Related Experiment Video
Updated: Aug 15, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Dispersion curves in the diffusional instability of autocatalytic reaction fronts
1Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom.
Abstract:
A (linear) stability analysis of planar reaction fronts to transverse perturbations is considered for systems based on cubic autocatalysis and a model for the chlorite-tetrathionate reaction. Dispersion curves (plots of the growth rate sigma against a transverse wave-number k) are obtained. In both cases it is seen that there is a nonzero value D0 of D (the ratio of the diffusion coefficients of autocatalyst and substrate) at which sigma(max), the maximum value of sigma for a given value of D, achieves its largest value, with sigma(max) being less for other values of D and becoming small as D decreases to zero. The existence of the optimum value D0 for initiating a diffusional instability is confirmed, in the cubic autocatalysis case, by an asymptotic analysis for small wave numbers.
Related Concept Videos
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Fast Reactions
Standard Entropy Change for a Reaction
Ostwald’s Dilution Law
Le Chatelier's Principle: Changing Concentration
Diffusion on Chromatography Columns
Longitudinal diffusion occurs when the solute molecules in the mobile phase diffuse from the more concentrated center of the chromatographic band to the more dilute regions on either side, both towards and against the flow direction. This...

