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Newton's Cradle Undone: Experiments and Collision Models for the Normal Collision of Three Solid Spheres

Carly M. Donahue, Christine M. Hrenya, Kenshiro Nakagawa, and Alexandra Zelinskaya. Department of Chemical and Biological Engineering, University of Colorado, UCB 424, Boulder, CO 80309-0424

Molecular dynamics is an essential tool in the field of solid particulate flows. However, the variety of simplified force laws built in to the simulations has not been tested experimentally beyond two-particle collisions. Using an apparatus inspired by Newton's cradle, high-speed photography is utilized to examine the simultaneous, normal collision between three solid spheres. Namely, an initially touching, motionless pair of particles (doublet) is impacted on one end by a third particle. Surprisingly, the impacting particle reverses its direction and separates from the middle particle after collision. This reversal is not observed if the “doublet” particles are separated by a small distance (not in contact) initially, though a separation still occurs between the impacting and middle particle, with both particles traveling in the same direction after collision. In other words, the expected Newton's cradle outcome of a motionless, touching particle pair at the bottom of the pendulum arc is not observed in either case. A subsequent implementation of a variety of hard-sphere and soft-sphere collision models indicate that a three-body (soft-sphere) treatment is essential for predicting the velocity reversal, consistent with the experimental findings. Finally, a direct comparison between model predictions and measurements of post-collisional velocities reveal the relative accuracy of existing collision models for three-body interactions.