that you might find interesting as well:
"Jamming is not just cool any more," A. J. Liu and S. R. Nagel, Nature 396, 21-22 (1998).


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