Hydrogel sphere impact cratering, spreading and bouncing on granular media

TL;DR

This study investigates how hydrogel spheres impact, deform, spread, and bounce on granular media, revealing scaling laws, energy storage effects, and conditions for rebound, with implications for understanding impact dynamics of soft particles.

Contribution

It provides new insights into impact crater scaling, elastic energy effects, and rebound conditions for hydrogel spheres on granular surfaces, extending previous droplet and hard sphere studies.

Findings

Crater diameter follows a power law with a sharper change below 200 Pa Young's modulus.

Elastic energy storage during impact affects crater formation energy budget.

Rebound occurs under specific Young's modulus and impact velocity conditions.

Abstract

The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of the spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and find the data to be consistent with those from earlier experiments using droplets and hard spheres. Most specifically, we find that the crater diameter data are consistent with a power law, where the power exponent changes more sharply when $Y$ becomes less than $200$ Pa. Next, we introduce an estimate for the portion of the impact kinetic energy that is stored in elastic energy during impact, and thus correct the energy that remains available for crater formation. Subsequently, we determine the deformation of the hydrogel sphere and find that the normalized spreading diameter data are well collapsed introducing an equivalent velocity from an energy balance of the the initial kinetic energy against surface and elastic energy. Finally, we observe that under certain intermediate values for the Young's modulus and impact velocities, the particles rebound from the impact crater. We determine the phase diagram and explain our findings from a comparison of the elastocapillary spreading time and the impact duration.