On Marangoni convective patterns driven by an exothermic chemical reaction in two-layer systems

This article is devoted to the investigation of Marangoni-driven pattern formation at the interface between two immiscible fluids filling a Hele-Shaw cell, each of them containing a reactant of an exothermic neutralization reaction. In such a system, convective patterns arise when one reactant diffuses through the interface to react with the other chemical species in one of the fluids. A chemo-hydrodynamical pattern appears due to Marangoni instabilities taking place because of heat and solutal driven changes of the surface tension. The mathematical model we develop consists in a set of reaction-diffusion-advection equations ruling the evolution of concentrations and temperature coupled to Navier–Stokes equation, written in a Hele-Shaw approximation. In our analysis, the time-dependent convectionless reaction-diffusion base state is first obtained and studied in detail. Next, we perform a linear stability analysis of this base state with regard to thermal and solutal Marangoni effects to determine the parameter values beyond which convection occurs. Finally, we perform numerical simulations of the fully nonlinear system and study the influence of the different parameters on pattern formation.