Bose, M. ; Kumaran, V. (2004) Velocity distribution for a twodimensional sheared granular flow Physical Review E, 69 (6). 061301_1061301_16. ISSN 1063651X

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Official URL: http://pre.aps.org/abstract/PRE/v69/i6/e061301
Related URL: http://dx.doi.org/10.1103/PhysRevE.69.061301
Abstract
The velocity distribution for a twodimensional collection of disks of number density n per unit area and radius a in a channel of width L is studied. The particleparticle collisions are considered to be inelastic with a coefficient of restitution e, while the particlewall coefficients of restitution are inelastic with a tangential and normal coefficients of restitution, e_{t} and e_{n}, respectively. The Knudsen number, which is the ratio of the channel width and the mean free path of the particles, is varied from K_{n} « 1 to K_{n} » 1. In the limit of high Knudsen number, the distribution function for the streamwise velocity is bimodal, as predicted by theory [V. Kumaran, J. Fluid Mech., 340, 3l9 (1997)], and the scalings of the moments of the velocity distribution with the Knudsen number are in agreement with the theory. In the low Knudsen number limit, the distribution function for the streamwise velocity is a Gaussian if the coefficient of restitution is close to 1, but assumes the form of a "composite Gaussian" if the coefficient of restitution is not close to 1. The distribution function has a complex structure in the intermediate regime, where there are three maxima in the distribution function near the wall, while the distribution function is bimodal at the center. The granular temperature is accurately predicted by kinetic theory at the center of the channel, but there is dissipation at the wall due to inelastic particlewall collisions, which results in a significant decrease in the temperature even when the coefficient of restitution is 0.9; this finding is in agreement with previous results with bumpy wall boundary conditions and with specular reflection conditions. The slip velocity at the wall has a power law dependence on the Knudsen number, and the exponent in this power law depends on the coefficients of restitution.
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Deposited On:  17 Nov 2010 12:44 
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