Bubble pinch-off in a rotating flow.

We create air bubbles at the tip of a "bathtub vortex" which reaches to a finite depth. The bathtub vortex is formed by letting water drain through a small hole at the bottom of a rotating cylindrical container. The tip of the needlelike surface dip is unstable at high rotation rates and releases bubbles which are carried down by the flow. Using high-speed imaging we find that the minimal neck radius of the unstable tip decreases in time as a power law with an exponent close to 1/3. This exponent was found by Gordillo et al. [Phys. Rev. Lett. 95, 194501 (2005)10.1103/PhysRevLett.95.194501] to govern gas flow driven pinch-off, and indeed we find that the volume oscillations of the tip creates a considerable air flow through the neck. We argue that the Bernoulli pressure reduction caused by this air flow can become sufficient to overcome the centrifugal forces and cause the final pinch-off.

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.

Role of air in granular jet formation.

A steel ball impacting on a bed of very loose, fine sand results in a surprisingly vigorous jet which shoots up from the surface of the sand [D. Lohse, Phys. Rev. Lett. 93, 198003 (2004)10.1103/PhysRevLett.93.198003]. When the ambient pressure p is reduced, the jet is found to be less vigorous [R. Royer, Nature Phys. 1, 164 (2005)10.1038/nphys175]. In this Letter we show that p also affects the rate of penetration of the ball: Higher pressure increases the rate of penetration, which makes the cavity created by the ball close deeper into the sand bed, where the hydrostatic pressure is stronger, thereby producing a more energetic collapse and jetting. The origin of the deeper penetration under normal ambient pressure is found to lie in the extra sand fluidization caused by the air flow induced by the falling ball.

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.

Impact on soft sand: void collapse and jet formation.

Very fine sand is prepared in a well-defined and fully decompactified state by letting gas bubble through it. After turning off the gas stream, a steel ball is dropped on the sand. On impact of the ball, sand is blown away in all directions ("splash") and an impact crater forms. When this cavity collapses, a granular jet emerges and is driven straight into the air. A second jet goes downwards into the air bubble entrained during the process, thus pushing surface material deep into the ground. The air bubble rises slowly towards the surface, causing a granular eruption. In addition to the experiments and the discrete particle simulations we present a simple continuum theory to account for the void collapse leading to the formation of the upward and downward jets.

Granular physics: 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.