Convection-dominated dispersion in channels with fractal cross-section

Abstract

We focus on the characterization of dispersion processes in microchannels with fractal boundaries (and translational symmetry in the longitudinal direction) in the presence of laminar axial velocity field. This article extends the theory of laminar dispersion in finite-length channel flows at high Peclet numbers by analyzing the role of the fractal cross-section in the convection-dominated transport regime. In this regime, the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number are determined by the local near-wall behavior of the axial velocity. Specifically, different scaling laws in the behavior of the moment hierarchy occur, depending whether the cross-sectional boundary is smooth or nonsmooth (e.g., presenting corner points or cusps). The limit case of a fractal boundary is analyzed in detail. Analytical and numerical results are presented for two fractal cross-sections (the classical Koch curve and the Koch snowflake) in the Stokes regime.