Diffusion of colloidal particles in model porous media

Brownian motion on an out-of-thermal-equilibrium surface

The motion of colloidal species on an out-of-thermal equilibrium surface is studied experimentally by optical microscopy. Water droplets of size in the micrometer range, spontaneously formed at a spherical-like interface between water and oil, are the colloidal species. The interface appears as a convex meniscus when putting water on oil with an added nonionic surfactant. Since the water density is greater than that of oil, the interface is produced into the oil. The spontaneously formed water droplets move attached to the interface while still growing from submicrometer sizes to a few micrometers. Although the dynamic nature of the process, with both the interface and the particles still changing, produces heterogeneities in the system, anomalous diffusion was not observed. The motion of the droplets has a well-identified Brownian component with a Gaussian distribution of steps due to the thermal agitation of the media surrounding the droplets and a drift component due to the effect of gravity.

Normal and anomalous diffusion in the disordered wind-tree model

Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities ρ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient D, as obtained from the simulation, with that predicted by kinetic theory where D^{-1} is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times t grows like t^{1-2ρ/3}. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.