Impact of Geometrical Constraints on Marangoni-Induced Instabilities in BZ Reaction Systems*

In this study, we conduct a comprehensive numerical investigation using computational fluid dynamics (CFD) to explore the Marangoni effect on free surfaces induced by chemical concentration gradients within the Belousov-Zhabotinsky (BZ) reaction. Our focus is on understanding the influence of geometrical constraints, specifically the presence of hydrophilic cylindrical pillars within a Petri dish, on symmetry-breaking mechanisms and the formation of instability patterns. The research highlights the development and utilization of a custom OpenFOAM solver that integrates hydrodynamic-chemical coupling and three-dimensional Marangoni effects.

Ssimulations reveal that the introduction of periodic arrays of cylindrical obstacles significantly impacts the spatio-temporal dynamics of chemical waves. These hydrophilic pillars act as central points for wave initiation, leading to the synchronous emission of circular waves that evolve due to surface tension gradients and evaporative cooling. In covered setups, these waves maintain their circular shape over multiple cycles, demonstrating typical excitable medium behavior. However, in open setups where evaporation is more pronounced, thermal Marangoni flows induce wavefront instabilities, resulting in distinctive flower-like patterns around the obstacles. We further investigate how the diameter of the pillars influences the number and nature of these instability patterns. A linear relationship between the pillar diameter and the number of petals formed is found, with a minimum diameter threshold required for the manifestation of such instabilities. Comparison with experimental data confirms the validity of our simulations and provides deeper insights into the observed phenomena.

This research offers insights into the manipulation and control of chemical wave propagation through engineered geometries and surface properties. By understanding the interplay between Marangoni flows, concentration gradients, and geometrical constraints within BZ reaction, we pave the way for furture innovations in chemical and biological systems.