# Regensburg 2019 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 43: Anomalous diffusion / Brownian motion

### DY 43.9: Vortrag

### Donnerstag, 4. April 2019, 12:15–12:30, H3

**Controlled dispersion in periodic microchannels and regular obstacle parks** — •Matthieu Mangeat^{1,2}, Thomas Guérin^{1}, and David S. Dean^{1} — ^{1}Univ. Bordeaux and CNRS, LOMA, Talence, France — ^{2}Universität des Saarlandes, Saarbrücken, Germany

The dispersion of Brownian particles in heterogeneous media is a widely studied problem which appears in many contexts (chemical reactions, biological systems, zeolites, porous media, pollutant spreading, ...). A cloud of particles disperses over time without reaching the Boltzmann equilibrium distribution and its spreading is then characterized by an effective long-time diffusivity *D*_{e} lower than the microscopic diffusivity. The analytical expression of *D*_{e} is given by an exact Kubo-type formula [Phys. Rev E **92**, 062103 (2015)] for periodic systems. The dispersion in periodic microchannels is controlled by the confinement geometry via an entropic trapping. Three different dispersion regimes are then identified for continuous and discontinuous channels [EPL **118**, 40004 (2017)]. The expression of *D*_{e} is thus well-described by the Fick-Jacobs’ approximation, narrow escape problems or the diffusion problem in comb-like geometries in each regime. This analysis can be extended to the dispersion in regular obstacle parks. The presence of short-range attractive potential on the surface of obstacles enhance the dispersion of Brownian particles. The optimal value of *D*_{e} is then analytically characterized in the dilute limit of obstacles.