Dynamics of impact cratering on granular bed by hydrogel sphere

Abstract

A lot of studies on the dynamics of a granular impact cratering by a liquid drop have been carried out. However, the results so far are controversial due to the complex impact dynamics of a liquid drop, such as deformation, splash, and penetration into the granular bed. In this study, we focused on the dynamics of the granular impact cratering by a hydrogel sphere, which deforms without splashing and penetrating. We investigated the maximal deformation time of the sphere and the lift-off time of the grains. Both the maximal deformation time and the lift-off time are similar to each other and depend on the −1/2 power of the Young’s modulus of the hydrogel sphere. This power law of the maximum deformation time is the same as an impact of a gel sphere on a flat solid surface. The angle of the ejected curtain was evaluated. The angle is larger for the impact with small deformation of the sphere than that for the impact with large deformation, and the angle is less dependent on the free-fall height. We also investigated the distributions of the ejected grains using the grains dyed by a fluorescent dye. The distribution was visualized by the fluorescent images captured before and after the impact. At the crater rim, the number of the dyed grains flying to and away are balanced. The number of the dyed grains gathered at the dimensionless distance from the crater center of 1.15, where the distance is nondimensionalized by the crater radius, is the largest. This maximum value for the number of the gathered grains is larger for the impact with small deformation than that with large deformation. This result is consistent with the dependence of the impact mode on the angle of the ejected curtain.