Exothermic Chemical Front Research Articles

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

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.

Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers

Spatial variations of concentrations and temperature across exothermic chemical fronts can initiate buoyancy-driven convection. We investigate here theoretically the spatiotemporal dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows when an exothermic autocatalytic front travels perpendicularly to the gravity field in a thin solution layer. To do so, we numerically integrate the incompressible Stokes equations coupled to evolution equations for the concentration of the autocatalytic product and temperature through buoyancy terms proportional to, respectively, a solutal R(C) and a thermal R(T) Rayleigh number. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection with regard to the isothermal system. In the cooperative case (R(C) and R(T) are of the same sign), the dynamics asymptotes to one vortex surrounding, deforming, and accelerating the front much like in the isothermal case. However, persistent local stratification of heavy zones over light ones can be observed at the rear of the front when the Lewis number Le (ratio of thermal diffusivity over molecular diffusion) is nonzero. When the solutal and thermal effects are antagonistic (R(C) and R(T) of opposite sign), temporal oscillations of the concentration, temperature, and velocity fields can, in some cases, be observed in a reference frame moving with the front. The various dynamical regimes are discussed as a function of R(C), R(T), and Le.

Hot spots revealed by simultaneous experimental measurement of the two-dimensional concentration and temperature fields of an exothermic chemical front during finger-pattern formation

A noninvasive optical technique combining digital interferometry in transmission and transparency measurement of concentration is developed to analyze spatiotemporal dynamics of physicochemical systems. This technique allows one to measure simultaneously the two-dimensional (2D) dynamics of concentration and temperature fields in both reactive and nonreactive systems contained inside a transparent cell. When used to experimentally analyze buoyancy-driven fingering of an exothermic autocatalytic chemical front, this method reveals in the 2D temperature field the presence of hot spots where the temperature locally exceeds the adiabatic one.

Forbidden interval of propagation speed for exothermic chemical fronts

We consider the propagation of an exothermic chemical front toward an unstable steady state. The hydrodynamic equations are solved numerically for increasing values of the activation energy of the reaction which controls the reaction front speed. For a large speed, the marginal stability criterion of the isothermal case is recovered. For a small speed, we observe two well-separated traveling waves: a heat front is preceding the reaction front. We find analytically a forbidden speed interval where the hydrodynamical system does not admit stationary traveling solutions.

Flow-field development during finger splitting at an exothermic chemical reaction front

Fingertip splitting may be observed at chemical reaction fronts subject to buoyancy-induced Rayleigh-Taylor fingering, as investigated in ascending fronts of the iodate-arsenous acid reaction in vertical Hele-Shaw cells. We study the properties of the flow-field evolution during a tip-splitting event both experimentally and theoretically. Experimental particle-image velocimetry techniques show that the flow field associated to a finger displays a quadrupole of vortices. The evolution of the flow field and the reorganization of the vortices after a tip-splitting event are followed experimentally in detail. Numerical integration of a model reaction-diffusion-convection system for an exothermic reaction taking into account possible heat losses through the walls of the reactor shows that the nonlinear properties of the flow field are different whether the walls are insulating or conducting. In insulating systems, the flow field inside one finger features only one pair of vortices. A quadrupole of flow vortices arranged around a saddle-node structure similar to the one observed experimentally is obtained in the presence of heat losses suggesting that heat effects, even if of very small amplitude, are important in understanding the nonlinear properties of fingering of exothermic chemical fronts.

Fingering of exothermic reaction-diffusion fronts in Hele-Shaw cells with conducting walls

We consider the influence of heat losses through the walls of a Hele-Shaw cell on the linear stability and nonlinear dynamics of exothermic chemical fronts whose solutal and thermal contributions to density changes have the same signs. Our analysis is based on the reaction-diffusion-convection equations obtained from the Darcy-Boussinesq approximation. The parameters governing the equations are the Damkohler number, a kinetic parameter d, the Lewis number Le, the thermal-expansion coefficient gammaT, and a heat-transfer coefficient alpha which measures heat losses through the walls. We show that for thermally insulating walls, the temperature profile is a front that follows the concentration profile, while in the presence of heat losses, the temperature profile becomes a pulse that leads to a nonmonotonic density profile which in turn may lead to a destabilization of an otherwise stable front.