The effect of elastic vibrations on collisions of fine powder with walls


Particles of granular gases are macroscopic bodies which allow us for a continuum description of their behavior. Their trajectories are often approximated by the quasi-static motion in which their static forces are given by contact theories (e.g. Hertzian [1]). Elastic vibrations of granular particles are usually ignored because their effect on particles' trajectory is so small for collisions of macroscopic bodies. However, elastic vibrations of fine particles with ultra slow speed affect their center of mass motion. We compute dynamics of elastic vibrations during collisions between a particle and a wall using the continuum model which is three dimensional cases of [2]. We find super rebounds [3] (rebounds in which the restitution coefficient is larger than unity) for the particle whose the radius, the speed and the temperature are, respectively 100 nm, 1 m/s and 300 K. We also find the correlation between the restitution coefficient and the excitation of quadrupole mode during collisions. We will discuss origin of this correlation using the perturbation theory.

[1] H. Hertz, J. Reine Angew. Math. 92, 156 (1882).
[2] F. Gerl and A. Zippelius, Phys. Rev. E 59, 2361 (1999); H. Hayakawa and H. Kuninaka, Chem. Eng. Sci. 57, 239 (2002).
[3] H. Kuninaka and H. Hayakawa, Phys. Rev. E 79, 031309 (2009); L. B. Han, Q. An, S. N. Luo, and W. A. G. III, Material Lett. 64, 2230 (2010); H. Kuninaka and H. Hayakawa, Phys. Rev. E 86, 051302 (2012).

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