# 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).

## 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.

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

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!):

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.

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:

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!

# Which would fall first in vacuum: A feather or a ball?

If you take a feather and a ball, and drop them simultaneously from your hand or from the top of a building what would you observe? Obviously the ball drops faster than the feather. But why?

Air resistance is the result of air molecules bombarding onto the object as it moves through the layer of air. The feather offers more air resistance and hence it falls slower.

Now you can up the ante and ask what if you remove the air resistance?

If you remove all the air molecules from the air,you would just get vacuum, a space devoid of any matter. With no molecules to bombard the object,

The feather and the ball would fall at the same rate as you can see in the animation. The demonstration was carried in the world’s biggest vacuum chamber.

( Extra: The same demonstration, but this time done on the moon :

Have a good day!

# 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.

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!

## 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.

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