Fingering induced by a solid sphere impact to viscous fluid

TL;DR

This study experimentally investigates the fingering instability caused by a solid sphere impacting a viscous liquid, deriving scaling laws based on dimensionless numbers and applying them to planetary crater analysis.

Contribution

It introduces a new scaling law for fingering instability during sphere impact on viscous fluids, linking it to dimensionless parameters and planetary crater structures.

Findings

Fingering instability depends on impact inertia and liquid viscosity.

Derived scaling law relates number of fingers to Reynolds, Weber, and Froude numbers.

Scaling law aligns with experimental data despite scatter.

Abstract

The number of splashed fingers generated by a solid projectile's impact onto a viscous liquid layer is experimentally studied. A steel sphere is dropped onto a viscous liquid pool. Then, a fingering instability occurs around the crater's rim, depending on the experimental conditions such as projectile's inertia and the viscosity of the target liquid. When the impact inertia is not sufficient, any fingering structure cannot be observed. Contrastively, if the impact inertia is too much, the random splashing is induced and the counting of fingers becomes difficult. The clear fingering instability is observable in between these two regimes. The number of fingers $N$ is counted by using high-speed video data. The scaling of $N$ is discussed on the basis of dimensionless numbers. By assuming Rayleigh-Taylor instability, scaling laws for $N$ can be derived using Reynolds number $Re$, Weber number $We$, and Froude number $Fr$. Particularly, the scaling $N=(\rho_r Fr)^{1/4}We^{1/2}/3^{3/4}$ is obtained for the gravity-dominant cratering regime, where $\rho_r$ is the density ratio between a projectile and a target. Although the experimental data considerably scatters, the scaling law is consistent with the global trend of the data behavior. Using one of the scaling laws, planetary nano crater's rim structure is also evaluated.