We consider the collision of a rough sphere with a plane by detailed analysis of the collision geometry. Using stochastic methods, the effective coefficient of restitution may be described as a fluctuating quantity whose probability density follows an asymmetric Laplace distribution. This result agrees with recent experiments by Montaine et al. [Phys. Rev. E 84, 041306 (2011)].
DOI:https://doi.org/10.1103/PhysRevE.89.022205
©2014 American Physical Society
Sketch of the collision of a rough particle with a flat surface. Only the asperity which is in contact with the plane is shown.
Reuse & PermissionsHistograms of the and components of the contact vector as found in numerical simulations together with the corresponding analytical results for the density distributions due to Eq. (18).
Reuse & PermissionsNumerical test of Eq. (28) by means of Monte Carlo simulations shows almost perfect agreement for the analytical and numerical data. The lower figure shows the same data in log-scale. For details, see the text.
Reuse & PermissionsThe numerical test of Eqs. (32) and (33) by means of Monte Carlo simulations shows almost perfect agreement for the analytical and numerical data. For details, see the text.
Reuse & PermissionsProbability density of the coefficient of restitution, , due to Eq. (28) for different values of the impact velocity. For the Monte Carlo simulation, we assume a particle of size mm covered by asperities of size mm. The distribution is approximately Laplacian (see exponential fits, full lines) and shows good agreement with the experimental data; see Fig. 4 in Ref. [19].
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