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 finite-size particles confined close to a single wall and in double-wall planar channel geometries. The local diffusion constants are modified near the confining boundaries and depend on the distance to the latter. Displacement parallel to the walls is diffusive as characterized by its second cumulant (the variance), but a non-Gaussian nature can be demonstrated by the fact that its fourth cumulant is non-zero. Establishing a link with the well-known problem of Taylor dispersion, we provide a general expression for the fourth cumulant for general diffusivity tensors and also in the presence of potentials generated by either the walls or externally, for instance due to gravity. We then analyse experimentally and numerically the motion of a colloid in the direction parallel to the wall, for which the measured fourth cumulant is correctly predicted by our theory. This system is a well-controlled physical realization of a Brownian yet non-Gaussian motion generated by a fluctuating diffusivity mechanism for which the local diffusivity is quantified. These results can be used to 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-03713580v1⟩