Universality of shearbanding instability and crystallization in sheared granular fluid
Alam, Meheboob and Shukla, Priyanka and Luding, Stefan (2008) Universality of shearbanding instability and crystallization in sheared granular fluid. Journal of Fluid Mechanics, 615 . pp. 293321. ISSN 00221120

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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–Stokeslevel 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 shearbanding instabilities (for perturbations having no variation along the streamwise direction), that lead to shearband 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 shearbanding instabilities, even though the original dense Enskog model is stable to such shearbanding instabilities. For any constitutive model, the onset of this shearbanding 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 shearinduced 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 viscousdissipation is responsible for the shearbanding state in many complex fluids. 
Item Type:  Article 
Copyright:  © 2008 Cambridge University Press 
Faculty:  Engineering Technology (CTW) 
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Link to this item:  http://purl.utwente.nl/publications/80345 
Official URL:  http://dx.doi.org/10.1017/S0022112008003832 
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Metis ID: 250727