Flow(#2) – Plateau- Rayleigh Instability

When you wake up in the morning and open/close your faucet when you brush your teeth, you might have noticed that it undergoes a transition between a smooth jet to a dripping flow like so :

When the velocity of the fluid exiting the faucet is high, it appears smooth for a longer time before it breaks into droplets:

But when you make the velocity of the fluid exiting the faucet low, it seems to form droplets much earlier than before.

Here’s the water breaking into smaller droplets shot in slow motion:

Notice that just by changing the exit velocity of the water you can control when the droplets form.

You can also control the nature of the droplets that form by changing fluids. Here’s how it looks like if you use water as the fluid (left), pure glycerol(center) and  a polymeric fluid(right).

Source

What is causing a jet of fluid to form droplets?

A simple answer to this is perturbations on the surface of the fluid. What does that mean?

Initially the fluid is just falling under the influence of gravity. And velocity of any freely falling object increases as it falls:

But the surface tension of the fluid holds the molecules of the fluid together as they fall down.

Therefore depending on the initial velocity of fluid, the surface tension of the fluid and the acceleration you get a characteristic shape of the jet as it falls down:

This is what you observe as the fluid exits the faucet.

Perturbations

Just after exiting the faucet, there are tiny perturbations on the surface of this fluid as it falls down. This is apparent when you record the flow at 3000fps:

                                            Source: engineerguy

Those tiny perturbations on the surface of the fluid grow as the fluid falls down i.e the jet becomes unstable.

And as a result the fluid jet breaks down to smaller droplets to reach a more thermodynamically favorable state. This is known as the Plateau-Rayleigh instability.

                                              Source

It takes different fluids different time scales to reach this instability. This depends on the velocity of the fluid, the surface tension and the acceleration it experiences. 

And some viscous fluids like honey are also able to dampen out these perturbations that occur on their surface enabling them to remain as fluid thread for an extended time.

A note on inkjet printers

By externally perturbing the fluid instead of making the fluid do its own thing, you can make droplets of specific sizes and shapes.

This engineerguy video explains how this is used in inkjet printers in grand detail. Do check it out.

We started today by trying to understand why water exiting a faucet behaves the way it does. Hopefully this blog post has gotten you a step closer to realizing that. Have a great day!

Sources and more:

* This is a topic that is home to a lot of research work and interesting fluid dynamics. If you like to explore more take a look into the mathematical treatment of this instability here.

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How to photograph shock waves ?

fyfd:

This week NASA released the first-ever image of shock waves interacting between two supersonic aircraft. It’s a stunning effort, requiring a cutting-edge version of a century-old photographic technique and perfect coordination between three airplanes – the two supersonic Air Force T-38s and the NASA B-200 King Air that captured the image. The T-38s are flying in formation, roughly 30 ft apart, and the interaction of their shock waves is distinctly visible. The otherwise straight lines curve sharply near their intersections. 

Fully capturing this kind of behavior in ground-based tests or in computer simulation is incredibly difficult, and engineers will no doubt be studying and comparing every one of these images with those smaller-scale counterparts. NASA developed this system as part of their ongoing project for commercial supersonic technologies. (Image credit: NASA Armstrong; submitted by multiple readers)

How do these images get captured?

It may not obvious as to how this image was generated because if you have heard about Schlieren imaging what you have in your head is a setup that looks something like:

But how does Schelerin photography scale up to capturing moving objects in the sky?

Heat Haze

When viewing objects through the exhaust gases emanating from the nozzle of aircrafts, one can observe the image to be distorted.

Hot air is less dense than cold air.

And this creates a gradient in the refractive index of the air

Light gets bent/distorted

Method-01 : BOSCO ( Background-Oriented Schlieren using Celestial Objects )

You make the aircraft whose shock-wave that you would like to analyze pass across the sun in the sky.

You place a hydrogen alpha filter on your ground based telescope and observe this:

                  Notice the ripples that pass through the sunspots

The different air density caused by the aircraft bends the specific wavelength of light from the sun. This allows us to see the density gradient like the case of our heat wave above.

We can now calculate how far each “speckle” on the sun moved, and that gives us the following Schlieren image.

Method-02: Airborne Background Oriented Schlieren Technique

In the previous technique how far each speckle of the sun moved was used for imaging. BUT you can also use any textured background pattern in general.

An aircraft with camera flies above the flight like so:

The patterned ground now plays the role of the sun. Some versions of textures that are commonly are:

The difficulty in this method is the Image processing that follows after the images have been taken. 

And one of the main reasons why the image that NASA has released is spectacular because NASA seems to have nailed the underlying processing involved.

Have a great day!

* More on Heat hazes

** More on BOSCO

*** Images from the following paper : Airborne Application of the Background Oriented Schlieren Technique to a Helicopter in Forward Flight

**** This post obviously oversimplifies the technique. A lot of research goes into the processing of these images. But the motive of the post was to give you an idea of the method used to capture the image, the underlying science goes much deeper than this post.

Why do shower curtains encroach your showering space ?

You are all set to kick start your day with a shower; You open the faucet and notice that immediately the shower curtain starts to bulge in to your showering space (irrespective of whether its hot or cold water).

What on earth is happening here?

Shower- Curtain effect

In 2001, Prof.David Schmidt from the University of Massachusetts won his way to the Ig Nobel prize when he found out that the reason why the curtain bends is Vortices!

Let’s run through the logical theories to explain this effect:

Buoyancy effect :

Hot air raises and cooler air moves down, and this causes the shower deflection. True only for hot air, but doesn’t explain why the curtain deflects even for cold water.

Bernoulli effect:

Pressure in a fluid decreases as its velocity is increased. The fast moving water molecules in the shower causes the pressure inside the shower lower than outside.

Since this pressure is lower than outside, this pressure differential independent of temperature would cause the curtain movement..

                                                    Source

When Prof.Schmidt ran his simulation, he found out that the spray of water droplets from the shower formed a vortex with its axis normal to the plane of the curtain.

And the pressure at the center of this vortex was lower than those predicted by either effect separately or combined:

                 Pressure plot

 Velocity vectors of air molecules in the shower. (Notice the circulation of air)

   Result : The deflection of the curtain

And now we understand that the major contributor that causes the deflection of the curtain is the vortex. But we are still in the dark when it comes to a theory to explain the Shower-curtain effect (A fun research project if anyone is interested).

The next time you step in to take a shower and become furious about the fact that the damn curtain is encroaching all your showering space, just know that a IgNobel was awarded and many research articles published in trying to find an answer for your frustration.*

Physics is life, Have a good one!

* or get a shower weight / a heavier curtain that would prevents this from happening.

Source: web.archive.org

fuckyeahfluiddynamics:

As a child, I loved to ride in the car while it was raining. The raindrops on the window slid around in ways that fascinated and confused me. The idea that the raindrops ran up the window when the car moved made sense if the wind was pushing them, but why didn’t they just fly off instantly? I could not understand why they moved so slowly. I did not know it at the time, but this was my early introduction to boundary layers, the area of flow near a wall. Here, friction is a major force, causing the flow velocity to be zero at the wall and much faster – in this case roughly equal to the car’s speed – just a few millimeters away. This pushes different parts of large droplets unevenly. Notice how the thicker parts of the droplets move faster and more unsteadily than those right on the window. This is because the wind speed felt by the taller parts of the droplet is larger. Gravity and the water’s willingness to stick to the window surface help oppose the push of the wind, but at least with large drops at highway speeds, the wind’s force eventually wins out. (Image credit: A. Davidhazy, source; via Flow Viz)

Amazing.. I tried it at the Freeway the other day and look at the traveling wave pattern that it generates:

Thanks @fuckyeahfluiddynamics​!

Throwback Mondays: Pilot Wave Hydrodynamics

Two months ago, FYPhysics! in collaboration with FYFD on Tumblr dedicated an entire series exploring Pilot wave hydrodynamics. (You can check it out here)

And from one of the posts we learned that when you blow air through a nozzle at a water surface, you can see a circular wave propagating outwards.

BUT when a vibrational excitation is given to this propagating wave, that wave is split into two traveling waves moving in opposite directions – One towards the source ( called time-reversed waves ) and one away from it.

Now this paper by Bacot ,et.al takes this to the next level by positioning these nozzles in the shape of an Eiffel tower.

Now when one changes the effective gravity through a vibration, the time-reversed waves refocus at the center giving us back the Eiffel tower structure.

The group was also successful in refocusing a smiley face using the same principles which is equally mind blowing. (You can watch the video here)

Have a great week

Chaotic pendulums

fuckyeahfluiddynamics:

A wall of lava lamps in a San Francisco office currently helps keep about 10% of the Internet’s traffic secure. Internet security company Cloudflare uses a video feed of the lava lamps as one of the inputs to the algorithms they use to generate large random numbers for encryption. The concept dates back to a 1996 patent for a product called LavaRand. The idea is that using a chaotic, unpredictable source as a seed for random number generators makes it much harder for an adversary to crack your encryption. 

With lava lamps, a lot of that chaos comes from the fluid dynamics involved – without perfect knowledge of thousands of variables, it would be impossible to simulate the lava lamp wall and get the same outcome as the real one – but there’s also randomness that comes from the measurement. People walking by, shifts in lighting, and random fluctuations of individual pixels all help make the video feed unpredictable. For those interested in the details of how Cloudflare uses their lava lamps, the company explains things for both technical and non-technical readers. You can also check out Tom Scott’s video for a good overview. (Image and video credit: T. Scott; submitted by Jean H.)

                                      Chaotic double pendulum

In addition to the Lava lamps, in it’s London office Cloudflare uses a
chaotic  pendulum with three arms that twist and turn together to
generate random numbers. 

Randomness from radioactive decay

A Geiger counter is a device used for the detection and measurement of all types of radiation: alpha, beta and gamma radiation.

When the counter detects a high energy particle, it creates an electric current. This current is amplified by electronic
circuitry, creating a crackling sound. 

           USB Geiger counter(amazon)

In Cloudflare’s Singapore office, a pellet of uranium encased in a glass
bell jar has its radiation monitored using a Geiger counter.

By monitoring how many counts are generated in a certain time, you can also generate truly random numbers.

Pilot Wave Hydrodynamics: Series Wrap-up

This week FYP in collaboration with FYFD brought to you an exclusive Tumblr series.on Pilot Wave Hydrodynamics. In case you had missed it out, here’s an overview:

1) We started with Chladni & inverse Chladni patterns – Basically normal modes of vibration on a plate with a subtle twist.

2) But what happens if the vibrating medium was water? This lead to a discussion on  Faraday instability;

3) Along the way, we discovered that at the right excitation, droplets placed atop a vibrating bath could be made to walk & bounce.

4) Using many of these bouncing droplets one could form extremely stable complex lattices

5) Then we started to subject the system to quantum experiments such as the single and double-slit experiments,

6) And found that they formed similar diffraction and Interference patterns with the bouncing droplets as well..

                                                   Source

7) Maybe it was luck, so we tried quantum tunneling.

8) But even that was reproduced on the macroscopic scale using these bouncing droplets

             

9) Absolutely fascinated by what we had seen thus far, we then explored Pilot wave theory in its raw essence and its potential as an interpretation for Quantum mechanics

10) Hoping that this fascinated you, we left you with a treasure of useful resources to aid you in your ecstatic adventure. 

We hope you enjoyed this journey that spanned almost two centuries’ worth of scientific discoveries, feel free to share with us your thoughts, comments, and questions on this series.

Have a great weekend!

– FYP! & FYFD

“If you place a small droplet atop a vibrating pool, it will happily bounce like a kid on a trampoline”. And when lots of these droplets are placed in a lattice, their behavior as a collective is absolutely fascinating.

In this series of gifs, you can see the evolution of complex lattices from simple droplets eventually leading to an instability that drives them apart.

Now a key thing to note is that when you have 7 droplets, you will not obtain a hexagonal lattice configuration per se. Those lattices had to be obtained artificially but can be very stable after they are formed.

Source: Archimedean lattices in the bound states of wave interacting particles

The key point of distinction when one talks about lattice in this vernacular is that in solid state physics, a crystal lattice is the depiction of three-dimensional solid as points.

And one obtains these crystalline solids through crystallization.

In contrast, when we are talking about lattices in pilot wave hydrodynamics, they are formed by the standing waves of the bouncing droplets.

In the upcoming posts, we will take a dive into some quantum mechanical experiments and their pilot wave hydrodynamic counterparts.

In case you had missed out, here are the previous posts on this collaborative series on Pilot wave Hydrodynamics with FYFD : 1) Introduction; 2) Chladni patterns; 3) Faraday instability, 4) Bouncing droplets

Water spirals are absolutely magnificent

This gif from one of the Slow mo guys videos is extremely fascinating. Water spirals have been of considerable research interest in Fluid Dynamics and as it turns out the gif is only a mode of ejection for the water.

Here are the other modes:

These are dependent on the angular velocity of the sphere The sphere is rotating
clockwise with an angular velocity of (a) 84, (b) 137, © 357, and (d)
406 rad/s.

And as one keeps increasing the angular velocity, the stability of the sheet is destroyed and the fluid ejects as small droplets from the equatorial region.

Source: Langley, Kenneth &
Maynes, Daniel & Truscott, Tadd. (2015). Eggs and milk: Spinning
spheres partially immersed in a liquid bath. Physics of Fluids. 27.
032102. 10.1063/1.4913574.

Impact of a laser on a drop

In this amazing work by the Fluids group at University of Twente, a drop’s response to a focused laser pulse has been analyzed in slow motion. The drop reacts to the energy imparted by the laser in many different ways, such as
vaporization or even plasma generation.

Tightly focused laser beam leading to a white plasma glow and a violent ablation from the drop

This extremely violent reaction propels the drop to several m/s before it explodes or breaks up. Now what cool applications can you think for this ? Let us know!

                    PC: xkcd      

Learn more at:

Physics of Fluids Group University of Twente

Laser Umbrella – What if? by xkcd