Collective behavior of particles in fluids

Paris, December 14-17, 2020

**Pierre Gaspard** (Université Libre de Bruxelles)

*From single active particles to active matter*

Active matter is composed of many active particles moving in some medium. Active particles are micrometric or submicrometric colloidal particles that are self-propelled in the surrounding medium by chemical reaction, thermal heating, flagella or cilia for the locomotion of microorganisms, so many mechanisms providing energy for the propulsion. The study of these systems is challenging because they are characterized by multiple scales from the molecular size of the propulsion mechanisms up to the macroscale of the many-particle collective dynamics in active matter. Moreover, the description is stochastic at the scale of micrometers and becomes deterministic at the macroscale. At the surface of the particles, the fluctuating hydrodynamic equations of the surrounding fluid are coupled to fluctuating reaction-diffusion equations or the heat equation by specific boundary conditions that are characteristic of the propulsion mechanism. The first part of this minicourse will be devoted to the stochastic motion of a single active particle and the second part to collective dynamics, as can be deduced from single-particle motion. The methods are based on the stochastic partial differential equations of fluctuating chemohydrodynamics, stochastic ordinary differential equations of Langevin type in the overdamped regime and their master equation, and hierarchies of equations for the particle distribution functions, leading to the macroscopic partial differential equations.

*References:*

[1] P. Gaspard and R. Kapral. Thermodynamics and statistical mechanics of chemically-powered synthetic motors. *Advances in Physics*:X, 4(1):1602480, 2019.

[2] P. Gaspard and R. Kapral. Active Matter, Microreversibility, and Thermodynamics. *Research*, vol. 2020, Article ID 9739231, 2020.

See slides and records (part 1 and part 2).