Coefficient of restitution of colliding viscoelastic spheres

Details Coefficient of restitution of colliding viscoelastic spheres Coefficient of restitution of colliding viscoelastic spheres

1999-05-26

arxiv.org/abs/cond-mat/9905382v1

Phys. Rev. E, Vol. 60, 4465 (1999)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 1 figure

Scientific paper

10.1103/PhysRevE.60.4465

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution $\epsilon$ depends on the impact velocity g as \epsilon=1-\gamma_1g^{1/5}+\gamma_2g^{2/5}\mp..., in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients \gamma_1 and \gamma_2. Using these and few next expansion coefficients for \epsilon(g) we construct a Pad\'e-approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence \epsilon(g) for ice particles.

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