Non-Gaussian diffusion near surfaces

Arthur Alexandre (1) , Maxime Lavaud (1) , Nicolas Fares (1) , Elodie Millan (1) , Yann Louyer (1) , Thomas Salez (1) , Yacine Amarouchene (1) , Thomas Guérin (1) , David S. Dean (1)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a non-zero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. This system is a well-controlled physical realization of Brownian-yet-non-Gaussian diffusion generated by a fluctuating diffusivity mechanism for which the local diffusivity is quantified. These results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Matière Molle [cond-mat.soft]; Dynamique des Fluides [physics.flu-dyn]; Mécanique des fluides [physics.class-ph]

Arthur Alexandre, Maxime Lavaud, Nicolas Fares, Elodie Millan, Yann Louyer, et al.. Non-Gaussian diffusion near surfaces. 2022. ⟨hal-03713580v2⟩