Convective dispersion without molecular diffusion

TL;DR

This paper presents a method to compute long-time transport properties of particles undergoing convective motion with state transitions, showing that even without molecular diffusion, particles exhibit Gaussian diffusive behavior due to stochastic state changes.

Contribution

It introduces a method-of-moments scheme to analyze long-time dispersion in a two-state system with reversible transitions, revealing diffusion-like behavior without molecular diffusion.

Findings

Particles exhibit Gaussian diffusive behavior asymptotically.

The method accurately predicts mean velocity and dispersivity.

Long-time behavior is governed by stochastic state transitions.

Abstract

A method-of-moments scheme is invoked to compute the asymptotic, long-time mean (or composite) velocity and dispersivity (effective diffusivity) of a two-state particle undergoing one-dimensional convective-diffusive motion accompanied by a reversible linear transition (``chemical reaction'' or ``change in phase'') between these states. The instantaneous state-specific particle velocity is assumed to depend only upon the instantaneous state of the particle, and the transition between states is assumed to be governed by spatially-independent, first-order kinetics. Remarkably, even in the absence of molecular diffusion, the average transport of the ``composite'' particle exhibits gaussian diffusive behavior in the long-time limit, owing to the effectively stochastic nature of the overall transport phenomena induced by the interstate transition. The asymptotic results obtained are compared with numerical computations.