The splash of a solid object into waterβbe it a coin or an Olympic high diverβis capped off by a thin jet of fluid shooting straight up from the surface. The detailed explanation of this seemingly simple event has proved elusive. Now researchers publishing in the 23 January Physical Review Letters think they have a more complete explanation than their predecessors. Using a combination of theory, simulation, and experiment, they studied the collapse of the air cavity trailing the submerged object, concluding that it ejects water like toothpaste squeezed rapidly from its tube.
A solid object plows a roughly symmetrical tube of air into a fluid. The sideways pressure exerted by the surrounding water quickly begins to collapse the cavity, first by pinching off the cylinder at its midpoint. Twin jets shoot straight up and down from the pinch-off point, called a pinch singularity. Researchers had assumed that the concentrated forces built up at the pinch point were sufficient to drive jet formation, says Stephan Gekle, a graduate student at the University of Twente in the Netherlands.
In some models, the build-up comes from a mix of so-called inertial focusingβthe concentration of energy as the cavity collapsesβand surface tension violently drawing the cavity shut.
But nobody had proved that the jet was a direct outgrowth of the pinch alone, says Gekle. Inertial focusing occurs because water accelerates as it rushes in to fill the cylindrical cavity. As the water begins to fill in, the circumference of the cylinder shrinks, but the total volume of water coming in per unit time remains constant.
With less space to move through, the water must speed up. Finally, hemmed in all around, the water has nowhere to go but up or down. The team pulled a 4-centimeter-diameter circular disk down through a water surface at 1 meter per second and used high-speed imaging to track the base of the jet as it moved up from the pinch-off point. Then they simulated the jet base on a computer. The simulated and real motion agreed closely, although the simulated jet base ascended faster than the real one, a discrepancy Gekle blames on the slight asymmetry of the real thing.
