Geometry controlled dispersion in periodic corrugated channels

Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux F-33400 Talence, France

Received: 11 May 2017
Accepted: 29 June 2017

Abstract

The effective diffusivity D_e of tracer particles diffusing in periodically corrugated axisymmetric two- and three-dimensional channels is studied. The majority of the 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 Padé 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.