recommend any reader who is not afraid of being late for breakfast to
keep a bag of marbles in his bath-room." A. M.
A Study of Splashes, footnote on page 121
Making a splash,
Feb 1, 2005
(L Xu et al. 2005 arXiv.org/abs/physics/0501149)
Sidney Nagel and colleagues at Chicago have now seen something that no one has seen before by releasing drops of alcohol from various heights onto a glass microscope slide inside a vacuum chamber and recording what happens with a high-speed video camera. The team used three liquids with different viscosities (methanol, ethanol and 2-propanol) and four gases with different molecular weights (helium, air, krypton and sulphur fluoride) inside the vacuum chamber. Moreover, they varied the pressure in the chamber from just 1 kilopascal up to 100 kilopascals (atmospheric pressure).
To their surprise, the Chicago physicists found that the surrounding gas played a key role in the splashing process. In particular, they found fewer droplets were ejected from the surface as the pressure was lowered, and that no droplets emerged below a threshold pressure (see figure). They also found that the threshold pressure scaled with the molecular weight of the surrounding gas. Moreover, they found that 2-propanol, which has the largest viscosity of the three liquids, had the lowest threshold pressure."
Photographs of a liquid drop hitting a smooth dry substrate. A 3.4 ± 0.1 mm diameter alcohol drop hits a smooth glass substrate at impact velocity V0 = 3.74 ± 0.02 m/s in the presence of different background pressures of air. Each row shows the drop at four times. The first frame shows the drop just as it is about to hit the substrate. The next three frames in each row show the evolution of the drop at 0.276 ms, at 0.552 ms and at 2.484 ms after impact. In the top row, with the air at 100 kPa (atmospheric pressure), the drop splashes. In the second row, with the air just slightly above the threshold pressure, PT = 38.4 kPa, the drop emits only a few droplets. In the third row, at a pressure of 30.0 kPa, no droplets are emitted and no splashing occurs. However, there is an undulation in the thickness of the rim. In the fourth row, taken at 17.2 kPa, there is no splashing and no apparent undulation in the rim of the drop.
"As the raindrop shape is a key parameter in, e.g., the remote measurement of rain fall rates and nowcasting of precipitation using dual-polarization radars, the accurate knowledge of the oscillation behavior of the raindrops is of great importance. In particular, it needs to be clarified whether the dynamic average axis ratio (affected by oscillation) is the same as the one in static equilibrium while the latter is assumed in calculations of the rain fall rate from radar data. In spite of its paramount importance, detailed study on the oscillation behavior of individual water drops falling at terminal velocity in air is still missing.
Here we present the results of our experiments on raindrop oscillations of freely suspended water drops floating inside the Mainz vertical wind tunnel at their terminal velocities. The comparison of the measured equilibrium raindrop shape with the theoretical models of Beard and Chuang (1987) and Pruppacher and Pitter (1971) is presented. We also show how the oscillation frequency, as well as the amplitude and the time averaged mean of the axis ratio of water drops depend on the drop size."
fragmentation determines size distribution of raindrops
Emmanuel Villermaux, Benjamin Bossa
Nature Physics 5, 697 - 702 (2009)
Caught on Film: Raindrop Forms Parachute, Explodes Into Motley Smaller Drops, Discover magazine commentary and animation
"Like many natural objects, raindrops are distributed in size. By extension of what is known to occur inside the clouds, where small droplets grow by accretion of vapour and coalescence, raindrops in the falling rain at the ground level are believed to result from a complex mutual interaction with their neighbours. We show that the raindrops' polydispersity, generically represented according to Marshall–Palmer's law (1948), is quantitatively understood from the fragmentation products of non-interacting, isolated drops. Both the shape of the drops' size distribution, and its parameters are related from first principles to the dynamics of a single drop deforming as it falls in air, ultimately breaking into a dispersion of smaller fragments containing the whole spectrum of sizes observed in rain. The topological change from a big drop into smaller stable fragments—the raindrops—is accomplished within a timescale much shorter than the typical collision time between the drops."
Water drop onto water, high speed video: At very low speed, showing sequential coalescence and new droplet from the "rebound pillar".
Study of Spashes by
Internet Archive's beautiful online scan.
The Project Gutenberg EBook of The Splash of a Drop, by A. M. Worthington
SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE, 1895
, 1963, Macmillan
A. M. Worthington, list of publications by
On Pendent Drops
"About two years ago I was led to examine the forms of pendent drops of liquid by a method of great simplicity, which seems capable of being used with considerable accuracy for determining the value of the surface tension."
and Splashes (Nature news item regarding "A Study of Splashes")
Nature 78, 666-667 (29 October 1908)
"THE few who have access to the Transaclions of the Royal Society, and who remember the first presentation of Prof. Worthington's beautiful photographs illustrating the successive movements that occur in the phenomenon of the splash of a drop, and some proportion of the many who may have seen his two articles on the subject in Pearson's Magazine, will welcome the appearance of the fascinating quarto volume entitled "A Study of Splashes." Not only will their recollection of an interesting research be revived, but the more perfectly executed and more numerous and complete series of photographs here presented will show the phenomena in all their original beauty as displayed on the lantern screens at the Royal Institution and elsewhere. Besides showing' the results and explaining the interesting cooperation of the forces of dynamics and of surface tension which have given rise to the phenomena, Prof. Worthington has given very full details of his method so that many who can extemporise physical apparatus will be able to follow him, and so to investigate the same or analogous movements."
New York Times review of "A Study of Splashes", August 29,
WONDER AND CHARM OF THE SPLASH; Fourteen Years' Study of Falling Drops Gives Material for Book of Remarkable Interest.
"AN ingenious and patient scientist has been investigating for fourteen years the phenomena that follow the falling of a drop of water into a pool. He has photographed these phenomena at every stage, and the result is a particularly fascinating volume called "A Study of Splashes," (Longmans, Green Co.,) the author of which is A.M. Worthington, C.B., M.A., F.R.S., head master and Professor of Physics at the Royal Naval Engineering College at Devonport."
A. M. Worthington, C.B., F.R.S
Obituary, Nature 98, 293-294 (14 December 1916)
THE death of Prof. A. M. Worthington at Oxford on December 5, after a short illness, will be deplored by many men of science and a large circle of students who came under his educational influence. Born in Manchester in 1852, Prof. Worthington was educated at Rugby and at Trinity College, Oxford, afterwards working at Owens College, Manchester, and at Berlin, in the laboratory of Prof. Helmholtz.
Introduction to drops and splashes, North Carolina School of Science and Mathematics
History, methods, projects, animations, video, links (on taking splash photographs)
A. M. Worthington – Simply brilliant (by Martin Waugh)
History of Stopping Time #1: A.M. Worthington, Ernst Mach and Doc
JF Ptak Science Books LLC Post #88
"...from the Scientific American from August 25, 1877 and records the experiments of A.M. Worthington.
They are perhaps one of the first revelations on the quiet residence of energy in something as simple as a drop of water or mercury. Much in the same way Robert Hooke revealed the microscopic universe to unsuspecting readers, so too did Worthington, in his way, reveal the explosive world of small, fast, and lost events. Worthington’s style is of course exceptionally restrained and free of exclamation, even while describing the first time any human has witnessed these events, like so: “…watching the changes of form of drops of various liquids falling vertically on a horizontal plane…the whole splash takes place so quickly that the eye cannot follow the changes of form…” This report, “On Drops” follows Worthington’s own earlier effort of 1876 and 1877 “A Second Paper on The Forms Assumed by Drops of Liquids falling vertically on a Horizontal Plate” (Proceedings of the Royal Society, 174 and 177), chronicles his brilliant adventure in the newly discovered world of fast time—a world he was pretty much creating as he moved along. (A particularly good description of the experiment as well as an image of the apparatus can be found on Martin Waugh’s lovely and arresting site—he is one of the leading modern practitioners making art in this genre of high-speed photography: liquid sculpture calls it.) ) It is particularly powerful to note that the illustrations here are drawings of the phenomena of his study of splashes—drawings, not photographs. The photos by Worthington (On A Splash from a Drop of Milk) would not appear until 1894. (An entire book is dedicated to this subject by Worthington, who published, in 1904, the wonderful A study of Splashes.) This means, I guess, like the heroic chroniclers of snowflake forms and such that he ran many, many experiments and painstakingly observe red different parts of the splashes and recorded them by hand. Worthington wouldn’t be able to photographically record the images of his splashes until later after the application of inventions and advances by C.V. Boys and Lord Rayleigh. Until that time his audience would have to depend upon his tenacious observational powers—or try the experiment themselves and make their own observations, as Worthington provided all the necessary data for his experiments to be replicated, of course."
Consumer high speed video (interpolated?):
Xacti high speed camcorder, 300 fps
Casio EX-F1 SuperSloMo, up to 1200 fps (interpolated?)