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What is common between drops in a cup of coffee and quantum mechanics?

This is a special section of the ITMO New Physics Institute . Here, scientists, teachers and students of the Faculty of Physics and Technology reflect on science, the educational process and workdays.



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A drop falling on the surface of a liquid disappears quickly, but not instantly. The confluence of the droplet with the liquid is delayed due to air leaving the intermediate layer. The effect can be seen in the fountain, sink in the kitchen and even a glass of coffee .

Drop in a cup of coffee

When the drop approaches the surface of the liquid, the air in the intermediate layer does not have time to go outside. The pressure increases, the drop loses its speed and may even bounce up. But each time it jumps lower and lower, as part of the energy is dissipated due to the influence of external forces. More and more air comes out of the intermediate, and when its thickness becomes critical, the water ball merges with the liquid due to the forces of molecular interaction.

How to make drops jump


An interesting fact is that a drop can be made to jump if the lost energy is continuously supplied to it - for example, by means of oscillations of the water surface. The liquid will push a drop up even before the air layer becomes thinner.

The phenomenon of bouncing droplets was first described by the American physicist Jearl Walker in 1978. But studying the dynamics of this phenomenon took up only 30 years later - French researchers from the University of Paris VII, led by Yves Couder (Yves Couder).

The installation necessary to observe the jumping drops is quite simple. It consists of a pathogen and a droplet generator . The role of the first can be played by a speaker on which a bath with soapy solution or silicone oil is installed. As a second, an ordinary toothpick is suitable. Here is an example of the apparatus we have assembled:


Installation casing, printed on a 3D printer, and its circuit A

drop falling into the bath will begin to “levitate” only at a certain frequency and amplitude of the oscillations of the speaker — these parameters are determined experimentally. But there is a basic condition: the amplitude should be sufficient to toss a drop, but not enough for the appearance of a Faraday ripple. These are standing waves on the surface of a liquid that destabilize it.

The ability of a water ball to bounce is also affected by its size. It determines the minimum amplitude necessary to achieve the effect. The smaller the droplet, the smaller the amplitude required for the rebound - that is, the droplet is capable of continuously jumping in a larger range of amplitudes and frequencies.


Ripple faraday

Interestingly, drops can not only bounce. They are able to move along certain trajectories and interact with each other. The phenomenon is due to the waves that the balls generate at each bounce from the surface. Drops tend to occupy a position corresponding to the local minimum of potential energy, determined by the interference of the generated waves. There are many such positions, but they are located at the same distance from each other - it is equal to half the wavelength. From one position, a drop can always be “pushed” into another.


A crystal of two stably jumping drops.

Also bouncing droplets form stable crystal-like structures. For example, the correct geometric shapes - triangles, squares, pentagons.

The wave nature of the interaction can explain an interesting effect - the scalability of the crystal with a slow frequency change. With its increase, the distance between the water balls grows, and with a decrease, on the contrary, it decreases.


Geometrical figures from drops.

The figures are sufficiently “elastic” so that they can be moved without destroying the structure of the crystal. Here is an example of such an effect:


Crystal movement

If bouncing droplets are close enough and their sizes are relatively large, then they will drift towards each other, forming another bound state - a cluster.


Clusters

Large droplets are heavy, so they “push” the surface of the liquid underneath. There is a potential hole where other large drops rush.

This pit prevails over potential pits of surface waves. Therefore, the wave type of interaction is not characteristic of large drops.

What relation do droplets have to quantum mechanics


The system of levitating drops is not only a beautiful effect of the macrocosm, but also a phenomenon that resonates in the quantum world.

American physicist John Bush (John Bush) with colleagues from MIT in 2013 observed the so-called "walking" drops appearing near the threshold of Faraday. They “jump” on their wave and move along the surface of the liquid. Like quantum particles whose speed does not exceed the speed of light, walking drops have a similar limitation - the speed of wave propagation in a liquid.

In turn, Yves Kuder discovered in 2006that drops exhibit properties characteristic of waves. The physicist directed the water balls into the slit and managed to observe the diffraction phenomenon - very similar to electron diffraction. Thus, bouncing droplets can be considered as objects (particles) exhibiting wave-particle duality .

And this is only a small part of interesting experiments. Scientists also found the following analogies:

  • Oscillations of droplets in a bound state and vibrational motion of photons in a crystal atom;
  • Rotational motion of droplets and the movement of electrons in orbit.

Thus, these experiments, phenomena, and dependences are of physical interest and allow one to observe quantum-like behavior on the scale of liquid droplets.



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