Bouncing gel balls

– We investigated impacts of nearly elastic spherical gels (very soft balls) onto a solid substrate. The Hertz contact deformation expected in the static (elastic) limit was observed only at very small impact velocities. For larger velocities, a gel ball deformed into flattened forms like a pancake. We measured the size of gel balls at the maximal deformation and a contact time as a function of velocities for samples different in the original spherical radius and the Young modulus. The experimental results revealed a number of scaling relations. To interpret these relations, we developed scaling arguments to propose a physical picture. Introduction. – Impact of spherical objects is concerned with a wide range of subjects from daily life to solid mechanics [1, 2, 3]. Accordingly, it has been studied for a long time in different contexts and still continues to be an important research subject. The Hertz contact theory [4] is a classic example in the static limit within the linear elastic theory. For larger impact velocities, internal vibrations [5] and dissipative processes such as solid viscosity [6], plastic deformation [2,7] should be considered. Impact of solid spheres in a granular medium has been found to be important fundamental processes in granular flow, and has attracted a considerable attention [7, 8, 9]. Impacts of balls of soft matter could also be an interesting problem: unique phenomena are expected due to variety of constitutive equations and due to large deformations. For example, impact or dynamics of liquid balls has attracted a wide audience [10, 11, 12, 13, 14, 15, 16, 17]. In this paper, we study another example from soft matter: impacts of soft gel balls vertically impinging onto a solid substrate. There the Hertz contact deformation is observed only for small velocities. For larger velocities, gel balls are flattened globally during the impact on the substrate, i.e., expanded into the lateral direction. We present experimental data on the lateral dimension of balls at the maximal deformation and a contact time as a function of impact velocities to show the existence of a number of scaling relations. These relations are interpreted via a naive physical picture.