Fingering induced by a solid sphere impact to viscous fluid

Department of Earth and Environmental Sciences, Nagoya University, Furocho, Chikusa, Nagoya 464-8601, Japan

^a e-mail: katsurag@eps.nagoya-u.ac.jp

Published online: 6 May 2015

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 = (ρrFr)^1/4We^1/2/3^3/4 is obtained for the gravity-dominant cratering regime, where ρ_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.