Three-dimensional advective--diffusive boundary layers in open channels with parallel and inclined walls

TL;DR

This paper investigates three-dimensional advective-diffusive boundary layers in open channels with various cross-sections, revealing that two-dimensional models can effectively approximate complex three-dimensional transport phenomena, simplifying analysis and design.

Contribution

The study demonstrates that two-dimensional calculations can accurately approximate three-dimensional advective-diffusive transport in open channels, despite complex boundary layer structures.

Findings

Sherwood number is well approximated by 2D models

3D boundary layers can be simplified to 2D for transport predictions

Results applicable to microfluidic and channel decontamination processes

Abstract

We study the steady laminar advective transport of a diffusive passive scalar released at the base of narrow three-dimensional longitudinal open channels with non-absorbing side walls and rectangular or truncated-wedge-shaped cross-sections. The scalar field in the advective--diffusive boundary layer at the base of the channels is fundamentally three-dimensional in the general case, owing to a three-dimensional velocity field and differing boundary conditions at the side walls. We utilise three-dimensional numerical simulations and asymptotic analysis to understand how this inherent three-dimensionality influences the advective-diffusive transport as described by the normalised average flux, the Sherwood $Sh$ or Nusselt numbers for mass or heat transfer, respectively. We show that $Sh$ is well approximated by an appropriately formulated two-dimensional calculation, even when the boundary layer structure is itself far from two-dimensional. This important result can significantly simplify the modelling of many laminar advection--diffusion scalar transfer problems: the cleaning or decontamination of confined channels, or transport processes in chemical or biological microfluidic devices.