Impact of spherical projectiles into a viscoplastic fluid

Scientific Reports

Physical Review Letters, 2003

We present the results of experiments on impact craters formed by dropping a steel ball vertically into a container of small glass beads. As the energy of impact increases, we observe a progression of crater morphologies analogous to that seen in craters on the moon. We find that both the diameter and the depth of the craters are proportional to the 1=4 power of the energy. The ratio of crater diameter to rim-tofloor depth is constant for low-energy impacts, but increases at higher energy, similar to what is observed for lunar craters.

Nature Communications, 2021

When a solid object impacts on the surface of a liquid, extremely high pressure develops at the site of contact. Von Karman’s study of this classical physics problem showed that the pressure on the bottom surface of the impacting body approaches infinity for flat impacts. Yet, in contrast to the high pressures found from experience and in previous studies, we show that a flat-bottomed cylinder impacting a pool of liquid can decrease the local pressure sufficiently to cavitate the liquid. Cavitation occurs because the liquid is slightly compressible and impact creates large pressure waves that reflect from the free surface to form negative pressure regions. We find that an impact velocity as low as ~3 m/s suffices to cavitate the liquid and propose a new cavitation number to predict cavitation onset in low-speed solid-liquid impact-scenarios. These findings imply that localized cavitation could occur in impacts such as boat slamming, cliff jumping, and ocean landing of spacecraft.

Journal of Non-Newtonian Fluid Mechanics, 2006

We present an experimental study of the impact of a solid sphere on the free surface of a viscoelastic wormlike micellar fluid. Spheres of various densities and diameters are dropped from different heights above the fluid surface, reaching it with a nonzero velocity which determines the subsequent dynamics. Measurements of the initial sphere penetration are found to scale with the ratio of the kinetic energy of the sphere at impact to the elastic modulus of the fluid. The cavity formed in the wake of the sphere, observed with high-speed video imaging, also undergoes transitions from a smooth to fractured surface texture, dependent on both the Deborah number and the ratio of the gravitational force to elasticity. 2 The formation of the cavity for a freely falling coin depends to some extent on the angle with which the coin enters the water.

Physical Review E, 2014

Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with non-circular cross-sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that the degree of anisotropy increases with the aspect ratio of the jet's cross-section. Our results illustrate the liquid-like behavior of granular materials during impact and demonstrate that a collective hydrodynamic flow emerges from strongly interacting discrete particles. We discuss the analogy between our experiments and those from the Relativistic Heavy Ion Collider (RHIC), where similar anisotropic ejecta from a quark-gluon plasma have been observed in heavy-ion impact.

2016

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 = (ρ r Fr) 1/4 We 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.

Physical Review Letters, 2008

We present evidence for the interactions between a ball and the container boundaries, as well as between two balls, that are mediated by the granular medium during impact cratering. The presence of the bottom boundary affects the final penetration depth only for low drop heights with shallow filling, in which case, surprisingly, the penetration becomes deeper. By contrast the presence of the side wall causes less penetration and also an effective repulsion. Repulsion is also found for two balls dropped side-by-side.

Nature Physics, 2007

Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events [1-5] and to probe the unusual nature of the granular state of matter [6-9]. While the findings are all strikingly different from impact into ordinary solids and liquids, no consensus has emerged regarding the interaction between medium and projectile. Observation that the final penetration depth is a power of the total drop distance was interpreted by a stopping force that is a product of powers of depth and speed [6]. Observation that the penetration depth is linear in initial impact speed was interpreted by a force that is linear in speed [7]. Observation that the stopping time is constant was interpreted by a force that is constant but proportional to the initial impact speed [8]. Observation that depth vs time is a sinusoid for a zero-speed impact was interpreted by a force that is proportional to depth [9]. These four experimental results, as well as their interpretations, would all seem to be in conflict. This situation is reminiscent of highspeed ballistics impact in the 19 th and 20 th centuries, when a plethora of empirical rules were proposed [10,11]. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 s precision. For a 1-inch diameter steel

Physical Review Letters, 2003

$d\sim({\rho_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}$. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.

Journal of Fluid Mechanics, 2013

The role played by gas compressibility in gas-cushioned liquid–solid impacts is investigated within a viscous gas and inviscid liquid regime. A full analysis of the energy conservation in the gas is conducted for the first time, which indicates that both thermal diffusion across the gas film and viscous dissipation play an important role in gas cushioning once gas compression becomes significant. Consequently existing models of gas compressibility based on either an isothermal or an adiabatic equation of state for the gas do not fully reflect the physics associated with this phenomenon. Models incorporating thermal diffusion and viscous dissipation are presented, which are appropriate for length scales consistent with droplet impacts, and for larger scale liquid–solid impacts. The evolution of the free surface is calculated alongside the corresponding pressure, temperature and density profiles. These profiles indicate that a pocket of gas can become trapped during an impact. Differe...