Oscillatory Hydrodynamic Flow due to Concentration Dependence of Surface Tension

Phys. Chem. Chem. Phys.

Wit

2012

A reaction-diffusion-convection (RDC) model is introduced to analyze convective dynamics around horizontally traveling fronts due to combined buoyancy-and surface tension-driven flows in vertical solution layers open to the air. This isothermal model provides a means for a comparative study of the two effects via tuning two key parameters: the solutal Rayleigh number Ra, which rules the buoyancy influence, and the solutal Marangoni number Ma governing the intensity of surface effects at the interface between the reacting solution and air. The autocatalytic front dynamics is probed by varying the relative importance of Ra and Ma and the resulting RDC patterns are quantitatively characterized through the analysis of the front mixing length and the topology of the velocity field. Steady asymptotic regimes are found when the bulk and the surface contributions to fluid motions act cooperatively i.e. when Ra and Ma have the same sign. Complex dynamics may arise when these numbers are of opposite signs and the two effects thus compete in an antagonistic configuration. Typically, spatiotemporal oscillations are observed as the control parameters are set in the region (Ra o 0, Ma > 0). Periodic behaviour develops here even in the absence of any double-diffusive interplay, which in previous literature was identified as a possible source of complexity.

Section: Introductionmentioning

confidence: 99%

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

Budroni

Phys. Chem. Chem. Phys.

Wit

2012

“…11 From a theoretical point of view, numerical studies have provided examples of buoyancy-driven deformation of traveling pulses in excitable systems. [24][25][26][27][28][29] Vasquez et al 30 have numerically shown that simple chemical fronts propagating horizontally in nonexcitable systems can be accelerated and deformed by the presence of a convective flow around the front. They find good agreement between their predicted reaction-diffusion-convection speed for iodate-arsenous acid fronts and values measured experimentally in thin capillary tubes.…”

Section: Introductionmentioning

confidence: 99%

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

The Journal of Chemical Physics

Goyal

Meiburg

et al. 2007

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as ͱ Ra for RaϾ 5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry ͓L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 ͑2006͔͒.

“…50 In particular, using a similar model has allowed to relate the presence of oscillating flows observed during the propagation of BZ spiral waves 14 to Marangoni effects induced by the surface activity of bromomalonic acid. 51 Similarly to the BZ reaction which is a canonical model for the study of pulse and spiral waves, the IAA reaction possesses rich dynamic behaviors. In a batch reactor, this reaction exhibits the so-called "clock dynamics," i.e., the reaction undergoes a sudden single switch from the reactants towards the products after an induction period depending on the initial concentrations.…”

Section: Introductionmentioning

confidence: 99%

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

Chaos: An Interdisciplinary Journal of Nonlinear Science

Assemat

Wit

2012

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...