Coefficient of restitution as a fluctuating quantity

Abstract

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (nonGaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, p(ε), is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.

Coefficient of restitution of aspherical particles

“…Here, the coefficient of restitution becomes a fluctuating quantity as its value depends on the details of the surface at the contact point, that is, on the random geometry of the collision. It was shown that this model leads to a characteristic probability distribution [11] which agrees well with large-scale experiments [10].…”

“…In many cases, in particular for dilute gases, successive collisions of particles are only weakly correlated [1], which suggests one considers the coefficient of restitution as a random variable with certain statistical characteristics describing the fluctuations. In a first attempt in this direction, rough particles have been modeled as spheres whose surface is covered by a large number of randomly distributed asperities [10]. Here, the coefficient of restitution becomes a fluctuating quantity as its value depends on the details of the surface at the contact point, that is, on the random geometry of the collision.…”

Movers and shakers: Granular damping in microgravity

“…Performing an automated drop test [41] of the granulate on to a silicon carbide plate yields an elasticity of ε ≈ 0.95. Due to the high rigidity of the base plate, this value should be close to the experimental value for particle-particle interactions.…”

Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

“…Guided by recent experimental, numerical and theoretical results (Montaine et al 2011;Gunkelmann et al 2014) concerning the distribution of coefficients of restitution, we considered here the case of Laplace distributed coefficients:…”

“…Though detailed analyses and experiments indicate that the coefficient depends on impact velocity (Schwager & Pöschel 1998;Pöschel, Brilliantov & Schwager 2003), a fixed coefficient of restitution has long been recognized to provide a reliable description. An aspect that has seldom however been addressed is the fact that even for virtually perfect spheres such as a ball bearing, significant scatter is observed in experimental measurements of the coefficient of restitution (Lifshitz & Kolsky 1964;Montaine et al 2011) which can be associated with microscopic surface asperities (Hatzes, Bridges & Lin 1988;Montaine et al 2011). A natural way of taking this scatter into account theoretically is to consider a randomly fluctuating coefficient of restitution (Gunkelmann, Montaine & Poschel 2014).…”