The role of fluctuations in bistability and oscillations during the H2 + O2 reaction on nanosized rhodium crystals.

A combined experimental and theoretical study is presented of fluctuations observed by field ion microscopy in the catalytic reaction of water production on a rhodium tip. A stochastic approach is developed to provide a comprehensive understanding of the different phenomena observed in the experiment, including burst noise manifesting itself in a bistability regime, noisy oscillations, and nanopatterns with a cross-like oxidized zone separating the surface into four quadrants centered on the {111} facets. The study is based on a stochastic model numerically simulating the processes of adsorption, desorption, reaction, and transport. The surface diffusion of hydrogen is described as a percolation process dominated by large clusters corresponding to the four quadrants. The model reproduces the observed phenomena in the ranges of temperature, pressures, and electric field of the experiment.

Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front.

A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a denser alkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally and theoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contact line between the two solutions as convective plumes develop in the acidic solution only. We investigate here by a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple A+B→C reaction the relative role of solutal versus thermal effects in the origin and location of this instability. We show that heat effects are much weaker than concentration-related ones such that the heat of reaction only plays a minor role on the dynamics. Computation of density profiles and of the stability analysis eigenfunctions confirm that the convective motions result from a diffusive layer convection mechanism whereby a locally unstable density stratification develops in the upper acidic layer because of the difference in the diffusion coefficients of the chemical species. The growth rate and wavelength of the pattern are determined experimentally as a function of the Brinkman parameter of the problem and compare favorably with the theoretical predictions of both LSA and nonlinear simulations.

Hot spots in density fingering of exothermic autocatalytic chemical fronts.

Measurements of two-dimensional (2D) temperature fields are performed by an interferometric method during density fingering of the autocatalytic chlorite-tetrathionate reaction in a Hele-Shaw cell. These measures confirm that, because of heat losses through the glass walls of the reactor, the temperature profile across the front is a pulse rather than a front. Moreover, the full 2D temperature field shows the presence in the reactive zone of hot spots where the temperature exceeds the maximum temperature measured in a stable planar front. We investigate here experimentally the increase of temperature in the hot spots when the composition of the reactants is varied to increase the exothermicity of the reaction. We back up these experimental observations by nonlinear simulations of a reaction-diffusion-convection model which show that the maximum temperature reached in the system depends on the intensity of convection.

Chemically driven hydrodynamic instabilities.

In the gravity field, density changes triggered by a kinetic scheme as simple as A+B-->C can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars A and B. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns. This is demonstrated both numerically and experimentally on the specific example of a simple acid-base neutralization reaction.

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.

Nonlinear reactive systems on a lattice viewed as Boolean dynamical systems.

We present a stochastic, time-discrete Boolean model that mimics the mesoscopic dynamics of the desorption reactions A+A-->A+S and A+A-->S+S in a one-dimensional lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations for the subset of moments involving contiguous lattice sites. The solution of the hierarchy allows to compute the exact dynamics of the mean coverage for both microscopic and coarse-grained initial conditions, which turn out to be different from the mean field predictions. The evolution equations for the mean coverage and the second-order moments are shown to be equivalent to those provided by a time-continuous master equation. The important role of higher-order fluctuations is brought out by the failure of a truncation scheme retaining only two-particle fluctuation correlations.