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A rheometer was used to study how torque, created by a rotating vane in a bed of 5mm diameter glass beads, can be dramatically reduced when smaller beads are added. This effect is most pronounced when the larger beads are around ten times the size of the smaller beads. Lubrication can be produced for a wide range of bead sizes; beads were used that ranged from 10 to 40% the size of the larger beads. As the beads become closer in size, fewer small beads must be added to create a lubrication effect, but this effect will be less pronounced. Lubrication changes proportionally with torque as the immersion depth of the rotating vane is varied.
An AR2000 Rheometer was used to measure torque, normal force, time, gap, and angular velocity of the rotating vane. A plastic bucket was filled with 4.1 kg of 5mm diameter glass beads and then various amounts of 0.5mm, 0.9mm, and 2mm glass beads were added. No more than two bead sizes were mixed during any given experiment. When adding the smaller beads, I added them all at once around the vane using either 100ml beakers for small amounts, or a flat metal funnel for larger amounts. See Picture 1. When immersion depth increases, torque also increases, and so immersion depth has been held constant for all experiments unless otherwise stated.
Most of the graphs follow a pattern of a sudden drop in torque and then a slow rise. The sudden drop is created when the smaller beads are added, and the rise is created as those small beads sink to the bottom of the bucket and leave the area surrounding the vane. There appears to be an ideal distribution of small and large beads, which allows torque to reach an ultimate minimum. This minimum torque and the corresponding mass of small beads necessary to achieve this torque both depend on bead size. See Figures 1 through 3. When too many 0.5mm or 0.9mm beads are added, the torque eventually reaches its lowest possible value, but this is not true for the 2mm beads. The reasons behind this possibly lie in the distribution of small beads within the 5mm beads. Please see Diagrams 1 and 2.
Figure 4 shows how increasing bead size, increases the time it takes for torque to reach a minimum. Figure 5 shows the ideal distribution for each small bead. The 0.5mm beads lubricate the best, and the 2mm, the worst. It appears that the minimum torque achieved through mixing approaches the torque created by the small beads alone; see Table 1. The larger the immersion depth, the greater the drop in torque, and this drop is proportional to the depth increase. See Figure 6.
When rotating a vane through monodispered granular media, one can dramatically reduce the torque by adding smaller beads. This drop in torque will increase proportionally with toque as immersion depth increases. It will also increase if the small beads are around ten times the size of the large beads. A greater drop might be possible with even smaller beads, but this has not been tested. There exists an ideal amount of small beads, which when added, will lower the torque to approximately the same level as if the bucket were filled with only small beads.
This material is based upon work supported by the Howard Hughes Medical Institute under Grant No.52003727 and by the Jackson Fellowship.
When rotating a vane through a granular mixture, torque can be reduced by adding smaller beads. The drop in torque will be greatest if the smaller beads are about 10 times smaller than the larger beads. If the smaller beads are bigger, they will not be able to reduce the torque as much, but a smaller mass of them will be necessary to produce a drop.
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