Mark Dow

Projects

"I can recommend any reader who is not afraid of being late for breakfast to keep a bag of marbles in his bath-room."  A. M. Worthington,  A Study of Splashes, footnote on page 121

Worthington's mercury droplet splash as an animation

Worthington's drawings of mercury droplet splash, small animation
Worthington_mercury_droplet_splash_small.gif   (~300 KB)

    This animation is assembled from A. M. (Arthur Mason) Worthington's drawings of .15 inch diameter mercury droplets falling from 3 inches onto a glass plate. Some of these were drawn as early as 1876, using a nearby spark for very brief illumination. The thirty drawings (see source scans, from 
The Splash of a Drop, 1894) are at different phases of the splash, separated by about 1/600 sec., using machines that could repeatably produce a drop and vary the timing of the spark. He refined his equipment and techniques over several decades, eventually moving to photography.

    Worthington, a physics professor, wrote and spoke eloquently about his methods, observations, and the physics behind drops and splashes, much of which is summarized in his 1908 book
A Study of Spashes.
.
From
The History of Stopping Time #1: A.M. Worthington, Ernst Mach and Doc Edgerton:
"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."

Source scans
Notes on constructing the animation
Other splash, rain and droplet stuff
References

Other formats (432x324 pixels)
Worthington's drawings of mercury droplet splash, large animation
Worthington_mercury_droplet_splash.gif    (~1MB)
Worthington_mercury_droplet_splash.swf
Worthington_mercury_droplet_splash.avi
Worthington_mercury_droplet_splash.mp4


Source scans

    Below are the raw scans copied directly from (accessed 10/09):

The Splash of a Drop, by A. M. Worthington
Being the reprint of a Discourse delivered at the Royal Institution of Great Britain, May 18, 1894.
Worthington mercury drop 1 - 6
Worthington mercury drop 7 - 12
Worthington mercury drop 13 - 18
Worthington mercury drop 19 - 24
Worthington mercury drop 25 - 30


Notes on constructing the animation

    The source images were roughly cropped near the black boundary, with any white at the edge blackened. These were saved with a filename that included a trailing frame number.

    The drawings are not coregisted with respect to the frame edges, and the edges aren't even. The raw frames were loaded into Space Software (File | Load serial images), resized ( Volume | Resize, x2 linear interpolation,) and resaved (File | Save as Serial Images). Initially using the third frame as a reference, the adjacent frames were examined to see how well they lined up (by flipping between frames usin <,> keys). Offsets in both directions were visually estimated, the corresponding frames adjusted in an image editor  (Paint Shop Pro 5, select all, drag, save). This was repeated for all frames, each time reloading as serial images. The center of mass and  the ellipsoid containing the image elements were used as a rough guide for coregistration. Several frames were rotated, up to 5 degrees, to find a best visual fit of the ellipsoid. The brightness distribution of several frames was adjusted using a luminance gamma.

    Between frame linear interpolation, added initial drop (alternating first two frames), overlapped beggining and ending frames. Save as .avi and as serial images, JASC Animation Shop for .gif, CinemaForge for .mp4 and .swf conversion.

Other splash, rain and droplet stuff

Making a splash, PhysicsWorld.com
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."

Alchohol splashes in a vacuum chamber
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.


    These droplets have a much higher speed that those of Worthington's mercury droplets. Each interval in the Worthington's series is about 1.5 ms, and the whole sequences is about 50 ms long.

A Wind Tunnel Study On The Oscillation of Freely Falling Raindrops
Miklós Szakáll, Karoline Diehl, Subir K. Mitra and Stephan Borrmann
ERAD 2008 - THE FIFTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

"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."

 

Single-drop 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."

large drop breakiing up

Water drop onto water, high speed video: At very low speed, showing sequential coalescence and new droplet from the "rebound pillar".

References

A Study of Spashes by A. M. Worthington, 1908, Longmans, Green Co.
Internet Archive's beautiful online scan.

This book is often not available. I've seen three copies advertised (10/09), in various conditions, with quoted prices from $150 - $315.

Alibris copies for sale.


The Splash of a Drop, by A. M. Worthington
Being the reprint of a Discourse delivered at the Royal Institution of Great Britain, May 18, 1894.
The Project Gutenberg EBook of The Splash of a Drop, by A. M. Worthington
SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE, 1895
This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with the eBook or online at www.gutenberg.net

Alibris copies for sale.

A Study of Splashes. Including his 1894 lecture: The splash of a drop and allied phenomena.
by A. M. Worthington, 1963, Macmillan

A. M. Worthington, list of publications by

On Pendent Drops (.pdf)
by A. M. Worthington,  M.A. Communicated by Professor B. Stewart, F.R.S. Received May 16, 1881.

"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."

Drops 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, 1908:
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."

Prof. 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 splashesNorth Carolina School of Science and Mathematics

History, methods, projects, animations, video, links (on taking splash photographs)

A. M. Worthington – Simply brilliant (by Martin Waugh)

The History of Stopping Time #1: A.M. Worthington, Ernst Mach and Doc Edgerton
JF Ptak Science Books LLC Post #88

"...from the Scientific American from August 25, 1877 and records the experiments of A.M. Worthington.


(detail)

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?):

Sanyo Xacti high speed camcorder, 300 fps
Casio EX-F1 SuperSloMo, up to 1200 fps (interpolated?)

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Comments are welcome (dow[at]uoregon.edu).