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-to-floor depth is constant for low-energy impacts, but increases at higher energy, similar to what is observed for lunar craters.

We study fingering that occurs when hot glycerine displaces cooler, more viscous glycerine in a radial Hele-Shaw cell. We find that fingering occurs for a sufficiently large initial viscosity contrast and for sufficiently high flow rates of the displacing fluid. The wavelength of the fingering instability is proportional to the cell width for thin cells, but the ratio of wavelength to cell width decreases for our thickest cell. Similar fingering is seen in numerical simulations of this system.PACS Nos.: 47.54.+r, 68.15.+e, 47.20.–k

We study the spreading and fingering of drops of silicone oil on a rotating substrate for a range of rotation speeds and drop volumes. The spreading of the drop prior to the onset of fingering is found to follow the theoretically predicted time dependence, but with a large shift in time scale. For the full range of experimental parameters studied, the contact line becomes unstable and fingers develop when the radius of the drop becomes sufficiently large. We study the growth of perturbations around the perimeter of the drop and find the growth rate of the most unstable mode to agree well with the predictions of lubrication theory. The number of fingers which form around the perimeter of the drop is found to be a function of both rotation speed and drop volume, and is also in excellent agreement with theoretical predictions.

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

International audienceWe study the deformation, spreading, and fingering of small droplets of a yield-stress fluid subjected to a centrifugal force on a rotating substrate. At low rotation rates and for small enough droplets, the droplets deform elastically but retain their essentially circular contact line. For large enough droplet volumes and rotation speeds, however, one or more fingers eventually form and grow at the edge of the drop. This fingering is qualitatively different from the contact line instability observed in other fluids, and appears to be a localized phenomenon that occurs when the stress at some point on the perimeter of the drop exceeds the yield stress