Impact of solid and liquids balls on a solid surface: a unified description

We study experimentally the impact of ultra soft spherical gel balls of millimetric size d0 on a rigid substrate covered by a thin layer of liquid nitrogen to avoid viscous dissipation .The balls largely deform like a pancake at high impact velocities. We measure the maximally deformed size dmax and the the time needed to reach this maximal size after impact Tmax, versus the impact velocity Ui for various elastic moduli . We do the same type of experiments with liquid droplets of various surface tensions . The experiments reveal a universal scaling behavior of the maximum deformation $d_{max}/d_0}$ of both solid balls and liquid drops provided that both bulk and surface elasticity are properly taken into account. Moreover, we show that , in absence of viscous dissipation, the dynamics of the system can be understood as a conventional spring-mass system with a stiffness given by a combination of surface tension and bulk elasticity and a mass given by that of the ball (or drop) ; the deformation of the small ball (drop) during the impact linearly depends on the impact velocity, and the contact time scales as the period of this spring-mass system.