Solute dispersion in axially strained tube flows: Large-time asymptotics and Ornstein-Uhlenbeck Gaussian profiles

TL;DR

This paper investigates how passive scalars disperse in axially strained flows within slender tubes, revealing that strong axial stretching leads to exponential variance growth and Gaussian profiles, contrasting classical Taylor dispersion.

Contribution

It introduces a new understanding of scalar dispersion dominated by axial stretching, highlighting a different transport mechanism than classical models.

Findings

Scalar forms an Ornstein-Uhlenbeck Gaussian profile at large times

Variance increases exponentially with local axial strain

Radial diffusion modulates amplitude slowly

Abstract

The dispersion of a passive scalar in an axially strained flow in a slender tube is studied, with particular focus on large-time asymptotics following the approach of~\cite{rajamanickam2020dispersion}. For times exceeding the cross-sectional diffusion timescale, the scalar field forms an axial (Ornstein--Uhlenbeck) Gaussian profile whose variance increases exponentially with the local axial strain, which itself varies with radial location, while radial diffusion only slowly modulates the overall amplitude. In other words, the scalar is dominated by strong axial stretching, completely overwhelming radial diffusion. In striking contrast to classical Taylor dispersion, where radial diffusion rapidly homogenizes the profile and axial convection appears only as a small correction, here axial stretching governs the dominant dynamics, producing a fundamentally different transport mechanism.