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The purpose of the present study is to extend the simple concept of apparentcoefficient of restitution, widely approached in the literature for the case ofa single-contact-point between a sphere and a wall, to the case of bouncingwhose complexity is increased due to the shape of the contacting object.  Experiments are carried out with a finite-length cylinder, freely falling ina liquid at rest. Complex 3D motions of the cylinder with respect to the walloccur during bouncing, including multi-contact-points between the cylinder andthe bottom as well as cavitation.  We investigate numerical modelling of an idealized situation (2D infinitecylinder falling parallel to the wall) with 2D simulations where the fluidequations of motion were coupled to the particle equation of motion through anImmersed Boundary Method. The particle equation of motion is coupled to anelastic force to model bouncing, requiring a parameterization of the cut-offlength (interpreted as a roughness) and the contact time (associated with thecontact elasticity) used here to capture the experimental observations. Thesimulations confirmed that i) the departure of the coefficient of restitutionfrom 0 is strictly dependent on the apparent roughness and ii) the coefficientof restitution depends on the contact time.  Finally, we model the coefficient of restitution as the product of twocontributions to the mechanical loss of energy: the collision-to-terminalvelocity ratio ($V_c/V_t$) of the approach-phase and the rebound-to-collisionvelocity ratio ($-V_r/V_c$) of the contact-phase. This leads to a reasonablygood prediction of the coefficient of restitution in the intermediate regime in$St$. This suggests the relevance of lumping the complex details of physicalphenomena involved during contact into a simple concept based on the contactapparent roughness and elasticity.

Viscous rebound of a quasi-2D cylinder on a solid wall