15 Septembre – Thesis defense - Arthur Alexandre

14 h Amphi 2 - building A9 (University of Bordeaux / Talence campus)

Dispersion in heterogeneous media: a study of hydrodynamic effects and surface-mediated diffusion.

The aim of this thesis is to study the dispersion, i.e. the spreading rate of tracer particles, in heterogeneous media, presenting a spatial periodicity. This process is quantified by an effective diffusivity coefficient. It is well known that the presence of walls or obstacles decreases dispersion, while a shear flow induces the opposite effect. However, most studies consider perfectly reflecting boundaries. In a first chapter, we derive a general expression for the effective diffusivity for a surface-mediated diffusion model that includes the possibility for particles to stick to and diffuse on walls. By applying this formula to two different systems (an array made of spherical osbtacles and a periodic channel), we show that this adhesion mechanism increases dispersion compared to the case of reflecting walls, even if the diffusion at the surface is slower than in the volume. In a second step, we examine the combined effects of viscous flow and confinement on dispersion for a corrugated channel. We put forward through analytical expressions the competition between these two antagonistic effects in the limit of small wall undulations. In the opposite limit, the strong corrugations of the walls have the effect of trapping the tracer particles. Thanks to the expression of diffusivity, we show an equivalence with a Taylor dispersion problem in a uniform channel with partially adsorbing walls. In a third step, we take into account simultaneously the corrugation of the walls, the flow and the surface effetcs. By deriving a general formalism, we show that the combination of these three parameters induces non-trivial effects on the dispersion. In a final chapter, we focus on the dynamics of a Brownian particle confined in a flat channel. We derive a generalized expression for the Taylor diffusivity by expressing the second cumulant. Similarly, we quantify the non-Gaussianity of the distribution of position along the channel axis by analytically studying higher order cumulants.

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