Exothermic Front Research Articles

Thermally Driven Convection Generated by Reaction Fronts in Viscous Fluids

Reaction fronts propagating in liquids separate reacted from unreacted fluid. These reactions may release heat, increasing the temperature of the propagating medium. As fronts propagate, they will induce density changes leading to convection. Exothermic fronts that propagate upward increase the temperature of the reacted fluid located underneath the front. For positive expansion coefficients, the warmer fluid will tend to rise due to buoyancy. In the opposite case, for fronts propagating downward with the warmer fluid on top, an unexpected thermally driven instability can also take place. In this work, we carry out a linear stability analysis introducing perturbations of fixed wavelength. We obtain a dispersion relation between the perturbation wave number and its growth rate. For either direction of propagation, we find that the front is stable for very short wavelengths, but is unstable for large enough wavelengths. We carry out a numerical solution of a cubic reaction–diffusion–advection equation coupled to Navier–Stokes hydrodynamics in a two-dimensional rectangular domain. We find transitions between the non-axisymmetric and axisymmetric fronts increasing with the width of the domain.

Convection induced by thermal gradients on thin reaction fronts.

We present a thin front model for the propagation of chemical reaction fronts in liquids inside a Hele-Shaw cell or porous media. In this model we take into account density gradients due to thermal and compositional changes across a thin interface. The front separating reacted from unreacted fluids evolves following an eikonal relation between the normal speed and the curvature. We carry out a linear stability analysis of convectionless flat fronts confined in a two-dimensional rectangular domain. We find that all fronts are stable to perturbations of short wavelength, but they become unstable for some wavelengths depending on the values of compositional and thermal gradients. If the effects of these gradients oppose each other, we observe a range of wavelengths that make the flat front unstable. Numerical solutions of the nonlinear model show curved fronts of steady shape with convection propagating faster than flat fronts. Exothermic fronts increase the temperature of the fluid as they propagate through the domain. This increment in temperature decreases with increasing speed.

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.

Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses

Across traveling autocatalytic fronts, density differences due to composition and temperature changes can lead to buoyancy-driven hydrodynamic instabilities deforming the front by convective motions. We study here the influence of heat losses through the walls of the reactor on the stability of such exothermic fronts in the gravity field. The stability domain is computed numerically in a parameter space spanned by the solutal R c and thermal R T Rayleigh numbers of the problem for various values of the Newton's coefficient α quantifying the intensity of heat losses.

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.

On problems involving gas flows associated with gasdynamic discontinuities

A review is given concerning the formulation of problems of nonviscous gas flows with discontinuities associated with a deposition of energy in the flowing medium. It is shown that with a known amount of energy at the exothermic front it is not possible to determine the solution of the problem uniquely. To find a unique solution, supplementary information is required; in particular, the mode of the propagation of the exothermic front must be known. In a number of cases this supplementary information can be obtained by considering the initial phases of the motion on the basis of a more detailed model of the gaseous medium and by the examination of the stationary structure of the discontinuity. Examples are given for the establishment of such criteria corresponding to different modes of the propagation of the exothermic front in problems where concentrated energy is deposited in media capable of self-generation of an exothermic process as a consequence of a chemical or a thermonuclear reaction. It is also demonstrated that when an exothermic front propagates under variable conditions, additional criteria are required in order to determine possible changes in the mode of its propagation. Example is given of an establishment of such a criterion in a simple problem involving a detonation wave.