Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function ψ(t) decays much faster than t obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of ψ(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter. A significant feature of the dynamics of dense fluids is the effect of correlations on transport coefficients [1, 2]. For a gas of elastic particles in the dilute limit, the transport coefficients are calculated using the molecular chaos approximation [3], that the two-particle velocity distribution is the product of the single particle velocity distribution functions. It is known that this procedure cannot be extended to higher densities due to the effect of correlations. For a D dimensional elastic fluid, the velocity autocorrelation function ψ(t) decays as t, and this power law decay is referred to as the “long time tail” in the velocity autocorrelation function [4]. This was recognized as a consequence of the diffusive transport of momentum proportional to the square of the wave vector in a system in which momentum and energy are conserved. This leads to a divergence of the viscosity in two dimensions. In three dimensions, there is a non-analytic contribution to the shear stress proportional to γ̇ in limit of zero shear rate [1]; this correction is larger than the Burnett terms (proportional to γ̇ in the constitutive relation for the shear stress obtained by the Chapman-Enskog procedure. These correlations have been anticipated to impact (a)Present Address: Chemical Engineering Division, National Chemical Laboratory, Pune 411008 India extention of kinetic theory to dense granular flows since its first application to dilute granular gases, and have been also seen in uniform granular flows [5]. Because dense flows are more prevalent, such observations have led to the belief that kinetic theory approaches are severely limited. However, more recently, it has been speculated that the decay of ψ(t) in sheared granular flows could be faster [6,7]. For a fluid under shear, a steady state can be obtained only when there is an energy dissipation mechanism, since there is a continuous increase in the fluctuating (thermal) energy of the fluid particles, and the rate of increase is equal to the product of the stress and the strain rate. The two most widely studied mechanisms are thermostats (where there is a drag force on the particles) and inelastic collisions. In a sheared elastic fluid in the absence of thermostats, there is a continuous increase in the thermal energy (temperature) of the particles. Due to this, it is not possible to calculate the decay of velocity autocorrelation functions at steady state; the decay of the autocorrelation function will depend both on the initial temperature and the rate of heating, and it will not be invariant with respect to translation in time. The steady state is completely defined only if we specify both the en-