Geometry controlled dispersion in periodic corrugated channels

Abstract

The effective diffusivity $D_e$ of tracer particles diffusing in periodically corrugated axisymmetric two and three dimensional channels is studied. The majority of previous studies of this class of problems are based on perturbative analyses about narrow channels, where the problem can be reduced to an effectively one dimensional one. Here we show how to analyze this class of problems using a much more general approach which even includes the limit of infinitely wide channels. Using the narrow and wide channel asymptotics, we provide a Pad{é} approximant scheme that is able to describe the dispersion properties of a wide class of channels. Furthermore, we systematically identify all the exact asymptotic scaling regimes of $D_e$ and the accompanying physical mechanisms that control dispersion, clarifying the distinction between smooth channels and compartmentalized ones, and identifying the regimes in which $D_e$ can be linked to first passage problems.

arXiv commentMain text (6 pages) + Supplementary Information (5 pages)

References in corpus (10)

• First-passage times in complex scale-invariant media
• Kinetic Equations for Diffusion in the Presence of Entropic Barriers
• Entropic transport: Kinetics, scaling and control mechanisms
• Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
• Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas
• Dispersion in the large-deviation regime. Part I: shear flows and periodic flows
• Kubo formulas for dispersion in heterogeneous periodic non-equilibrium systems
• Stochastic and Deterministic Vector Chromatography of Suspended Particles in 1D-Periodic Potentials
• Dispersion in rectangular networks: effective diffusivity and large-deviation rate function
• A Fick-Jacobs equation for channels over 3D curves

Cited by in corpus (6)

• How stickiness can speed up diffusion in confined systems
• Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited
• Dispersion in two-dimensional periodic channels with discontinuous profiles
• Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks
• Transport of a passive scalar in wide channels with surface topography
• Splitting probabilities for dynamics in corrugated channels: passive VS active Brownian motion