Microscopic dissipation in a cohesionless granular jet impact

Abstract

Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. We investigate the continuum limit of an unconfined, dense granular flow. To do this we use as a test system a two-dimensional dense cohesionless granular jet impinging upon a target. We simulate this via a timestep driven hard sphere method, and apply a mean-field theoretical approach to connect the macroscopic flow with the microscopic material parameters of the grains. We observe that the flow separates into a cone with an interior cone angle determined by the conservation of momentum and the dissipation of energy. From the cone angle we extract a dimensionless quantity $A-B$ that characterizes the flow. We find that this quantity depends both on whether or not a deadzone --- a stationary region near the target --- is present, and on the value of the coefficient of dynamic friction. We present a theory for the scaling of $A-B$ with the coefficient of friction that suggests that dissipation is primarily a perturbative effect in this flow, rather than the source of qualitatively different behavior.