Granular Gases Beyond the Dilute Limit

• Dynamics of Sheared Granular Fluid Meheboob Alam In first part of this talk, I will briefly review the dynamics of sheared granular fluid, focusing on instabilities, patterns and bifurcations in plane shear flow. It is shown that a universal criterion holds for the onset of the shear-banding instability (for perturbations having no variation along the stream-wise direction), that lead to shear-band formation along the gradient direction. The same shear-banding criterion appears to hold in other complex fluids as well as in the singular limit of atomistic fluids (i.e. elastic hard-spheres). A weakly nonlinear analysis of the shear-banding instability unveils that the lower branch of the neutral stability curve, that corresponds to dilute flows, is sub-critically unstable. In the presence of gravity, the origin of such shear-banding transition is shown to be tied to the spontaneous symmetry-breaking shear-banding instabilities of the gravity-free uniform shear flow, resulting in universal unfolding of pitchfork bifurcations in gravity-modulated plane shear flow. In the second part of this talk, I will show results from particle simulations of the uniform shear flow of a rough granular fluid. It is shown that the translational and rotational velocities are strongly correlated in direction, but there is no orientational correlation-induced singularity at perfectly smooth (β = -1) and rough (β = 1) limits for elastic collisions (e = 1); both the translational and rotational velocity distribution functions remain close to a Gaussian for these two limiting cases. Away from these two limits, the orientational as well as spatial velocity correlations are responsible for the emergence of nonGaussian high velocity tails. The tails of both distribution functions follow stretched exponentials, with the exponents depending on normal (e) and tangential (β) restitution coefficients. There are sizable micropolar effects (that increase with inelastcity) in the sense that the mean vorticity differs from the spanwise rotational velocity in a shear flow.