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I was in the shower one day washing my hair, and noticed that the water falling off my hair formed perfect streams that ceased to break into droplets for quiet some distance (probably about 5-6 cm). I have kinda long hair so that greatly aided in the formation of the streams. I decided to see what would happen if the stream collided with a relatively flat perpendicular surface. I put my finger under the stream and was pleasantly surprised to see ripples upstream of the "impact". I then decided to move my finger up and noticed that these ripples became increasingly pronounced and seemingly formed a "wave". When very close to the origin of the stream (my hair) they began to turn into spherical beads. I decided to film the phenomenon to show you guys, and further below I have some theories as to what may be happening.

https://www.youtube.com/watch?v=4QVGvU1xubU

One theory I had was that the ripples are caused by a longitudinal wave traveling up stream, and since the compression zones are in water, they manifest as high pressure zones that cause the stream to bulge outwards as the surface tension holding the stream together is fairly flexible. The wavelength is most likely dependent (either directly or indirectly) on the speed of the falling as when I use faster flowing streams the wavelngth is a lot shorter, possible due to the faster impact. This may also be why when the impact is near the origin the stream begins to bulge more dramatically as the wavelength is a lot shorter due to the water not accelerating from free fall for as long and colliding with less force.

Another theory I had as to why the wavelength changes with finger height is that as you move down the stream since the water is moving a lot faster and the differences in speed become greater between the individual particles the water begins to decrease in density (thing spaghettification near black holes). If this does occur I don't believe it is as strong of a factor as the stream thins as it falls. This shows that rather than the spaces between the particles growing and remaining, they more likely come back together and instead manifest as the thinning of the stream.

If the cause is by both states above I may be able to formulate the density of the falling water based on the wavelength, but this is just a loose thought I have and needs more support.

I may be able to figure out if the cause is speed by looking at whether the wavelength changes as a parabolic function of finger height (as the impact speed and does, and this would possible show they're linked) but this would only be the case if impact shock waves wavelengths were linearly proportional to the impacts impulse. I would love to hear what you guys think of this idea.

My final, weaker theory I had was that the ripples are caused by the surface of the water attempting to establish a smooth transition onto the perpendicular plane, and as it curves outward, it causes a bend in the opposite way upstream which therefore causes another bend opposite to that until it smoothens out. I attempted to crudely illustrate this below.

enter image description here

These are lose thoughts that came to mind to support the theory, and am eager to get any feedback and share any results with you guys. If you have a completely new theory or disprove my theories please post them below, any information may help bring this question to a close.

I'm currently doing a physics extended essay, and am willing to drop my current essay for something related to this phenomenon as it seems very interesting and would be pleasure writing about.

EDIT: A friend proposed that the waves are propagated from small currents resulting from the bottles/taps shape or the hole shape. I tested this using a uniform bowl and drilled a hole in it instead of poking one to get a more uniform hole and got identical results.

23scurtu
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2 Answers2

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I reckon I'm going to get lit up like RoboCop because of this post but here we go:

I think the apparent separation of the water into droplets the higher up you go is caused because of two reasons: gravity and the cohesion/adhesion of water (also see Van der Waal forces).

Essentially, the cohesive/adhesive forces are responsible for keeping the water droplets stuck together as droplets, and even sticking to other things like the underside of your finger or (rather annoyingly) the side of a water pitcher when a waiter is trying to refill your glass.

Because these forces are really weak, we only see them at very short distances, and even a force as weak as gravity can easily disrupt them:

When your finger is far from the source, the falling water droplets have a greater potential energy (PE= Gravity x Mass x Height), and thus far too much energy to survive the impact on your finger, and get torn up and splashed about with little care for the cohesive force.

Gravity wins.

However, when you raise your finger toward the source, the distance that the water droplets fall is reduced, and the thus the water has a lower potential energy.

Because of this shorter distance, the droplets don't have enough energy to completely splash off your finger, and instead they have to compete against the cohesive/adhesive forces keeping them bound together. As you bring your finger higher and higher, we start to see the effects of surface tension more and more clearly.

When you get pretty high up the stream starts to form almost complete droplets due to LaPlace's Law, and they seem to be able to even stack up on on top of one another. I also believe the kind of odd separation of the droplets is due to a pressure wave (At least it looks that way after watching "Surface Tension Droplets at 2500fps - The Slow Mo Guys" on Youtube and seeing the exact same pattern you described!).

Cohesion wins.

EDIT This might have been too simple an answer (if I even answered your question) for what you're going for, sorry for my noobery. I do believe the separation of the drops themselves is due to a pressure wave resultant from the water droplet's impact, they just don't separate completely because there's another drop crashing down on them before they can split up.

EGreen
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  • I get that when my finger is near the top there should be less energy in the droplets and thus they are able to form droplets, but I don't get how the "periodic" structure of the droplets are formed. If left alone the water will stick, but in your proposition, how do you think cohesion accounts for the periodic structure? Reading this reminds my a lot of the last theory I proposed where surface tension causes a ripple pattern as a propogation from it bending to conform to the perpendicular plane. Btw, all perspectives are appreciated :D – 23scurtu Aug 17 '15 at 01:32
  • P.S. My last theory, I don't know if I explained it well, but think of bending a metal sheet so that it forms a sinusoidal pattern. That pattern is formed from your hand forming the first bend, and the other bend in the opposite direction is a result. – 23scurtu Aug 17 '15 at 01:34
  • Hmm that's a great question! I'm honestly not sure, sorry. I think it could be the trisection of gravity, surface tension, and LaPace's law. Maybe at the longer distances the droplets have more energy, and can only sustain smaller droplets? There's gotta be an equation somewhere, I'll keep searching... – EGreen Aug 17 '15 at 01:39
  • I think the rarefaction of the pressure wave would explain the separation. In the Slow MO Guys video you can see the wave move and separate the drops! – EGreen Aug 17 '15 at 01:47
  • Do you think you could link the video? cant seem to find it :/ – 23scurtu Aug 17 '15 at 01:48
  • https://www.youtube.com/watch?v=ynk4vJa-VaQ it wouldn't let me link my post! – EGreen Aug 17 '15 at 01:49
  • Oh my, yes I see what you saying. For a brief moment, the falling drop pops up sending a wave up that water "cylinder" reminiscent of the ones I created. So impact could very well be the cause, only question now is how the wave stays so steady for each height. – 23scurtu Aug 17 '15 at 01:56
  • It's most likely due to the consistent flow, but that fact that each speed ad height has its own wave is remarkable. In fact, this reminds me a lot of resonance. Maybe every falling speed has a specific resonance which corresponds with the impact, and that wave shows through. – 23scurtu Aug 17 '15 at 01:57
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Suppose in zero gravity you squirt a smooth stream of water from a nozzle. A cylindrical tube of water with surface tension is not a minimum energy configuration. Spherical drops are minimum energy.

The cylindrical tube is a metastable state, like a ball perfectly balanced on a point. Any slight variation from a perfect cylinder will be increasingly amplified as it grows, and you end up with spherical drops. (I wonder if the astronauts have tried this fun experiment?)

I think this explains what is going on even with gravity. It does not directly explain why you get regular periodic ripples, although I think there are theories about this.

Keith McClary
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  • Mmm, spheres may be the minimum energy configuration but when shot with a velocity I think water from a nozzle is more likely to conform to a cylinder rather than spheres. I say this because water shot from a nozzle is somewhat extruded and guaranteed to come out as a cylinder intially, from that point the water should just continue this cylindrical shape through cohesion. Eventually it should turn back to spheres but that happens on earth too, all the streams I created turned to drops further down. – 23scurtu Aug 18 '15 at 00:51
  • I found this video showing the same effect in space: https://youtu.be/o8TssbmY-GM?t=1m41s – 23scurtu Aug 18 '15 at 00:52
  • I think it needs a change to turn to drops even though they are a lower sate, like you said its like a balancing ball. The forces required to tip it need to be great enough that they in fact only manifest a good distance along the stream ( in the video about 10 cm) – 23scurtu Aug 18 '15 at 00:54
  • These ripples only happen during a collision with a relatively perpendicular surface. Are you saying that this collision attempts to induce the waters minimum energy state? – 23scurtu Aug 18 '15 at 01:00
  • @23scurtu No, I think the cylinder of water has started to form thinner and thicker regions along it's length, but it hits the surface before it has time to break up into droplets. – Keith McClary Aug 18 '15 at 06:17
  • But wouldnt the act of those regions climbing as I raise my finger suggest it to be dependent on the collision/mergence of it? If that were the case, the thickness doesnt change when I raise my finger so should the point where it begins to turn to drops and wave regions remain constant? – 23scurtu Aug 19 '15 at 07:32
  • Sorry, I misunderstood what you were saying. I tried it myself and noticed that I get the effect if I touch the stream with a single hair. The waves also appear downstream from the hair, but do not grow rapidly as my argument would suggest. When I Search Google Images for FLUID THREAD BREAKUP I don't see anything that looks like this. From the abstract of Break-up dynamics of fluctuating liquid threads my theory only covers a special case. – Keith McClary Aug 19 '15 at 15:45
  • @23scurtu I started a related thread on Physics Forums. – Keith McClary Aug 21 '15 at 05:26