Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2008-11-15
Journal of Fluid Mechanics (2008), vol. 615, pp. 293-321
Physics
Condensed Matter
Soft Condensed Matter
26 pages
Scientific paper
10.1017/S0022112008003832
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 $\nu_{m}$) and the shear viscosity is allowed to diverge at a density $\nu_\mu$ ($< \nu_{m}$), with all other transport coefficients diverging at $\nu_{m}$. 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 $\nu_m$) 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 {\it 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.
Alam Meheboob
Luding Stefan
Shukla Priyanka
No associations
LandOfFree
Universality of shear-banding instability and crystallization in sheared granular fluid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Universality of shear-banding instability and crystallization in sheared granular fluid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universality of shear-banding instability and crystallization in sheared granular fluid will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-39210