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I mentioned in passing in a previous video that I could get good laminar flow from my kitchen taps, which is nice
But I also noticed something really strange recently
Not just from this particular kitchen tap, but from any laminar flow really coming from a faucet. Watch this.
Look what happens when I put my finger into the stream of water.
I get these ripples above my finger
Look as I move my finger down the ripples get tighter
And as I move up the ripples get broader
Strange
My kitchen isn't the best environment to investigate this sort of phenomena. So I set something up in my studio
I really wanted to see if we can figure out where these ripples come from
But I also wanted to capture a really good example of it
The first thing you need is you need that flow of water to be really stable
Really consistent I managed to achieve that with this funnel and just some cloth over the bottom of it
You get this beautiful laminar flow from this setup a lot of other considerations as well. But look, let's just see what we got
Isn't that amazing. As soon as the obstruction goes in those standing waves just suddenly appear
It seems like further downstream. The ripples are tighter. Then as you move up the stream
They get wider. Look at that. So cool. Is that a standing wave? What is it?
I also noticed that there are sweet spots like if the obstruction isn't in quite the right place you get these
Vibrations, but where do these ripples come from? Well for one thing you definitely need laminar flow
I've mentioned that a couple of times
I've not really said what it is, but imagine this imagine you've got a column of water like we have and
It's all streaming downwards, but the water is traveling at different speeds
So maybe on the inside the water is traveling more quickly than on the outside and with laminar flow
you don't have any interaction between those layers of different speed they just kind of
Slide past each other. If water was transferred between those layers of different speeds
Then you'd end up with turbulent flow which is like the opposite of laminar flow
You can see it really well with the smoke from a candle
So to begin with the smoke rises through the still air around it, but doesn't interact with it at all
But eventually it catches if you like on the air around it and creates these turbulent
Spinning twisting motions. I've done a bit of research and there doesn't seem to be much literature around these ripples above an obstruction
But I have found a clue and that cure is the Rayleigh-Plateau
Instability which is a fancy name for
Something you've probably seen many times before if you turn your tap down until it's just a fine stream eventually
You'll see it breaking into droplets and that moment that it breaks into droplets
That's Rayleigh-Plateau instability. But the cool thing is if you take a freeze-frame of that happening
It looks like this look at those ripples very similar to what we're getting here
interesting application of the Rayleigh plateau instability is if you've got a jet of fluid hitting a surface and you want to reduce splash back
Simply reduce the distance to the surface until you remove all instability
But why is it that you can only see those ripples in freeze-frame you can't see them with the naked eye
It's because they're moving around they're moving up and down the stream as time goes on
It's too fast for you to see so maybe when you obstruct the flow of the stream
You're generating the ripples at that point, but you're fixing them in space somehow
I've got a theory for how that might happen
But where are the ripples come from in the first place in the Rayleigh-Plateau instability?
Well, there is literature on that and it's all to do with surface tension
You can think of the surface tension of water as like an elastic property that the water has on its surface. So
How's it gonna behave? Well think about an elastic band mean you stretch an elastic band
It pulls itself in. An elastic band tries to minimize its length, and it's similar with
elastic surfaces, they try to minimize their area and
This is also true of soap film
so when you blow a bubble it encapsulates a
Volume of air and it slowly kind of wobbles into its preferred shape
Which of course is a sphere because a sphere is the lowest surface area that can enclose a given volume
And it's also why droplets of water
Forms spheres, but what does this mean for a column of water like we have here?
Well, we can actually model it with soap film
How does a cylindrical soap film minimize its surface area? Look as the cylinder grows in height
the soap film starts to bow inwards
This is always the minimum surface area
If it was more pinched to the surface air would be greater
if it was less pinched the surface air would be greater as well and as
The cylinder grows in height that bowing inwards grows more pronounced
Anyway, it gets to the point where it pinches all the way in and it separates into two
separate soap films a bit like the formation of a droplet of water
How does that apply to a column of water?
Like why do the ripples appear in the particular location that they appear and why are they the size that they are?
Well the ripples grow from tiny
Perturbations in the otherwise very smooth flow of water and they grow like this imagine that you've got some ripples
That are kind of sinusoidal
so you've got some pinch points and you've got some bulge points like this and here's an interesting fact about
elastic surfaces if an
Elastic surface is tightly curved. Then the pressure inside will be great
whereas if the elastic surface is
Loosely curved the pressure inside will be less and you can apply that to these bulges here
So look at the neck here, you've got a tightly curved
Elastic surface, so the pressure inside is very great. At the bulge, you've got a loosely curved surface
So the pressure is less that means that the neck will squeeze water into the bulge and you will have this growing ripple
Except it's a little bit more complicated that because the curvature at the pinch points
it's actually a saddle point and
saddle points are a bit more complicated a good example of
Saddle point is a Pringle crisp
So you've got a curve going this way and you've got a curve going that way like it like a saddle essentially
But look imagine that this is a little section of our pinch point. You've got the inside curve here
That's generating pressure inside but then you've got this this is actually a negative curve. It's going the other way
So it's reducing the pressure inside the neck. So it's actually not clear who's gonna win the fight
Is it the the Bulge that has like both curves of the curve in this direction the curve in this direction?
They're both adding to the pressure inside. But look at this curve here. This curve is going the other way
It's a negative curvature and it actually reduces the pressure inside
So there's a balance between those two effects and it turns out that who wins the fight
Depends on the wavelength of the ripples
so with those short wavelength ripples that the Bulge is gonna win the fight and they're just going to disappear but with
longer curvature ripples where the external curvature is lower
Then the the pressure inside the neck is going to win and the pinch point is going to get greater and greater
It's those bulges that are going to grow. It's that optimum wavelength that you're ultimately going to see
So there's got to be a link between this Rayleigh-Plateau Instability
and the ripples that we're seeing when we obstruct the stream of water
My thinking is this when you put your finger into the stream
you're forcing the water to bow out at that fixed point and it's a bit like a
Standing wave in wave mechanics. So you've got a kind of boundary condition
so in wave mechanics a boundary condition is when you fix a certain point like on a guitar string one end is fixed as you've
Got two boundary conditions. Both ends are fixed and that forces a
Standing wave in the vibrations of the guitar string and in a similar sense here
you're saying look we're forcing an anti-node
At this point and the rest of the wave is gonna grow
Upwards from that point like a standing wave on a guitar string. That's my theory anyway.
I love investigating these sorts of things just for their own sake really like I'm sure nothing useful will ever come of it
but I actually think curiosity for curiosity's sake is important because
some of these investigations do turn out to be important like the Rayleigh-Plateau instability is really useful for
Making printers work like inkjet printers and all sorts of other applications actually bizarrely
Even black holes like some physicists are investigating
what black holes look like in the extra dimensions of string theory and
they're modeling it as what they call black strings and it seems like these black strings are unstable in a similar way to
streams of water and
They're gonna break up into like black hole droplets like the Rayleigh-Plateau droplets really interesting stuff
This video is sponsored by Squarespace
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