Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

Abstract

Segmented waves in a reaction-diffusion-convection system Chaos 22, 037109 (2012) Instability in evaporative binary mixtures. I. The effect of solutal Marangoni convection Phys. Fluids 24, 094101 (2012) Coalescence of surfactant covered drops in extensional flows: Effects of the interfacial diffusivity Phys. Fluids 24, 082101 (2012) Transient Rayleigh-Bénard-Marangoni solutal convection Phys. Fluids 24, 074108 (2012) Additional information on Chaos Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated. As a chemical reaction induces changes in the temperature and in the composition of the reactive medium, it can modify the properties of the solution (density, viscosity, surface tension) and thereby trigger convective motions, which in turn affect the reaction. Such a coupling can typically be observed around reactive interfaces in liquid solutions. Two classes of convective flows are then commonly developing in solutions open to air, namely Marangoni flows arising from surface tension gradients and buoyancy flows driven by density gradients. As both flows can be induced by compositional changes as well as thermal changes and in turn modify them, the resulting experimental dynamics are often complex. The purpose of our study is to gain insight into these intricate dynamics thanks to the theoretical analysis of model systems where only one type of convective flow is present. We address here the dynamics of an exothermic autocatalytic front propagating in the presence of Marangoni flows, when the density remains uniform. The surface tension gradient across the front has both a thermal component linked to the exothermicity of the reaction and a s...

Dynamics due to combined buoyancy- and Marangoni-driven convective flows around autocatalytic fronts

“…Again, the introduction of the thermal contribution can induce a double-diffusive interplay and the emergence of complex spatio-temporal dynamics such as oscillatory patterns. 42 While the separate role played by pure buoyancy-driven and pure surface-driven flows in chemical traveling fronts has thus been successfully understood, the combined effect of these two contributions still remains unexplored from a theoretical point of view, though this is a genuine situation encountered for fronts propagating in thin layers open to the air.…”

“…In past years many efforts have been devoted towards understanding how the mutual interaction between kinetics and convective transport phenomena enhances complex behaviours. The influence of bulk and surface flows on the front dynamics has been pointed out in both experimental [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and theoretical works, [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] showing that chemical fronts can be distorted, accelerated or even broken by the hydrodynamic feedback. The reaction-diffusion-convection coupling has proved to be also responsible for order-disorder transitions in chemical oscillators, where it controls the route from periodic regimes to spatiotemporal chaos.…”

Making a Simple A+B→C Reaction Oscillate by Coupling to Hydrodynamic Effect

“…Most previous works on reactive flows triggered by an active RDC coupling focused either on the impact of chemical reactions on the symmetry and evolution of classical hydrodynamic instabilities [27], or, vice versa, on unraveling the influence of convective flows on bifurcations that occur in already complex chemical systems [28][29][30][31]. For example, self-propagating autocatalytic fronts can be periodically deformed by antagonistic solutal and thermal density [32,33] or surface-driven flows [34] in the presence of differential diffusion, by the competition between buoyancy and Marangoni forces [35] or due to high surface-tension-driven stresses [36,37]. In the former cases, the autocatalytic nature of the chemical kinetics is crucial to restore, on a proper timescale, a fairly flat interface after deformation and the periodic dynamics is sensitive to the direction of front propagation.…”

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field

“…To try to clarify this situation, numerous theoretical works have been devoted to the study of chemically-driven flows around horizontally propagating fronts and to the effect the flow has on the shape and speed of these fronts. These theoretical studies can be classified depending on the type of flow considered: buoyancy-driven, 12,[30][31][32][33][34][35][36][37][38][39] Marangoni-driven, [40][41][42][43][44][45][46][47] or a combination of both flows. 12,19,48,49 In the case of pure buoyancy-driven flows, a good agreement exists between numerical simulations and experiments in closed reactors, both for isothermal 31,35,38,39 and exothermic fronts.…”