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When a stone lands in water

Jan. 29, 2009
World Science staff

One of na­ture’s most beau­ti­ful spec­ta­cles is simply the way a wa­tery sur­face dances when a fall­ing stone hits it, es­pe­cially in the first in­stants after the strike. 

But physicists aren’t entirely clear how this pro­cess un­folds.

Courtesy D. A. van der Bos/Univ. of Twente
Now, re­search­ers say they have cla­ri­fied one per­plex­ing ques­tion: how the fast, up­ward wa­ter jet forms after an ob­ject strikes a wa­ter sur­face.

If one drops a peb­ble in­to a pond, a very rap­id, thin plume of wa­ter spouts up­wards. The sci­en­t­ists at the Uni­ver­s­ity of Twente in the Neth­er­lands and the Uni­ver­s­ity of Se­ville in Spain stud­ied the phe­no­me­non us­ing a super-fast cam­era, and made a com­put­er sim­ula­t­ion of the pro­cess.

As the ob­ject en­ters the wa­ter, a tube-shaped air ca­vity forms be­hind it, the in­ves­ti­ga­tors not­ed. Mo­ments lat­er, the wa­ter closes in on the ca­vity and fills it again, but in the pro­cess, the wa­ter squeezes some of it­self up­ward. It’s like tooth­paste be­ing squeezed out of a tube, ac­cord­ing to the re­search­ers.

In­ci­den­tal­ly, they added, a sec­ond jet is also formed and forced down­ward, deeper in­to the liq­uid, at the same time. This sec­ond jet is­n’t vis­i­ble from above.

When the ca­vity col­lapses, the first point of clo­sure is at its mid­dle. Re­search­ers pre­vi­ously thought forc­es ac­cu­mu­lat­ed at this “pinch point” alone drove the jets, Stephan Gekle, a grad­u­ate stu­dent at the Uni­ver­s­ity of Twente, told Phys­i­cal Re­view Fo­cus, a web­site of the Amer­i­can Phys­i­cal So­ci­e­ty, in an ar­ti­cle pub­lished this week.

In­stead, Geckle said, his group’s re­search, which com­bined the­o­ry, sim­ula­t­ion and ex­pe­ri­ment, showed that the con­tin­ued clos­ing of the air ca­vity is nec­es­sary to pro­vide the nec­es­sary force. It’s like the dif­fer­ence be­tween squeez­ing a tooth­paste tube once and squeez­ing it in a con­tin­u­ous mo­tion to­ward the noz­zle, very quick­ly, he added.

The find­ings are published in the Jan. 23 is­sue of the re­search jour­nal Phys­i­cal Re­view Let­ters.

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One of nature’s most beautiful spectacles is simply the way a watery surface dances when a falling stone hits it, especially in the first instants that follow. But scientists know surprisingly little about precisely how this process unfolds. Now, researchers say they have explained the formation and behaviour of the fast upward water jet formed when an object strikes a water surface, long a perplexing subject for physicists. If one drops a pebble into a pond, a very rapid, thin plume of water spouts upwards. The scientists the University of Twente in the Netherlands and the University of Seville in Spain studied what happens using a super-fast camera and made a computer simulation of the process. As the object enters the water, a tube-shaped air cavity forms behind it, the investigators noted. Moments later, the water closes in on the cavity and fills it again, but in the process, the water squeezes some of itself upward. It’s like toothpaste being squeezed out of a tube, according to the researchers. Incidentally, they added, a jet which is forced downward, deeper into the liquid, is also created at the same time. This second jet isn’t visible from above. When the cavity collapses, the first point of closure is at its middle. Researchers previously thought forces accumulated at this “pinch point” alone could drive the jets, Stephan Gekle, a graduate student at the University of Twente, told Physical Review Focus, a website of the American Physical Society in an article published this week. Instead, Geckle said, his group’s research, which combined theory, simulation and experiment, showed that the continued closing of the air cavity is necessary to provide the necessary force. It’s like the difference between squeezing a toothpaste tube once and squeezing it in a continuous motion from bottom to top, he added. The researchers are publishing their findings in the Jan. 23 issue of the research journal Physical Review Letters.