Steady Marangoni flow traveling with chemical fronts

Abstract

When autocatalytic chemical fronts propagate in thin layers of solution in contact with air, they can induce capillary flows due to surface tension gradients across the front ͑Marangoni flows͒. We investigate here such an interplay between autocatalytic reactions, diffusion, and Marangoni effects with a theoretical model coupling the incompressible Navier-Stokes equations to a conservation equation for the autocatalytic product concentration in the absence of gravity and for isothermal conditions. The boundary condition at the open liquid/air interface takes the surface activity of this product into account and introduces the solutal Marangoni number M representing the intensity of the coupling between hydrodynamics and reaction-diffusion processes. Positive and negative Marangoni numbers correspond, respectively, to the cases where the product decreases or increases surface tension behind the front. We show that, in both cases, such coupled systems reach an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front and deforming it, with, however, an asymmetry between the results for positive and negative M. A parametric study shows that increased propagation speed, front deformation, and possible transient oscillating dynamics occur when the absolute value of M is increased.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

“…9,10 In that case, the gradient of surface tension across the front triggers Marangoni flows deforming and accelerating the front. The system reaches a steady regime too, characterized by a convection roll traveling with the chemical front at a constant speed.…”

“…Eventually, we have also provided a comparison of the dynamics and of the important scalings of the pure buoyancydriven chemohydrodynamic flows studied here with those previously studied in the case of pure Marangoni-driven spatiotemporal dynamics. 9,10 The present work has considered isothermal fronts as a first step. In this case, the density jump across the front is only due to a solutal contribution ⌬ s related to compositional changes in the course of reaction.…”

“…[1][2][3][4][5][6][7][8] It remains, however, most often difficult to discriminate the relative influence of buoyancy-and surfacetension-driven flows in the complex dynamics of the system. In a previous theoretical study, 9,10 we have quantitatively analyzed the spatiotemporal dynamics of chemical fronts traveling horizontally in a thin solution layer open to the air when Marangoni forces are acting at the surface in the absence of gravity. We have characterized the asymptotic dynamics of the system as a function of the important parameters of the problem that are a Marangoni number and the thickness of the solution layer.…”

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

“…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.…”

Diffúzív és konvektív instabilitás tanulmányozása autokatalitikus reakciófrontokban

“…Ez a határfelületi jelenség egy boros pohár oldal-, valamint felülnézeti képén látható leginkább, amit a 2.3. ábra mutat be. Rongy és De Wit a jelenség elméletét már számos szemszögből megvizsgálta [44,45], és lejegyezte. Kísérletileg ezt vízszintesen haladó reakció-diffúzió frontok esetében lehet jól tanulmányozni [46].…”