A centrifuge without thermostat, and without gravity
Channel: Nils Berglund
Date: 22/05/2022

Like the video https://youtu.be/CRIrtdR-Cag this simulation shows a simple model for a centrifuge, allowing to separate particles with different densities. Unlike in the previous simulation, there is no thermostat here, and no gravity. This allows the particles to spread more easily towards the outside of the rotating bins. I had to add some viscous damping, though, to avoid numerical instabilities, which explains why particles don't quickly move away from the rotating walls when the centrifuge decelerates. 
There are 436 particles of two different types. 70% of the particles are shown in red in the first part of the video, the other 30% are shown in blue. The red particles are smaller, but 5 times as heavy as the blue ones. The idea is that red particles could represent a solid substance that is diluted in water, and that one wants to separate from the water by using the centrifuge.
The centrifuge consists here of 6 bins. The speed of rotation of the centrifuge, indicated in radians per second, is first increased, and then decreased again. Due to the forces from the walls of the bins, the particles are pressed against each other, which results in the heavier particles partially separating from the lighter ones.
The simulation has two parts, showing the same evolution with two different color codes: 
Particle type: 0:00
Direction of velocity: 2:35
In the first part, the particles' color indicates their type.In the second part, colors indicate the direction of the particles' velocity: white particles move to the right, blue ones upward, purple ones to the left, and red ones move downward. In addition, the luminosity depends on the particle's kinetic energy, so that very slow particles appear black. 
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle. 
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see https://en.wikipedia.org/wiki/Lennard-Jones_potential

Render time: 51 minutes 
Color scheme: Part 1 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight

Music: "Sirdar 3" by Mylar Melodies@mylarmelodies

Current version of the C code used to make these animations: 
https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)