Effective description of Taylor dispersion in strongly corrugated channels

TL;DR

This paper derives analytical expressions for Taylor dispersion in highly corrugated channels, linking complex porous media flow to simplified models with effective parameters, validated by numerical calculations.

Contribution

It extends the concept of slip-length in hydrodynamics to Taylor dispersion in tortuous channels, providing a new analytical framework.

Findings

Analytical expressions for diffusion constant and drift derived

Effective model for porous media dispersion established

Results confirmed by numerical calculations

Abstract

Taylor dispersion in periodic but highly corrugated channels is studied. Exact analytical expressions for the long-time diffusion constant and drift along the channel are derived to next-to-leading order in the limit of small channel period. Using these results we show how an effective model for Taylor dispersion in tortuous porous media can be framed in terms of dispersion in a uniform channel with absorption/desorption at its surface, an effective slip length for the flow at the surface and an effective, universal, diffusion constant on the surface. This work thus extends the concept of an effective slip-length for hydrodynamics flows to Taylor dispersion by those flows. The analytical results are confirmed by numerical calculations, and present a robust method to understand and upscale the transport properties of flows in porous media.