Taylor dispersion with absorbing boundaries: A Stochastic Approach

TL;DR

This paper introduces an exact stochastic method to analyze Taylor dispersion with absorbing boundaries, providing explicit formulas for particle displacement moments and revealing how absorption affects dispersion and skewness.

Contribution

It offers a novel stochastic approach that yields closed-form expressions for moments of dispersion in the presence of absorption, extending understanding of boundary effects.

Findings

Effective velocity and skewness are increased by absorption.

Taylor dispersion is suppressed due to boundary absorption.

Long-time distribution approaches Gaussian with linear growth of cumulants.

Abstract

We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to closed-form expressions for all the moments of the convective displacement of the dispersing particles in terms of the transverse diffusion eigenmodes. We also find that the cumulants grow asymptotically linearly with time, ensuring a Gaussian distribution in the long-time limit. As a demonstration of the technique, the first two longitudinal cumulants (yielding respectively the effective velocity and the Taylor diffusion constant) as well as the skewness (a measure of the deviation from normality) are calculated for fluid flow in the parallel plate geometry. We find that the effective velocity and the skewness (which is negative in this case) are enhanced while Taylor dispersion is suppressed due to absorption at the boundary.