Chemoconvection patterns in the methylene-blue–glucose system: weakly nonlinear analysis

Pons, A.J., Sagués, F. and Bees, M.A. (2004) Chemoconvection patterns in the methylene-blue–glucose system: weakly nonlinear analysis. Physical Review E, 70(6), 066304. (doi: 10.1103/PhysRevE.70.066304)

Abstract

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bees, Dr Martin
• Authors: Pons, A.J., Sagués, F., and Bees, M.A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Physical Review E
• ISSN: 1539-3755
• ISSN (Online): 1550-2376
• Copyright Holders: Copyright © 2004 American Physical Society
• First Published: First published in Physical Review E 70(6):066304
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher