Multiscale motion in the shear band of granular couette flow
We probe the nature of slow flow in the shear band of a 2D granular Couette experiment. The experiment consists of an inner shearing wheel, an outer circular boundary, and particles which occupy the space between these two. The mean flow is strictly azimuthal, maximal at the shearing wheel, and decaying roughly exponentially with distance from wheel. In addition to the mean flow and its implied shear, there is also inherently stochastic non-affine motion that is associated with diffusion of the particles and not describable in terms of a smooth deformation. We represent the motion of particles in such small local regions over a short time by the sum of three parts: a mean flow, characterized by the exponential velocity profile; a smooth affine deformation; and a non-affine component. The key observation from this analysis is that each of these components has comparable magnitude. Displacements from mean, affine, and non-affine motion are all described within an O(1) scale factor by the same function of distance from the shearing wheel. The same function also describes the diffusivities determined from variance-vs.-time traces. The non-affine displacements are distributed according to a guassian-like function, except that the exponent is closer to 3/2 rather than 2. © 2009 American Institute of Physics.
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