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When a sphere moves through a Bingham liquid it moves in an envelope of sheared fluid. The envelope separates the sphere from a rigid solid in which the stress does not exceed the yield stress. At the top and bottom of the sphere regions of solid exist. The fluidity of the material adjacent to the sphere is a result of the stress created by the sphere's weight. The left pictures shows flow fields around a falling sphere that have been proposed by various authors. The shape in b) has been widely accepted by various groups studying this problem experimentally and theoretically. However, at least to my knowledge, there isn't any experimental study that would directly show the shape of the envelope. |
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We try to determine the influence of the walls of cylinders on a moving sphere so that we can estimate the radius of the envelope around the sphere and how the interaction between the envelope and rigid cylinder walls effect the velocity of the sphere. For these studies we constructed a rather simple system. It consists of two pulleys, motion detector, counter weight, brass and steel spheres, and cylinders with different diameters. So instead of dropping the sphere we can pull it and thus control the speed. |
Right now we have only done some preliminary runs to estimate the range of counter weights, tubes sizes, sphere sizes, and Bingham fluid concentrations which would satisfy our needs.
Here is a poster that shows some preliminary results
presented at the Principles of Soft Matter Conference in
Santa Fe, New Mexico, May 2001.
Some basic rheology.
