Raymond Bergmann

Controlled impact of a disk on a water surface : cavity dynamics

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h 0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations. We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr 1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume V bubble of air entrained by the process, namely, V bubble / h 0 3 ∝(1 + 0.26 Fr 1/2 ) Fr 1/2 .

Giant Bubble Pinch-Off

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a downward jet. Only in the limiting case of large Froude numbers does the purely inertial scaling h(-logh)(1/4) proportional tau(1/2) for the neck radius h [J. M. Gordillo et al., Phys. Rev. Lett. 95, 194501 (2005)] become visible. For any finite Froude number the collapse is slower, and a second length scale, the curvature of the void, comes into play. Both length scales are found to exhibit power-law scaling in time, but with different exponents depending on the Froude number, signaling the nonuniversality of the bubble pinch-off.

Creating a dry variety of quicksand

Sand can normally support a weight by relying on internal force chains. Here we weaken this force-chain structure in very fine sand by allowing air to flow through it: we find that the sand can then no longer support weight, even when the air is turned off and the bed has settled — a ball sinks into the sand to a depth of about five diameters. The final depth of the ball scales linearly with its mass and, above a threshold mass, a jet is formed that shoots sand violently into the air.

Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude(1/3) power law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary wave effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the nonuniversality of the void collapse.

The origin of the tubular jet

A vertical cylindrical tube is partially immersed in a water-filled container and pressurized to lower the fluid level inside the tube. A sudden release of the pressure in the tube creates a singularity on top of the rising free surface. At the very beginning of the process a jet emerges at the centre of the surface, the strength of which strongly depends on the initial shape of the meniscus. Here, the time-evolution of the complex shape of the free surface and the flow around the cylindrical tube are analysed using high-speed imaging, particle image velocimetry, and numerical simulations. The tubular jet is found to be created by the following series of events, which eventually lead to the flow focusing at the tubes centre. A circular surface wave, produced by the funnelling of flow into the tube, is pushed inwards by the radial flow directly underneath the surface. As the wave moves inward and eventually collapses at the centre of the tube, a bump of fluid grows in the centre due to the converging flow in the bulk. This converging flow continues to feed the jet after the circular wave has collapsed. The singularity of the wave collapse is manifested in the initial sharp tip of the jet. All of the above events are traced back to a single origin: the convergence of the flow as it enters the tube. Movies are available with the online version of the paper.