Microscopic flows and mechanism of diffusion in liquid phase
Dominika Lesnicki (Département de chimie de l’ École normale supérieure, Paris, France)

A particle immersed in a bath exchanges momentum with the surrounding particles through collisions, leading to a friction force opposing the particle motion plus a random force at the origin of the Brownian motion of the tagged particle. In 1905, Einstein proved the fluctuation-dissipation theorem that relates the fluctuation of the random force to the friction coefficient and enforces the Boltzmann distribution at equilibrium [1]. Assuming that the friction exerted on an immersed particle results from the hydrodynamic flow of the bath around the particle, this leads to the famous Stokes-Einstein . In its turn, the momentum transferred to the solvent induces excitations in the bath, which ultimately triggers hydrodynamic modes. The coupling of the particle motion with the bath hydrodynamic modes has been revealed by molecular dynamics simulations [2] and more recently by experiments [3]. While several theories have proposed to extend this model and leave open questions, molecular dynamics simulations can explore the latter. Nevertheless, molecular dynamics simulations are systematically carried out without addressing the problem of the origin of the coupling since they are reduced to the calculation of the diffusion coefficient. We propose here a novel approch by evaluating the flow in the fluid induced by the equilibrium velocity fluctuations of a tagged particle and in return the force induced by the bath on the tagged particle from molecular dynamics simulations. We recover respectively a Stokes flow and a Basset-Boussinesq force at the microscopic scale at the cost of a reformulation of concepts such as the boundary conditions or the added mass.

[1] A. Einstein, Uber die von der molekularkinetischen Theorie der Wrme geforderte Bewe- gung von in ruhenden Flssigkeiten suspendierten Teilchen. Annals of Physics (Leipzig) 17, 549 (1905).
[2] B. J. Alder, T. E. Wainwright, Decay of the Velocity Autocorrelation Function. Phys. Rev. A 1, 18 (1970).
[3] T. Franosch and all. Resonance arising from hydrodynamic memory in Brownian motion. Nature 478, 85–88 (2011).