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Universality of shear-banding instability and crystallization in sheared granular fluid

Published online by Cambridge University Press:  25 November 2008

MEHEBOOB ALAM ,
PRIYANKA SHUKLA  and
STEFAN LUDING
MEHEBOOB ALAM*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientific ResearchJakkur PO Bangalore 560064, India
PRIYANKA SHUKLA
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientific ResearchJakkur PO Bangalore 560064, India
STEFAN LUDING
Affiliation:
MultiScale Mechanics, Faculty of Science and Technology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier–Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νμ (<νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at νm) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a universal criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower ‘dynamic’ friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 615 , 25 November 2008 , pp. 293 - 321
Copyright
Copyright © Cambridge University Press 2008

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References

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