A centrifuge with rounded bins
Channel: Nils Berglund
Date: 2022-06-06

This variant of the video https://youtu.be/eTTPUYqcvaA shows a centrifuge with bins that have a more rounded shape, which, as suggested in comments, makes the behavior of particles much more realistic. It shows 435 particles of two different types: 70% of the particles are shown in blue in the first part of the video, the other 30% are shown in red. The blue particles are smaller, but twice as heavy as the red ones. The idea is that blue 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, then kept constant, and finally 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 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: 1:21
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: 25 minutes 46 seconds 
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: "The Call" by Track Tribe@TrackTribe

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)