Coefficient of restitution of colliding viscoelastic spheres

Abstract

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(1)g(1/5)+gamma(2)g(2/5)-/+..., 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 Padé 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.

Simulation of cohesive head-on collisions of thermally activated nanoclusters

“…[1,2,3,4] For example, in the case of collisions between icy particles, we can easily find the monotonic decrease of the restitution coefficient against impact velocity without any flat region. [5] The dependence of the restitution coefficient on the low impact velocity is theoretically treated by the quasistatic theory [6,7,8,9,10]. In Ref.…”

Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit

“…This exponent comes out considering in the Boltzmann equation a granular gas composed by viscoelastic spheres [28]. To this exponent corresponds a time-decay of the temperature of order t −5/3 .…”

“…This dependence has been made explicit in [30] by assuming (4), where the exponent γ characterizes the asymptotics of the restitution coefficient with respect to the relative velocity. This choice is the analogous of the classical case of viscoelastic spheres obtained by the Hertz equation [7,28].…”

Measuring Impact Rebound with Photography

“…The constants C are [3]: C 1 = 1.153449, C 2 = -0.798267, C 3 = 0.483582, and C 4 = -0.285279. Four terms are usually more than necessary especially for low speeds as considered here.…”