# What Are Some Discoveries at the Frontiers of Fluid Physics?

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

Fluid dynamics, mechanics, equations…you name it and it’s a challenge to talk about. Molecular interactions, tensions, forces, and so on cause a complete description to be difficult and especially so in extreme conditions. But frontiers are being broken, and here are but a few of them.

## Navier-Stokes Equations May Break

The best model we have to demonstrate fluid mechanics comes in the form of the Navier-Stokes equations. They have been shown to have high utilization in physics. They also remained unproven. No one knows for sure yet if they always work. Tristan Buckmaster and Vlad Vicol (Princeton University) may have found cases where the equations give nonsense in regards to physical phenomenon. It has to do with the vector field, or a map outlining where everything is going at a given moment. One could trace out the steps in their path using one and get from step-to-step. Case-by-case, different vector fields have been shown to follow the Navier-Stokes equations, but do *all* vector fields work? Smooth ones are nice, but reality isn’t always like that. Do we find that asymptotic behavior arises? (Hartnett)

With weak vector fields (which are easier to work with than smooth ones based on the detailing and number used), one finds that the uniqueness of the outcome is no longer guaranteed, especially as the particles move faster and faster. One may point out that the more precise smooth functions would be better as a reality model but that may not be the case, especially since we cannot measure to such precision in real life. In fact, the Navier-Stokes equation took off so well *because* of a special class of weak vector fields called Leray solutions, which average vector fields over a given unit area. Scientists usually build up from there to more complex scenarios, and that may be the trick. If it can be shown that even these class of solutions can give bogus results then maybe the Navier-Stokes equation is just an approximation of the reality we see (Ibid).

## Superfluid’s Resistivity

The name really does convey how cool this type of fluid it. Literally, it’s cold with temperatures near absolute zero Kelvin. This creates a superconductive fluid where electrons flow freely, with no resistance impeding their travels. But scientists are still not sure why this happens. We usually make the superfluid with liquid helium-4, but simulations done by the University of Washington used a simulation to try and model out the behavior to see if hidden behavior is present. They looked at the vortices that can form as fluids move, like the surface of Jupiter. Turns out, if you create faster and faster vortices, the superfluid loses its lack of resistivity. Clearly, superfluids are a mysterious and exciting frontier of physics (University of Washington).

## Testing Quantum Mechanics

Crazy as it may sound, fluid experiments can possibly shed light into the strange world of quantum mechanics. Its results conflict with our view of the world and reduce it to a set of overlapping probabilities. The most popular of all these theories is the Copenhagen interpretation where all possibilities for a quantum state happen at once and only collapse into a definite state once a measurement is done. Obviously this raises some issues such as how specifically this collapse occurs and why it needs an observer to accomplish. It’s troubling but the math confirms experimental results such as the double slit experiment, where a beam of particles can be seen to go down two different paths at once and create a constructive/destructive wave pattern on the opposite wall. Some feel the path can be traced and flows from a pilot-wave guiding the particle via hidden variables while others see it as evidence that no definite track for a particle exists. Some experiments seem to support pilot-wave theory and if so could upend everything quantum mechanics has built up to (Wolchover).

In the experiment, oil is dropped into a reservoir and allowed to build waves. Each drop ends up interacting with a past wave and eventually we have a pilot wave that allows for particle/wave properties as subsequent drops can travel on top of the surface through the waves. Now, a two-slit setup is established in this medium and the waves are recorded. The droplet will only pass through one slit while the pilot wave goes through both, and the droplet is guided to the slits specifically and nowhere else – just like the theory predicts (Ibid)

In another experiment, a circular reservoir is used and the droplets form standing waves that are analogous to those “generated by electrons in quantum corrals.” Droplets then ride the surface and take seemingly chaotic paths across the surface and the probability distribution of the paths creates a bullseye-like pattern, also like how quantum mechanics predicts. These paths are influenced by their own motions as they create ripples that interact with the standing waves (Ibid).

So now that we have established the analogous nature to quantum mechanics, what power does this model give us? One thing may be entanglement and its spooky action at a distance. It seems to happen nearly instantly and over vast distances, but why? Maybe a superfluid has the motions of the two particles traced on its surface and via the pilot wave can have the influences transferred to one another (Ibid).

## Puddles

Everywhere we are finding pools of liquids, but why don't we see them continue to spread out? It's all about surface tension competing against gravity. While one force pulls the liquid to the surface, the other feels particles fighting compaction and so pushes back. But gravity should win out eventually, so why don't we see more super-thin collections of liquids? It turns out that once you get to about 100 nanometers in thickness, the edges of the liquid experience van der Waals forces courtesy of electron clouds, creating a charge difference that is a force. This coupled with the surface tension allows a balance to be reached (Choi).

## Works Cited

Choi, Charles Q. "Why Do Puddles Stop Spreading?" *insidescience.org.* Inside Science, 15 Jul. 2015. Web. 10 Sept. 2019.

Hartnett, Kevin. “Mathematicians Find Wrinkle in Famed Fluid Equations.” *Quantamagazine.com.* Quanta, 21 Dec. 2017. Web. 27 Aug. 2018.

University of Washington. “Physicists hit on mathematical description of superfluid dynamics.” *Astronomy.com*. Kalmbach Publishing Co., 09 Jun. 2011. Web. 29 Aug. 2018.

Wolchover, Natalie. “Fluid Experiments Support Deterministic ‘Pilot-Wave’ Quantum Theory.” *Quantamagazine.com*. Quanta, 24 Jun. 2014. Web. 27 Aug. 2018.

**© 2019 Leonard Kelley**