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Dynamics of sheared inelastic dumbbells

Published online by Cambridge University Press:  16 August 2010

K. ANKI REDDY ,
J. TALBOT  and
V. KUMARAN
K. ANKI REDDY
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
J. TALBOT
Affiliation:
Laboratoire de Physique Théorique de la Matiére Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex, France
V. KUMARAN*
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: kumaran@chemeng.iisc.ernet.in
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Abstract

We study the dynamical properties of the homogeneous shear flow of inelastic dumbbells in two dimensions as a first step towards examining the effect of shape on the properties of flowing granular materials. The dumbbells are modelled as smooth fused disks characterized by the ratio of the distance between centres (L) and the disk diameter (D), with an aspect ratio (L/D) varying between 0 and 1 in our simulations. Area fractions studied are in the range 0.1–0.7, while coefficients of normal restitution (en) from 0.99 to 0.7 are considered. The simulations use a modified form of the event-driven methodology for circular disks. The average orientation is characterized by an order parameter S, which varies between 0 (for a perfectly disordered fluid) and 1 (for a fluid with the axes of all dumbbells in the same direction). We investigate power-law fits of S as a function of (L/D) and (1−en2). There is a gradual increase in ordering as the area fraction is increased, as the aspect ratio is increased or as the coefficient of restitution is decreased. The order parameter has a maximum value of about 0.5 for the highest area fraction and lowest coefficient of restitution considered here. The mean energy of the velocity fluctuations in the flow direction is higher than that in the gradient direction and the rotational energy, though the difference decreases as the area fraction increases, due to the efficient collisional transfer of energy between the three directions. The distributions of the translational and rotational velocities are Gaussian to a very good approximation. The pressure is found to be remarkably independent of the coefficient of restitution. The pressure and dissipation rate show relatively little variation when scaled by the collision frequency for all the area fractions studied here, indicating that the collision frequency determines the momentum transport and energy dissipation, even at the lowest area fractions studied here. The mean angular velocity of the particles is equal to half the vorticity at low area fractions, but the magnitude systematically decreases to less than half the vorticity as the area fraction is increased, even though the stress tensor is symmetric.

JFM classification

Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 475 - 498
Copyright
Copyright © Cambridge University Press 2010

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