Abstract:
We consider collections of spherical frictional particles that roll and slip on a flat substrate. Experiments performed by Painter et al. (Phys. Rev E (2000)) on two particle collisions emphasized the importance of the role played by substrate friction, in particular kinetic friction, on the particle dynamics after collision on a substrate. We present a numerical model which accounts for collisional and surface frictional dissipation and their influence on particle dynamics for a quasi 2-dimensional cooling granular material. We apply this model to a simulation of a granular collider experiment (Painter et al., Physica D (2003)), in which collections of particles collided as they moved radially inward on a substrate. We find the gradual birth and growth of a central cluster for the final state of the particles, dependent upon the number of particles, kinetic frictional dissipation and average initial kinetic energy. For systems where a central cluster is observed in the final state, the autocorrelation function C(r) of the inter-particle spacing fits the Gaussian functional form seen in experiments. We also compute the fluctuation speed distributions which adheres to a Maxwell-Boltzmann distribution for early times, but evolves to a strongly non-Gaussian form as the process evolves. The slipping phase of the motion of the particles is responsible for the high rate of energy dissipation. For example, by decreasing the effect of kinetic friction to unrealistically low values or by discounting the effects of substrate friction, most of the particles escape the system. © 2005 Taylor & Francis Group.
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