Neutral soap and water at decreasing temperature











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Like the video    • Neutral soap and water with increasin...   , this one shows a simulation of a mixture of water and soap molecules, where the soap molecules are globally neutral. The difference is that here, the Coulomb interaction between molecules is kept constant, while the temperature is decreased. • Water and fat do not easily mix. This is related to the fact that water molecules are polar, while fats are not. Soap molecules consist of a hydrophobic and lipophilic tail , that tends to mix with fat molecules, and a hydrophilic and lipophobic head , that tends to mix with water molecules. This helps mixing fat and water, and therefore cleaning objects, and people from fatty dirt particles. • This simulation shows a simple model for soap molecules, interacting with water molecules. The soap molecules consist in a tail made of ten neutral atoms, and a head consisting of two atoms of opposite charge. The soap molecules tend to latch on the oxygen atoms in water molecules. There are periodic boundary conditions, and the temperature is controlled by a thermostat with decreasing temperature. • This simulation has two parts, showing the evolution with two different color schemes: • Charge: 0:00 • Kinetic energy: 1:32 • In the first part, the particles' color depends on their charge. The background indicates the local charge density, slightly averaged over space and time. In the second part, the particles' color hue depends on their kinetic energy. • 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 temperature is controlled by a thermostat, implemented here with the Nosé-Hoover-Langevin algorithm introduced by Ben Leimkuhler, Emad Noorizadeh and Florian Theil, see reference below. The idea of the algorithm is to couple the momenta of the system to a single random process, which fluctuates around a temperature-dependent mean value. Lower temperatures lead to lower mean values. • 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... • Render time: 11 minutes 28 seconds • Compression: crf 23 • Color scheme: Part 1 - Twilight by Bastian Bechtoldhttps://github.com/bastibe/twilight • Part 2 - Turbo, by Anton Mikhailov • https://gist.github.com/mikhailov-wor... • Music: Erykah by Otis McDonald • Reference: Leimkuhler, B., Noorizadeh, E. Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). https://doi.org/10.1007/s10955-009-97... • http://www.maths.warwick.ac.uk/~theil... • Current version of the C code used to make these animations: • https://github.com/nilsberglund-orlea... • https://www.idpoisson.fr/berglund/sof... • Some outreach articles on mathematics: • https://images.math.cnrs.fr/_Berglund... • (in French, some with a Spanish translation) • #molecular_dynamics #ions #soap

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