How “hydrophobic water” and silicon oil are being used to study quantum mechanics

Image courtesy: NIH Publications

Water drops floating on water may be the queeriest thing youve ever heard, but this isn’t as queer as it might sound, in fact this phenomenon occurs all the time! From raindrops falling on puddles to the coffee that you might be drinking while you read this!

Source: Destin Sandlin

It looks like water itself is hydrophobic! But how can that be? And if you’ve experimented with this before, you must’ve noticed that it is easier to create this phenomenon when the solution has soap or detergent in it. But what could be connecting all these ideas? there must be some inner mechanism that were overlooking here.

When a droplet of liquid falls onto the surface of the same liquid, instant coalescence, i.e mixing into one liquid, is expected, but in certain conditions these water droplets float on the water surface for some time before coalescing into it. And for how unexpectedly common this phenomenon is, renowned physicists, including, Reynolds, Mahajan, Hazlehurst and Neville all took their chances at putting forth hypotheses to explain the weird phenomenon, but back then a deciding onto a particular hypothesis was no possible.

How ever scientists, over the years, have been able to come up with a fairly simple idea to explain it! Lets look at a short video clip to get see what’s actually happening

The water droplet doesn’t immediately coalesce, instead it bounces in the spot for some time, called the residence time, before forming a water bridge and coalescence. Scientists believe the formation of air cushion, or trapped air as shown in the picture shown above, which slows down along with bending the surface of water the tension of which, acting like a rubber band, pushes the drop back again until its velocity reduces and coalescence to be the reason for this. As the air slowly seeps out after successful bounces and decrease in the velocity of the water ball, the two surfaces come in contact really, quickly forming the water bridge that we see in the video! Though this theory was initially opposed by some scientists like Mahajan, it has been proven under extensive researches. One research paper published by the National Institutes of Health verified this theory by lowering the pressure around the experiment which led to lower residence times.

Though the idea of air acting as a cushion may sound preposterous, it can actually be demonstrated with a similar experiment! Attaching a speaker below the water to create standing waves can help us understand this to a much deeper level. As the water droplet now falls on the standing wave formed on the water surface, two things might occur (on a broad aspect) it may either fall on: the crest, the convex part of the surface or the part that is bulged outwards, or the trough which is the concave part or the part that bulged inwards. When it falls down on the trough as the water surface is pulled backwards, due to tension. It is like the water surface just catches the water drop.

water droplet being slowed down (“catch”) by a trough

Here’s an example to help you understand it better: If you were to catch a water balloon, what would you do? you would try to pull you hands backwards to match the velocity of the water balloon so it doesn’t burst right? This is exactly what happens here, as the surface goes down forming a trough, its velocity almost matches that of the water droplet falling, resulting in a collisional kinetic energy (the energy due to movement in a collision) which is measured by this equation:

As the velocity of the water droplet almost matches that of the water surface and they are in the same direction (i.e the droplet falling into the trough), the third term in the equation approaches zero, leading to a lowered CKE value that cannot cut the air trapped to ~100 nanometers which is the minimum distance it would require for it to coalesce, but if the water droplet falled on the crest:

water droplet coalescing on hitting crest

The velocities add up as they are in opposite direction, leading to a high enough CKE value to cut thorugh the air cushion and hence the water droplet coalesces the moment it hits the surface. Just like the water balloon would if you, instead of pulling your hands towards yourself, forced it towards the water balloon!

For the very same reasons as discussed above, the collisions and gravity fit in the system in a manner that once a droplet falls on a trough, it interacts with, both, the standing wave being created by the speaker and the smaller wave created with its interaction with the water surface to bounce off just the right way to fall into another trough, as long as its movement remains synchronised with the wave, thereby reducing its chances of coalescence:

movement of the water droplet through troughs

These droplets are called “walkers,” as it looks like they’re walking around on the water surface. But it doesn’t just end here! A recent study conducted by Daniel M. Harris and John W. M. Bush studied silicon oil walkers under an exactly similar set up found that this could be used to replicate many quantum mechanical phenomenon even though the objects being used here fall in the range of classical physics.

One of the core ideas of quantum mechanics comes from Young’s Double slit experiment: if you send a beam of electrons at a pair of slits laid in front of a screen, the electron, instead of behaving as particles, behaves as waves leading to a interference pattern on the screen in front. When walkers put into a similar set up, the pilot wave, the wave caused due to the interaction of the droplet with the surface, passes through both of the slits but the droplet passes through just one, but they interact with the slits in such a way that the resultant distribution formed on the screen looks very much like the one from Young’s double slit experiment:

This was a remarkable physical representational of a postulated put forth by De Broglie nearly a century ago, he postulated that every object has a wave created by their tiny oscillations that accompanies them and guides their motion, just like the droplet creates the wave interacting with the standing waves on the water surface that eventually influences the motion of the droplet.

Another application of De Broglie’s hypothesis can be seen in a more mind boggling finding that these walkers exhibit quantisation. The complex interaction of the droplet with the waves leads to a very chaotic movement, when observed over time, it begins to display patterns:

Whats astonishing is how well it represents the probability density of an electron in a Quantum system (atom)!

But does this mean this is how the motion of quantum particles are governed? Well, no but this can be a possible dynamics that may contribute to the statistics as observed in the quantum mechanical theory. This simple contraption expresses the mere beauty how things in nature can be used to explain each other, and is perhaps one of a handful examples where classical objects display quantum properties.

Hello there! I am Ahitagni and I love math, physics & cheese!

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