Spatial and Temporal Oscillations of Surface Tension Induced by an A + B → C Traveling Front

Abstract

This work describes a new mechanism for the emergence of oscillatory dynamics driven by the interaction of hydrodynamic flows and reaction-diffusion processes with no autocatalytic feedback nor prescribed hydrodynamic instability involved. To do so, we study the dynamics of an A+ B → C reaction-diffusion front in the presence of chemically-driven Marangoni flows for arbitrary initial concentrations of reactants and diffusion coefficients of all species. All the species are assumed to affect the solution surface tension thereby inducing Marangoni flows at the air-liquid interface. The system dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection equations for the three chemical species. We report spatial and temporal oscillations of surface tension triggered by differential diffusion effects of surfactant species coupled to the chemically-induced Marangoni effect. Such oscillations are related to the discontinuous traveling of the front along the surface leading to the progressive formation of local extrema in the surface tension profiles as time evolves.

Marangoni-driven nonlinear dynamics of bimolecular frontal systems: a general classification for equal diffusion coefficients

“…As a natural extension of this work, we could investigate differential diffusion effects on the system dynamics, starting with the case a0Da=b0Db, where the RD front is stationary, since it is naturally more common in experiments that species diffuse at different rates. On the basis of the recent findings that differential diffusion effects coupled with Marangoni stresses can trigger spatio-temporal oscillations of surface tension along with a discontinuous motion of the front along the free surface [13], we expect much more exotic possibilities for the dynamical properties of the reaction front when all the species diffuse at different rates. Along the same line, the effects of reaction exothermicity in both cases of cooperative and competitive solutal and thermal effects and the coupling to buoyancy-driven convection for unequal initial reactants concentrations and/or differential diffusion effects could be envisioned.…”

“…When the surface tension changes during the reaction are large enough, transient oscillations can also be observed in the presence of Marangoni-driven convection, while sustained oscillations are noted when combined with buoyant forces [10][11][12]. Recently, as a unique feature of differential diffusion effects coupled with Marangoni stresses, transient spatio-temporal oscillations of surface tension along with a discontinuous motion of the front have been shown to emerge for appropriate conditions on the model parameters, the mechanism of which does not require any autocatalytic feedback nor prescribed hydrodynamic instability [13].…”

Marangoni-vs.buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems

“…25 When those fronts are studied in aqueous media, convective flows can be triggered if the reaction induces changes in density (Δ R ≠ 0) or in surface tension (Δ M ≠ 0). The pure buoyancy- 60 and Marangoni- 61 driven convective cases have shown propagating fronts, and transient oscillatory dynamics have been reported in the latter case for both equal 30 and differential 33 molecular diffusion coefficients.…”

“…29 It was recently shown that simple A + B -C reactions can also exhibit spatiotemporal oscillations, provided that the reaction combines with hydrodynamics. [30][31][32][33] In reactive fluids, natural convection can indeed arise spontaneously from changes in the composition/temperature of the system, further inducing in situ local gradients in the physical properties (i.e. density and/or surface tension), thereby activating convective motions within the fluid itself.…”