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).

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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.

Note on average density and why ships do not sink

Floating on the dead sea

Let’s ask a very generic question: I hand you an object and ask you to predict whether the object would float or sink. How would you go about doing that ? Well, you can measure the mass of the object and the volume of the object and can derive this quantity called Average Density (\rho_{avg} )

\rho_{avg} = m_{object}/V_{object}

It is the average density of the entire object as a whole. If this object is submerged in a fluid of density \rho_f , then we can draw the following force diagram:

If \rho_{avg} > \rho_{f} , we note that this generic object would sink and if \rho_{avg} < \rho_{f} it would float!. Therefore in order to make any object float in water, you need to ensure its average density is less than the density of the fluid its submerged in!

Why does a ship stay afloat in sea?

A ship is full of air! Although it is made from iron which sinks in water but with all the air that it is full of, it’s average density (m_{ship}/V_{ship} ) drops down such that \rho_{avg-ship} < \rho_{sea-water} .

Fun Experiment:

If you drop some raisins in soda, you will notice that they raise up and fall down like so (Try it out!):

Source

This is because air bubbles that form on the top of the raisin decrease its average density to the point that its able to make the raisin raise all the way from the bottom to the top. BUT once it reaches the top all the air bubbles escape into the atmosphere (its average density increases) and the raisin now falls down.

Questions to ponder:

  • Why do people not sink in the dead sea ?
  • How are submarines/divers able to move up and down the ocean ? How would you extend the average density argument in this case.
  • Why do air bubbles in soda always want to raise up ?
  • If the total load that needs to on a ship is 25 tons. What should be the total volume of the ship in order to remain afloat if the density of sea water is 1029 kg/m3,

Powering a 13W CFL light bulb using a 3V battery

Recently I stumbled upon this cheap high voltage converter on Amazon which claims a boost from 3-6V to 400kV. Although really skeptical about the 400kV claim, a lot of comments indicated that it did boost atleast to 10kV so I got one of these to test it out.

Schematic diagram for lighting up a CFL using the high voltage converter
Using a 1.5V battery to power the circuit
Using a 3V battery to power the circuit

And boom! There we go, that’s how you light up a CFL light bulb using a 3V battery!

If you do have access to a plasma globe or a tesla coil, things become a little bit more simpler:

Source

The way CFL light bulbs works is by exciting the electrons in the lamp and when they return to the ground state they radiate ultraviolet light. This emitted light is converted to visible light when it strikes the fluorescent coating on the glass.

So it really does not matter how you decide to excite the electrons to the higher energy state. It might be a high voltage converter, a tesla coil, a plasma globe, etc but all you need is a device that will kick those electrons inside the bulb from their ground state to the higher excite state. That’s all you need!

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:

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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.

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Hot air is less dense than cold air.

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

Light gets bent/distorted

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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:

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                  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:

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

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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.

The acoustic sweet spot.

The acoustic sweet spot is defined as the listening position equidistant to each of the two front channels as they are from each other, so the arrival time of the sound is equal at your ears.

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It was brought in the vogue of the public by the big bang theory where Sheldon cooper tries to find the sweet spot in a theater.

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Why is it important?

It is called the ‘sweet spot’ for a real good reason. 

In a motion picture, an image is considered to be ‘good’ if the location of the performers can be clearly located. This is known as stereo imaging and it adds realism to the image. 

The only person who hears this perfectly is the one who is in the sweet spot. ( no wonder Sheldon is obsessed with his spot! )

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At this juncture, it is highly recommended that you check out the virtual barber shop to experience the acoustic sweet spot for yourself. 

The virtual barber shop places you in the sweet spot and abuses sound technology to bring you this high-quality audio realism.

We will dive deeper once you are done with your haircut! Have a good day.

ISS is the third brightest object in the night sky!

It often comes as a surprise to people when i tell them that the space station can be seen with the naked eye! Flying at 400 km above your head, the ISS looks like a really fast moving airplane in the sky.

The ISS isn’t brighter than the day sky and hence cannot be seen during the day. But in the night, it’s the third brightest object in the sky! It reflects the sunlight off the solar panels on its surface.

Spot the station!

If you would like to see the ISS for yourself, NASA ‘s Spot the station! is at your disposal. Register with your email address/mobile number and every time the ISS passes by your town/city, you will get a notification with the time, duration and inclination.

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Have fun!

(Extras: There are mobile phone apps which you could use too, like the ISS detector satellite detector for android. At the end of the day all that matters is what is convenient to you.

ISS tracker– Real time tracking of the ISS)

Baffling Polymer Balls Behavior

I was fascinated by the polymer balls so i went to the shop to treat myself with one. As i was exploring these balls, this bizarre behavior caught my eye.When you immerse these colored polymer balls in water, they seem as if they are 2-d objects although they are spheres! Crazy right?

If you liked this and want to read more about polymer balls and the physics that underlies it, do check out:

Physics of invisibility.

Why is glass transparent?

Have a great weekend!

The Miura Fold

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The Miura fold is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Koryo Miura.

Why it is awesome?

The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat.

This property allows it to be used to fold surfaces made of rigid materials; for instance, it has been used to simulate large solar panel arrays for space satellites in the Japanese space program.

The fold can also be unpacked in just one motion by pulling on opposite ends of the folded material, and likewise folded again by pushing the two ends back together.

In the application to solar arrays, this property reduces the number of motors required to unfold this shape, reducing the overall weight and complexity of the mechanism.

Other cool stuff.

Miura folded maps. Snug it into your pocket when not in need and open it up in style when you are lost !

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(Source : http://www.bun-sho-do.co.jp/english/nextg/miura-fold/ , wikipedia )

Physics of the ballpoint pen

People often brag about Large Hadron Collider as having one of the most sophisticated Technology in the world. True, but even if you are living in France, it’s still inaccessible! I believe that accessibility is the true trait of technology.

Look around the place that you are sitting in. Do you see a Ball Point pen lying around in the vicinity? Chances are that it is, are really high. Today on FYP, we will unravel the modest physics that governs it.

The physics.

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Behold the ball in a ball point pen!.

To write you glide your pen onto the paper right? So what you are doing is rolling the ball that is present on the pen’s tip.

The ink flows continuously under the influence of gravity from the ink reservoir to the ball.

The ball rolls and the ink gets transferred onto the paper.

How does the ink stay inside the pen?

Put a drinking straw into a glass of water (or any liquid) and then put your finger over the top end of the straw so it’s air tight. You can now lift the straw out and the liquid will not fall out of the straw!

Now switch characters and imagine the liquid to be the ink and the straw to be the ink reservoir and voila!

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Fun Fact.

Rollerball pen and Ballpoint pens work on the same principle. They differ in the type of ink used. While Ballpoint pens have a thicker oil based ink, the rollerball uses a liquid ink, thus giving its fluidity.

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(Sources : http://home.howstuffworks.com/pen3.htm )

How does an eraser work?

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What happens when you write?

Although we call the black stuff in pencils “lead,” it’s not the real metal known as lead.It’s actually a mineral called “graphite,” which is made up of carbon. When you write with a pencil, graphite particles from the pencil rub off and stick to the fibers of the paper you’re writing on.

What do erasers do?

When you rub an eraser across a pencil mark, the abrasives in the eraser gently scratch the surface fibers of the paper to loosen the graphite particles. The softeners in the eraser help to prevent the paper from tearing. The sticky rubber in the eraser grabs and holds on to the graphite particles. 

The physics.

Erasers work because of friction.

As the abrasives in your eraser are rubbed against paper, friction produces heat, which helps the rubber become sticky enough to hold onto the graphite particles. As the rubber grabs the graphite particles, small pieces of combined rubber and graphite get left behind. That’s the “stuff” you brush off of your paper when you’re finished erasing. 

PC: 123rf