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Extended kinetic theory applied to dense, granular, simple shear flows

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Abstract

We apply the extended kinetic theory (EKT) to the dense, simple shear flow of inelastic hard spheres. EKT is a phenomenological extension of kinetic theory which aims at incorporating in the simplest possible way the role of pre-collisional velocity correlations which are likely to occur at a concentration larger than the freezing point. The main effect of that correlation is the decrease in the rate at which fluctuating energy is dissipated in inelastic collisions. We use previously published results of numerical simulations performed using an event-driven algorithm to obtain analytical expressions for the radial distribution function at contact (which diverges at a concentration lower than the value at random close packing for sheared inelastic spheres) and the correlation length (i.e., the decreasing factor of the dissipation rate) at different values of the coefficient of restitution. With those, we show that when the diffusion of fluctuating energy of the particles is negligible, EKT implies that three branches of the analytical relation between the ratio of the shear stress to the pressure and the concentration (granular rheology) exist. Hence, for a certain value of the stress ratio, up to three corresponding values of the concentration are possible, with direct implications on the existence of multiple solutions to steady granular flows.

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  1. Department of Civil and Environmental Engineering, Politecnico di Milano, 20133, Milan, Italy

    Diego Berzi

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Correspondence to Diego Berzi.

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Berzi, D. Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mech 225, 2191–2198 (2014). https://doi.org/10.1007/s00707-014-1125-1

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  • DOI: https://doi.org/10.1007/s00707-014-1125-1

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