Sand goes to center in swirling water. Why?

Discussion in 'Physics & Math' started by Billy T, Jun 10, 2007.

  1. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    Messages:
    23,198
    Why does the more dense matter not "centrifuge" to the outer edge of a flat bottomed container of swirling water? Assume only one spherical particle of sand to keep it simple, unless sand-sand colisons are part of your answer.

    If a sand particle were a sphere with same side towards the container center and near edge, then the part of the sphere most distant from center of container would have lower tangential velocity than the water in contact with that point (and conversely point closest to center, a greater velocity). Thus, sand sphere should tend to spin about it own center so as to reduce these velocity difference. I do not see how or why this would tend to move it towards the center. Can anyone explain why it does so? I am open to suggestions.
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Syzygys As a mother, I am telling you Valued Senior Member

    Messages:
    12,671
    I assume it depends on the speed of spinning. As long as the centripetal force is smaller than the gravitational force, the sand will go to the center. If you increase the spinning, the sand should go to the outer edge after a while...
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    Messages:
    23,198
    I think that true also.
    What '"gravity force" are you speaking of? I stated the container has a flat bottom. Thus, the gravitational potential of the sand does not depend upon its location. The gradient of this potential is zero. Hence the there is no "gravity force" in the radial direction.

    To all: Assume a rotation speed low enough to produce the effect that you can easily produce by hand stirring some some water with a spoon to get it rotating then remove the spoon and watch where the sand goes. - Very simple experiment I do not understand.
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Kubex Isn't personal. Just gravity. Registered Senior Member

    Messages:
    33
    Consider holding a pole at the center with both ends sticking out to your side. You then rotate in a circle. Are the ends of the poles moving at a higher speed in terms of rate than, say, your shoulders? If the same analogy is applied to water versus sand, then dense matter would gravitate toward the center. The speed of the outer edge combats gravity the most, the center the least.

    My question is, would the same occur in an environment where gravity was not?
     
  8. Read-Only Valued Senior Member

    Messages:
    10,296
    I believe it might be the result of a buoyant effect. Although sand is denser that water, the spinning effect on the water may serve as pressure which in turn increases it's density gradient somewhat, pushing the sand toward the center. That's nothing but pure speculation on my part but I cannot think of anything else right at the moment.
     
  9. URI IMU Registered Senior Member

    Messages:
    729
    >> hand stirring some some water with a spoon to get it rotating

    ENERGY in- sand out; system positive acceleration

    >> then remove the spoon and watch where the sand goes

    ENERGY out- sand in; system negative acceleration

    Now you try the experiment with "neutrally buoyant" particles

    and again with floating particles.

    Then consider the energy/fluid flow.

    There is a lot to learn from this experiment. I have studied it and put the principles to good use.

    Basically it demonstrates Newton's bucket in a tea cup (tea leaves instead of sand). Douglas Adams was also interested in this phenomena.
     
  10. Read-Only Valued Senior Member

    Messages:
    10,296
    And now that I've thought about it a bit more I've realized it's exactly the same principle used in industrial "cyclone separators." Material is carried by a draft induced by fans to the inner-edge of a large cylinder and forced to swirl inside. The result is that the air escapes and the heaver material falls out from the precise center of the device.

    They are found in lots of applications. Sawmills, grain/chaff separators (in field combines and mills) and many other places.
     
  11. Vern Registered Senior Member

    Messages:
    695
    I think the key is in the dynamics of the stationary tub and spinning water in it. Spin the whole tub and the effect goes away.
     
  12. Pete It's not rocket surgery Registered Senior Member

    Messages:
    10,167
    That's interesting... have you actually done this?
     
  13. Pete It's not rocket surgery Registered Senior Member

    Messages:
    10,167
    Hmm.... at first I thought that couldn't be right, but now I'm changing my mind.

    I think the key is that the water is deeper on the perimeter. This means that the pressure gradient from center to perimeter is steeper than you would get from centrifugal force alone. Crunching the numbers will be necessary to see if it's enough.

    A spinning fluid makes a paraboloid, right?
     
  14. one_raven God is a Chinese Whisper Valued Senior Member

    Messages:
    13,433
    The water itself pushes toward the center, doesn't it?
    Think of the water as discrete particles, rather than a single "mass".
    What happens to the particles?
    Centripetal force pushes it to the edge of the tub, where it's energy is released (friction), and the lower energy water particles will be pushed toward the top edge of the funnel, then drop and be sucked down into the funnel like a vaccuum.
    Picture what happens when you flush your toilet.
     
  15. (Q) Encephaloid Martini Valued Senior Member

    Messages:
    20,855
    Water is deeper at the outside of the vortex, hence the pressure is higher there forcing the water, and anything carried along, to flow towards the center. Since the water slows down near the center, the sand gets deposited there.
     
  16. Vern Registered Senior Member

    Messages:
    695
    I haven't done the experiment but I suspect it is so. I'm sure engineers who design the cyclone seperators have the math for the mechanism of seperation.
     
  17. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    Messages:
    23,198
    Yes, except for surface tension effects, which try to (and do) make slightly less surface, the water/air interface is a parabola. (There have been several attempts to cheaply make large telescope mirrors by spinning mercury, but as far as I know slight vibrations / waves have caused all to fail to produce image as good as the easy to make spherical surface mirror.)

    Let me try to turn your POV back to the original doubt (and later explain why I in post 1 spoke about the relative velocity at the sand sphere/ water interface as no one has commented on its effects.)

    Lets call the shape of the water air interface P but NOT neglect the very slight surface tension effects that keep P from being an exact paraboloid. On this surface, the centrifugal force is exactly compensated by the component of gravity parallel to the interface and the gradient of the surface tension (if any) so there is no net force causing the water molecules to move either way radially. (If at constant rotation, there were a net radial force with shape P then water mass would move radially to make a "new P shape" so there is no radial force when P is static.)

    Now consider a horizontal plain tangent to the lowest point of the air/water inteface. (Called the highest "fully wet" plain.) In this plain, the is no radial component of gravity (by definition of "horizontal"), but there is a pressure gradient. Roughly speaking, the pressure in this fully wet plain is only 1/4 as great at R/2 as at R, because at the max radius, R, the air/water interface is 4 times higher above this plain than at R/2 and this also matches how the radial centrifugal force varies.* Hence in this plain also there is no net radial force.

    Now consider a second plane d below the first which is parallel the first. Here too the there is no radial net force, but the pressure is not uniform to make this so.
    --------------------
    *Perhaps not exactly true. The centrifugal force and the pressure gradient are both linear functions of radius, but the sand particle is not a point. Thus, the pressure difference across it is not exactly proportional to the radial gradient of the pressure, but a little larger and in the direction to make movement towards the center. I.e. instead of exactly proportional to the pressure gradient, it is the finite difference, not the derivative of the pressure that acts. However, the pressure is not increasing quite as fast as the square of the radius due to surface tension in this highest "fully wet" plain, so the radial derivative of the pressure is slightly less than linear. If the "finite size inward push" is larger than the deviation from linear in the pressure gradient, this could move sufficiently large sand towards the center, but spheres smaller should then go to the outside.

    All of the above discussion has ignored the gross effect that the density of the sand is at least twice that of water, so the centrifugal force is at least twice that on an equal mass of water. Thus, I have not the slightest understanding of this problem. Clearly, if the sand were moved outward by this extra centrifugal force acting (DOING WORK, like gravity on a ball rolling down hill) and an equal volume were pushed (against less than half the centrifugal force) into the space where the sand was, by PART OF THIS WORK, then the system is in a lower energy state, all other things being unchanged.
    ---------------------------------------------
    ---------------------------------------------
    Now lets consider why the sand sphere goes around, at least initially if placed off center:

    As it rubs or rolls on the bottom there is some loss of its kinetic energy, but if the water is streaming by it, there can be a steady state with the sand taking slightly longer to complete a 360 degree circuit than the water (neglecting water's velocity drop to near zero velocity as the distant to the edge of the glass vanishes.) Thus, except very near the side walls of the glass, the water passing between the sand and the wall is passing by the sand grain faster than on the other side of the sand grain. This is like a poorly designed airplane wing and produces slight "lift" radially outward. - Not much help in explaining why the sand grain moves radially inward despite this "lift" force.

    This simple problem has me stumped.
     
    Last edited by a moderator: Jun 10, 2007
  18. iceaura Valued Senior Member

    Messages:
    30,994
    How about: The sand is only moved by fast water - it keeps getting moved until it by chance tumbles into a slow spot, where it settles. The slower the water, the more time the sand spends in that spot.

    Just like dust bunnies always ending up in corners and under the bed. Anywhere else, they get kicked. Once there, they settle. Or eddies in streams - sand piles up in them.
     
  19. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    Messages:
    23,198
    That is at least plausible but without mechanism. Also it ignores the fact that not far from the circular outer wall is the max tangential speed of the water. From that max speed the speed decreases to essentially zero one H2O 'diameter" from the wall. (Probably there is a completely stationary layer several H2O molecules thick bound to the wall because water is highly polar.- Sort of like a curved 2D ionic crystal of "ice" at the wall, I would think.)

    Also ignored in a realistic "spoon stirred" experiment there will be eddy structures in the water so that the zero tangential speed is seldom at exactly r = o but dynamically moving around. If ever the sand is a location other than the exact center of rotation (eddy effects included) then we are stuck with the problem - centrifugal force on it is more than twice that on equal volume of water. Why do they not "trade places"? I.e. why is denser sand not thrown to the outside in a wet centrifuge?
     
  20. iceaura Valued Senior Member

    Messages:
    30,994
    More detail of my proposal: The sand is not being independently moved, but is moved by the water. The water flow is not laminar, but turbulent - rolling and bouncing off the walls. The sand does not move throught water easily - too viscous, at those grain sizes - but rather is carried long in the flow if the flow is fast enough.

    Anywhere near the outside, the sand will be entrained by the water and carried inwards by rolling flow rebounding off the sides. If roiled far enough inwards this entraining water will be slowed by collision, and if slowed enough will drop its load of sediment. Once dropped, the sand will remain until entrained by sufficiently fast moving water - not a common event, near the center.

    The sand will not be dropped from the fast, turbulent flow at the outside. All sand toward the outside will be kept moving, entrained in the water. Only sand near the center can drop out of the water and settle.

    The sand does not require stopped water, only slow water, to settle. The water near the center has a hard time picking up speed, because it will be constantly meeting already accellerated water coming in.

    Is that more clear?
     
  21. Pronatalist Registered Senior Member

    Messages:
    750
    I find it hard to understand all the proposed solutions in the time I have available to ponder them, but I suspect it may be because the water is "more pourable" than sand. Both the sand particles, and the water molecules are drawn by the centripedal force towards the outside of the vortex. But they can't share the same space. So who wins? Who might more quickly squeeze through a crowd? (Assume the crowd to be "ideal" or "friendly" with no "retaliation" for "shoving.") A little skinny guy who can find the voids to shove through, or some big fat guy, who contacts more people, and jams up against them?

    I think I saw something like this, on PBS or American Scientific Frontiers. I think it was a container of vibrating sand, lifting up larger objects towards the top. I'm kind of hazy on what it was and the explanation. Now if the object being lifted up, has a higher density than that of the sand, then "work" is being done, presumably at the expense of the vibration motors, or in damping the vibration to a lower level?
     
  22. spidergoat pubic diorama Valued Senior Member

    Messages:
    54,036
    Imagine a flat bottomed cup of tea. At the bottom there are some tea leaves, which stay there because they are rather heavier than the liquid they have displaced. If the liquid is made to rotate by a spoon, the leaves will soon collect in the center of the bottom of the cup. The explanation of this phenomenon is as follows:- The rotation of the liquid causes a centrifugal force to act on it. This in itself would give rise to no change in the flow of the liquid if the latter rotated like a solid body. But in the neighborhood of the walls of the cup the liquid is restrained by friction, so that the angular velocity with which it circulates is less there than in other places near the center. In particular, the angular velocity of circulation, and therefore the centrifugal force, will be smaller near the bottom than higher up. The result of this will be a circular movement of the liquid of the type illustrated in fig. I. which goes on increasing until, under the influence of ground friction, it becomes stationary. The tea leaves are swept into the center by the circular movement and act as proof of it's existence. The same sort of thing happens with a curving stream...

    Albert Einstein, The Formation of Meanders, from Essays in Science, 1934

    Please Register or Log in to view the hidden image!


    Fig. I.
     
  23. Dinosaur Rational Skeptic Valued Senior Member

    Messages:
    4,885
    If the sand moves toward the center, why do gas centrifuges cause the heavier isotopes to move outward? If you rotate a half full bucket of water, the heavier water moves outward, while the air moves down & inward. If you rotated a bucket containing sand & water, would the sand & air move inward, while the water moved outward? I do not think so.

    Does sand really tend to move toward the center of a less dense rotating fluid? I do not think so. If it does when you stir the mixture, then stirring does not result in rotation of the fluid.

    Suppose you had a closed rotating cylinder containing mostly water, with some oil, and some mercury? I would expect the mercury to move away from the center of rotation and the oil to move toward the center.

    Staying with classical physics: Inertial effects cause an object to maintain its current velocity unless acted on by an external force. A rotating object at any given instant is moving tangentially. The forces causing the rotation apply an acceleration toward the center of rotation, forcing the object to change its velocity. The rotation simulates gravity, so that objects fall away from the center.

    If you rotate a fluid, the effect is to have minimum pressure at the center of rotation and increasing pressure further from the center, resulting in denser objects sinking away from the center. Once again, the rotation mimics gravity: the less dense objects float on the ocean; The less dense objects float toward the center of rotation.

    BTW: Centrifugal force is an illusion. There is no such force related to rotation. There are amusement park rides which spin people. You perceive a force pushing you against the wall of the rotating cylinder. Actually, you are feeling the accelerating force causing you to follow a circular rather than a straight path.

    Your perception of an outward force is an illusion. If you spin a weight on the end of a string, what force is acting on the weight? It is the force you are exerting which is directed toward the center of rotation.
     

Share This Page