Physics question

<p>The only light source in this image is the sun, which, last I checked, was a very continuous light source. I did not use any sort of strobe. The subject is in a shower, and the shower head is out of the frame, to the upper right. Exposure speed was 1/100 sec. You can see the water drops coming from the shower head; they are the large, continuous streaks heading toward the skin. You can also see drops bouncing off the skin – but here's the big mystery: why are they dotted? They look for all the world like single drops that have been lit stroboscopically as they traverse a path, and yet that can't be. (I was there, for one thing, and you would expect the drops coming from the shower head to be similarly dotted.) And if they do represent a path, then they appear to be going substantially faster than the drops coming from the shower head. Can it be that these are actually lines of drops flying neatly through the air? That suggests an orderliness I find completely unexpected. I am completely baffled. Any physicists or engineers out there who can explain what's going on?<p>

<p>Barry, I think what you've described can be explained by the sensor's datasheet, specifically the read/write timing diagram relative to its circuit architecture. In other words, how the sensor acquires and reads the rows and columns of data. </p>

<p>My guess would be that the streaks of water from the shower head hit the skin, bounce of, maybe losing speed, and then split into separate drops as a result of the surface tension of the water. The separate drops would of course all follow the same trajectory. But that is just a guess.</p>

The effect does seem to suggest that it is an artifact of digital image processing. To confirm this you could

reshoot the same subject using a film camera and compare the two results, digital vs film.

<p>I'll take a guess, Barry. It appears they are not really dots but dashes of varying lengths. I think what we are seeing is droplets bouncing off the skin and catching sun highlights but those specular highlights are being interrupted, in varying degree, by the the fast moving primary water shafts. Due to the relatively long exposure time, 1/100 sec, a "trail" of interrupted highlights is giving the "dotted/dashed" effect.</p>

<p>I don't even play a physicist on TV, but I wonder if this is something like the "rods" in video ( http://en.wikipedia.org/wiki/Rod_%28optics%29 ), that is that it is an effect of the methods used to capture the image.</p>

<p>If you'll notice, the effect is primarily seen on the droplets that are bouncing off of the skin. When drops of liquid strike something and rebound, they don't maintain a steady round shape. Waves of energy propagate through the droplet, causing them to flex and change shape (thus changing how the light is reflected). Think of dropping a pebble into the smooth surface of a pond and the ripples that radiate outward. Then imagine those ripples trapped inside a single droplet.</p>

<p>Here are a couple of slo-mo videos of water droplets. Watch, in particular, how the droplets on the rebound change shape.</p>

<p><a href="

(skip to the 1:10 mark) </p>

<p><a href="https://www.youtube.com/watch?v=6KKNnjFpGto">https://www.youtube.com/watch?v=6KKNnjFpGto</a></p>

<p>What causes the dotted line effect is the droplets repeatedly flexing into and out of a shape that reflects light back to the sensor. Similar to the dotted line you get if an airplane flies through your long exposure shot with it's blinking navigation lights.</p>

<p>P.S. I'm not a Physicist, but I do have a degree to teach Physics. :-)</p>

<p>Digital vs. film – not gonna go there! :)<br>

Thanks for all the responses. I was kind of thinking something along the lines of Cory's answer, but only have a degree in literature (with a few math and science courses thrown in to combat ignorance). Oscillating droplets makes sense. This is particularly suggested by the fact that the "dots" aren't uniform. Some, as has been pointed out, are little dashes. Some are dot-pairs. Some of the dashed ones are dashed at an angle to the overall line of dashes (sort of like cars in angled parking). Though each trail consists of evenly spaced dots (or dashes), the trails consist of different numbers of dots/dashes, and the spacing suggests that some are "flashing" at a different rate than others. All of that would, I suppose, be consistent with waves propagating around various-sized droplets in various ways as they flew away.</p>

<p>The streams from a shower head are what is called "turbulent flow", and break into droplets within an inch or two of the orifice. To get a solid stream of any length, you must establish "laminar flow". What looks like solid streams to your eye (visual retention) are actually strings of beads.</p>

<p>You have probably seen fountain displays where a solid stream of water arcs 15 feet into the air and disappears into the pool with barely a splash. The stream never breaks into droplets, and looks like a transparent tube. The fountain in the lobby of McCormick Place in Chicago is one example. To create laminar flow, the water is directed through a bundle of hundreds of soda straws, then through a gradual restriction to the nozzle.</p>

<p>Streams in these fountains are fairly large to remain laminar throughout their trajectory. The smaller the stream, the shorter the time laminar flow is maintained - a function of diameter, velocity and viscosity (q.v., Reynolds Number). It works with air too, and is the basis for laminar flow hoods used for aseptic manufacturing and laboratory safety hoods.</p>

I think Cory has it: the droplets after bouncing flex and vibrate. The periodically changing reflection reflects the periodically changing shape.

<p>Both Edward and Cory are correct. The water coming out is not a solid stream, the stream quickly begins to break down and form drops. After the drops collide with a solid body, they change direction. The result of the collision and rapid change of direction results in deformity. (Remember that this is a liquid, not a solid.) Water is highly "polar", meaning it has a strong charge. It wants to resume its sphere after the collision and will go through several "flexes" before it can do that.</p>

<p>Kent in SD</p>

<p>I can guarantee you that the equally-spaced-trail-of-dots effect seen throughout the cited photo is not due to shape oscillations of the droplets. </p>

<p>The reason is that other than for the smallest droplets, all larger droplets support multiple modes of deformation (eg, oblate-to-prolate ellipsoid, "three leaf clover" modes, 4 lobed modes, etc. along one axis, as well as numerous circumferential modes around that same axis. Each specific combination of an axial and a circumferential mode will be at a different oscillation frequency. In the real world, none of these modes of oscillation are degenerate (ie, have the same frequency). Even worse, if the amplitude of the shape oscillation is large, the oscillations will be nonlinear (vs quasi-linear), and the resulting motion is almost always quasi-chaotic instead of being able to be represented by linear combinations of fundamental modes (aka, "eigenmodes").</p>

<p>When a droplet is formed, or if it splits into two, or hits something, etc., etc. a huge variety of oscillation modes is excited 99.9% of the time. It fact, experimentalists in this field find it extremely difficult to prepare droplets in just one pure mode of oscillation (ie, one frequency) without using special techniques. The consequence of this is that the glinting of light from such droplets will almost always appear random, NOT equally spaced such as seen in many of the trajectories shown in the cited example.</p>

<p>Tom M</p>

But have another look: they are not regular nor equally spaced.

<p>I think you are pointing out that there are moderate deviations from regularity / equal spacing in any one trajectory. This, of course is true.</p>

<p>However, the point is that the randomness in refraction / glints / diffractive scattering produced by shape oscillations of droplets is usually so extreme, you would never see anything looking even vaguely regular in the "dots and dashes" patterns that we are seeing in this photo.</p>

<p>FWIW, back in the late 1980's I did some experimental work in shape oscillations of droplets acoustically levitated in a flow of surrounding air. We looked at droplets from about 100 microns up to a few mm. The goal was to see if such oscillations significantly enhanced evaporation of the droplets when compared to mass transport theories of the time which assumed no such oscillations. Enhanced mass transport would be important for modeling for both environmental issues and clouds of chemical agents.</p>

<p>Cheers,</p>

<p>Tom M</p>

<p>Wow! Fascinating stuff. So what appear to be neat formations of droplets really are neat formations of droplets? That might explain why there's such a variation in their length (though I suppose there's no reason to assume that all the reflected droplets would be moving the same velocity away from the impact point.</p>

<p>I think that we can get a rough estimate of the distance traveled during the shutter opening by applying Bernoulli's equation to one jet in the shower head and by assuming an upstream velocity of zero. If I assume an upstream pressure of two atmospheres, then the pressure difference to ambient is one atmosphere and the distance traveled in approximately 1/100 s is on the order of 5 inches. Taking the width of the shoulder in the photograph as approximately 8 inches, then the length of the longest streaks is a little less than the 5 inches calculated (3 inches?), but reasonably close considering all the approximations necessary. This calculation shows that the smaller streaks in the photo of less than one inch are not due to individual drops but due to one drop, with light reflecting unevenly from moment to moment.</p>

<p>The attached image is from research that I performed about twenty years ago on drop interaction with particles. I have better photos somewhere, and, now that I am retired, no longer have records of drop sizes or velocities, etc. While the image, which shows two separate jets of water that have broken into drops, supports Tom's description of semi-chaotic drop motion, it does show that reflection from an individual drop would not produce a nice uniform streak characteristic of a spherical drop.</p><div></div>

<p>After further thought, my guess as to what we are seeing in the image is that water drops that bounce off the skin at an oblique angle are deformed from the inelastic collision and tumble. At least for a short distance, the tumbling asymmetrical drop might reflect light toward the camera once per revolution. But, this is just a guess. I would not be surprised if someone has published a research paper on the subject.</p>

<p>Hey, Glen, thanks for posting those photos. They were very well done and interesting. To be honest, knowing the work I would have to go through to dig out my own notes and photos from our levitated droplet experiments that many years ago, I didn't even try, LOL. <br /><br />Given the subject matter, it sounds like there was a reasonable chance we might have overlapped at some conferences back in the day, although the work of my group was more directed towards understanding CBW aerosol clouds, not reactor / nuclear waste applications, and probably a decade earlier than yours.<br /><br />Anyway, take a look at some other photos of water emerging from shower heads. Note the presence of reasonably regular strings of droplets in all of these photos:<br /><br />http://janiceperson.com/wp-content/uploads/2013/03/9IMG_8755BW.jpg<br />http://img.alibaba.com/img/pb/725/893/239/1270026448706_hz_myalibaba_web_temp2_2794.jpg<br />http://us.123rf.com/450wm/janka3147/janka31471204/janka3147120400020/12997085-showerhead-and-falling-water-drops.jpg<br />http://www.patdolanplumbing.com/wp-content/uploads/shower-head.jpg<br />http://www.4freephotos.com/images/u/Shower-head-horizontal346.jpg<br />http://www.4freephotos.com/images/u/Round-shower-head-with-water1712.jpg<br />http://www.waterwise.org.uk/data/Waterwise_Images/Water_images/Adarshr.jpg<br />http://thumbs.dreamstime.com/z/close-up-water-flowing-out-chrome-shower-head-30844300.jpg<br /><br />In the late 1800's, Lord Rayleigh proposed a mechanism for these. The mechanism has been validated under a wide range of conditions and it now carries his name, the "Rayleigh instability" (http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability). A short explanation for it is given in the 2nd section of the Wikipedia article. That discussion focuses on estimating the size of the resulting droplets, but once you have the size, indirectly, you also have an estimate of their spacing. <br /><br />Here are some more images that illustrate this phenomena. <br /><br />http://www-rohan.sdsu.edu/~rcarrete/teaching/M-596_patt/images/waterjet.jpg<br />http://www.aa.washington.edu/research/combustion/images/image008.jpg<br />http://www-rohan.sdsu.edu/~rcarrete/teaching/M-596_patt/images/waterjet_color.jpg<br /><br />So, yes, Barry, I'm quite sure these really are formations of droplets, not glints from oscillations of individual droplets, although the latter certainly will modulate (to varying degrees) the intensity of the brightness of each droplet in the photo.<br /><br />That being said, I can not explain all of the details in the image under question, particularly questions like why some of the tracks are long "dashes" whereas others are short drops, why some are pointed in different directions (...are they really droplets that have bounced), etc.<br /><br />This was definitely a good fun thread and great conversation. Let's hope that with the removal of the old off-topic section, the powers-to-be feel this thread has sufficient photography content so that they don't pull it for being more related to physics and engineering. <br /><br />Cheers,<br /><br />Tom M</p>

<p>This is not only a remarkable phenomenon, but also a very excellent discussion. It is clear that we really are seeing (in Barry's photo) strings of droplets (droplets of different sizes and velocities), and that they appear as dashes of varying lengths because their motion is not absolutely "frozen" by the shutter. A very, very fast shutter would not show the "dash" effect but would render strings of droplets, each droplet flexing to achieve the lowest total surface area consistent with the "Rayleigh instability" mentioned by Mann,<em> i.e.</em>, that the drops are "trying" to achieve a perfectly round shape because that would represent a lower energy level than elongated droplets would--but this only occurs only after instabilities are produced by undulations in the original "rod-like" stream of the fluid in question (water in this case).</p>

<p>The trails produced by the moving droplets are spaced differently in part also because some droplets really are leaving the point of impact at higher velocities than others, but they are still discrete droplets. Yes, of course, hydrogen bonding between O and H atoms across water molecules is producing the surface tension, but the role of hydrogen bonding in creating surface tension--and droplets in the first place--is a given and not controversial or in question.</p>

<p>What is quite astonishing to me is that, although we have only relatively recently been able to see what is going on with modern high speed cameras, the "Rayleigh instability" cited just above by Tom Mann is nothing new, with theoretical foundations going all the way back to 1873 or so--almost one hundred fifty years. (See again the link provided by Tom Mann: <a title="Link added by VigLink" href="http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability" rel="nofollow">http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability )</a><br /> <br /> I am not suggesting that no breakthroughs in fluid dynamics have occurred since the late 1800s, but Barry's basic quandary (and our own--with the exception of those above who have done work in this area and who instantly knew without question that, yes, these were indeed streams of discrete droplets) could be explained remarkably well by insights gained by Rayleigh so long ago.<br /> <br /> How many photography sites are going to have discussions such as this? It is threads such as this--and the remarkable number of highly trained and intelligent contributors who seem perpetually ready to jump in and explain such things to the rest of us--that give me renewed faith in this site.<br /> <br /> <strong>AH, PHOTO.NET, WE LOVE YOU!</strong><br /> <br /> --Lannie</p>

<p>I finally decided that I just had to try taking photographs of water drops from a spray bouncing off skin in order to hopefully see more clearly what is going on. The attached photo shows the back of my hand under a water spray formed by a single jet. The flash duration was approximately 1/40,000 s (provided by an old Sunpak 611 flash at 1/128 power). Rather than clearing up what is going on, it shows the complexity of mechanisms involved. Smaller drops appear to bounce off readily, while larger ones appear to slow on impact and are either shed as jets, which in turn break into drops, or form a film that drips from my bottom knuckle. I am afraid that this photo does not help much in clearing up the the original poster's question, but it does show that a lot of interesting phenomena are going on.</p>

<p>Tom: we may well have crossed paths at a conference or two a couple of decades ago, but remembering details of conferences I attended, let alone whom I met, has faded into the dustbin of memory.</p><div></div>

<p>And here is a close-up cropped from the above image.</p><div></div>