Generalized Taylor dispersion for translationally invariant microfluidic systems

TL;DR

This paper derives a general formula for effective diffusion in microfluidic channels considering wall interactions, variable diffusivity, and flow, facilitating experimental comparisons and applications in complex systems.

Contribution

It introduces a simple, general formula for effective diffusion in microfluidic channels accounting for wall effects, flow, and interactions, applicable to diverse experimental setups.

Findings

Derived a universal formula for effective diffusion constant.

Validated the formula with applications to various diffusivity profiles.

Enabled straightforward numerical implementation for experimental comparison.

Abstract

We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the walls become important. We provide a simple and general formula for the effective diffusion constant along the channel as well as the first non-trivial finite time correction for arbitrary flows along the channel, arbitrary interaction potentials with the walls and arbitrary expressions for the diffusion tensor. The formula are in particular amenable to a straightforward numerical implementation, rendering them extremely useful for comparison with experiments. We present a number of applications, notably for systems which have parabolically varying diffusivity profiles, to systems with attractive interactions with the walls as well as electroosmotic flows between plates with differing surface charges within the Debye-H\"uckel approximation.