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Dispersion in heterogeneous media : how boundaries shape transport properties
Identifying transport properties of tracer particles in heterogeneous media at large time and length scales has applications in wide range of physical systems including microfluidics, hydrology, chemical engineering or soft matter. The effective diffusivity is a crucial input for problems of mixing, sorting, chemical delivery, as well as chemical reactions. Spatial variations of diffusion and advection can lead to drastic changes in the effective diffusion constant with respect to homogenous systems. Classic examples include Taylor dispersion in hydrodynamics, and the decrease of diffusivity due to the crowding effect produced by spatially-varying boundaries or the presence of an external periodic potential.
In particular, the effect of the confining geometry on the effective diffusivity has been widely studied, but the vast majority of existing theories focuses on perfectly reflecting boundaries. Using a general framework that incorporates surface-mediated diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion [1]. We notably show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk.
Our formalism can be generalized to encompass drifts or spatially-dependent diffusion tensor [2, 3]. Indeed, his spatial dependency results from hydrodynamic interactions between the tracer and the wall and are not negligible in the situation of strong confinement. In particular, we examine how the latter mechanism modifies the tracer displacement distribution by computing cumulants beyond the mean-squared displacement. Our results were confirmed by numerical simulations and experimental data.
References
[1] Alexandre, A., Mangeat, M., Guérin, T. & Dean, D. S. How stickiness can speed up diffusion in confined systems. Physical Review Letters 128, 210601 (2022).
[2] Alexandre, A., Gu´erin, T. & Dean, D. S. Generalized taylor dispersion for translationally invariant microfluidic systems. Physics of Fluids 33 (2021).
[3] Alexandre, A. et al. Non-gaussian diffusion near surfaces. Physical Review Letters 130, 077101 (2023).