Olga Nekhamkina

Pattern formation in homogeneous and heterogeneous reactor models

This work qualitatively and quantitatively compares spatiotemporal patterns in homogeneous and heterogeneous models of a fixed catalytic bed for reactions with oscillatory kinetics. Pattern selection is based on the oscillatory or bistable nature of the kinetics and on the nature of fronts. The heterogenous model can exhibit local bistability while the homogeneous model does not admit this property: when flow terms are accounted for both models can be approximated by a cell-model suggesting a simple conversion between the parameters of both models. The parameter-conversion approximation (1/Pe,eff=1/Pe+1/β, where β is the external transport parameter) can predict quite well the dynamics of the heterogenous model with a pseudohomogeneous one when β≫Pe, but it fails when both parameters are comparable. The dynamic behavior is sensitive to the boundary conditions applied. Several qualitative differences between the two models are pointed out.

Modeling of temporally complex breathing patterns during Pd-catalyzed CO oxidation

A mathematical model is formulated to account for experimental infrared thermography observations of spatiotemporal patterns during catalytic oxidation of CO over Pd supported on a glass-fiber disk-shaped cloth in a continuous reactor with feed flowing perpendicular to and through the disk. The model predicts the following observed features: (a) The sustained pattern that the system exhibits is a breathing motion in which a hot spot expands and contracts continuously. This motion emerges due to the imposed cold-edge boundary condition and a qualitative analysis of the experiments supports this suggestion and rules out other mechanisms. (b) The emerging temporally complex patterns can be classified as mixed-mode oscillations with a large relaxation-type conversion peak superimposed with several smaller peaks. (c) The mathematical mechanism that accounts for the change in the number of smaller peaks with varying operating conditions (the reactor temperature) could be characterized as period adding. The math...

Pattern formation in models of fixed-bed reactors

Abstract This work reviews and compares spatiotemporal patterns in three models of adiabatic fixed catalytic beds for reactions with oscillatory kinetics: homogeneous and heterogeneous models, which are studied using generic first-order kinetics, and a detailed model of CO oxidation in the monolithic reactor. These three models describe reactors with one, two or all three phases (fluid-, solid- and adsorbed-phases), respectively. Pattern selection is based on the oscillatory or bistable nature of the kinetics and on the nature of fronts. The heterogenous and detailed models may exhibit local bistability while the homogeneous model does not admit this property: a simple conversion between the parameters of the homogeneous and heterogeneous models is suggested. The spatiotemporal patterns in the reactor can be predicted from the sequence of phase planes spanned by the reactor. Stationary or oscillatory front solutions, oscillatory states that sweep the whole surface or excitation fronts may be realized in the homogeneous and heterogeneous models. The detailed model of the converter may exhibit oscillatory motion, which may be periodic or chaotic, in which typically a hot domain enters the reactor exit and moves quickly upstream; the following extinction occurs almost simultaneously due to strong coupling by convection.

Thermal patterns in simple models of cylindrical reactors

The propagation of fronts and the emergence of spatiotemporal patterns on a cylindrically shaped thin catalytic reactor is simulated with a homogeneous model of a .xed catalytic bed, with characteristically large Lewis and Peclet numbers, and a .rst-order Arrhenius kinetics (i.e., thermokinetic model) which may be coupled with slow changes of catalytic activity (i.e., oscillatory kinetics). Planar fronts of the thermokinetic model may undergo symmetry breaking in the transversal direction only at relatively low Lewis number, but for high Le the front remains 4at. Patterns due to oscillatory kinetics in reactors of high Le are shown, for the .rst time, to undergo symmetry breaking in the azimuthal direction when the perimeter is su6ciently large. The generic regular patterns simulated then are rotating multi-wave patterns of constant rotation-speed and oscillatory-‘.ring’ ones, and theirs selection is highly sensitive to governing parameters and initial conditions. The results are organized in bifurcation diagrams showing the coexisting two-dimensional solutions with varying perimeter. Increasing convective velocity or reactor radius leads to symmetry breaking of regular patterns and the system may switch to chaos. ? 2003 Elsevier Science Ltd. All rights reserved.

Reaction-diffusion patterns on a disk or a square in a model with long-range interaction

A condensed model that captures the main features of high- or low-pressure catalytic oscillators is used to simulate spatiotemporal patterns in a catalytic disk or square. This model includes a single autocatalytic variable (activator), a slowly changing and localized inhibitor, and a very fast and highly diffusive variable that provides the long-range interaction. The extremely rich plethora of patterns is classified according to their symmetries, capitalizing on the inversion symmetry of the model. The simpler case of the bistable system (with no inhibitor) exhibits a very high sensitivity to initial conditions that leads to large multiplicity of stationary patterns. The effect of the parameter that defines the system stability (oscillatory, excitable, or bistable) is investigated, in the three variable model, either by using the same initial conditions for all simulations or, in an “experimental mode,” by stepping up or down the parameter. Patterns on a disk may be classified as circular, like stationa...

Catalytic spatiotemporal thermal patterns during CO oxidation on cylindrical surfaces: Experiments and simulations

Dynamics of spatiotemporal thermal patterns during the catalytic CO oxidation over Pd supported on a glass-fiber catalytic cloth rolled into a tube of 20 mm diameter and 80 mm length has been studied in a continuous flow reactor by IR thermography. A specially designed aluminum mirror built in the reactor provided image of the entire surface of the horizontally held catalytic tube. With flow in the main axial direction and through the tube surface, we observed periodic motions of a pulse, which was born downstream and propagated upstream. The temperature pulse motion was accompanied by conversion oscillations of CO2. With flow in the main axial direction, parallel to the surface, we observed a stationary hot zone after an oscillatory transient. These patterns can be simulated with a plug-flow-reactor-like heterogeneous reactor model that incorporates previously determined kinetic and transport parameters.

Moving waves and spatiotemporal patterns due to weak thermal effects in models of catalytic oxidation

We analyze the behavior of a microkinetic model of a catalytic reaction coupled with weak enthalpy effects to show that under fixed gas-phase concentrations it can produce moving waves with an intrinsic length scale, when the underlying kinetics is oscillatory. The kinetic model incorporates dissociative oxygen adsorption, reactant adsorption and desorption, and surface reaction. Three typical patterns may emerge in a one-dimensional system (a long wire or a ring): homogeneous oscillations, a family of moving waves propagating with constant velocities, and patterns with multiple source/sink points. Pattern selection depends on the ratio of the system length to the intrinsic wave length and the governing parameters. We complement these analysis with simulations that revealed a plethora of patterned states on one- and two-dimensional systems (a disk or a cylinder). This work shows that weak long-range coupling due to high feed rates maintains such patterns, while low feed rates or strong long-range interaction can gradually suppress the emerging patterns.

Modeling and optimization of a periodic process of adsorption and catalytic regeneration

Abstract An adsorption process of water pollutants on a bed of activated carbon (AC) modified with metal oxide catalysts, was integrated in a single unit with periodic catalytic gas-phase regeneration at 240–290°C. In the present contribution we report on the kinetics of the regeneration process: it exhibit an induction period and the rate passes through a maximum. Replotting the data scaled with respect to the maximal rate and the corresponding time shows that the curves overlap. In the process of regeneration the adsorbate moves from the carbon to the metal catalyst crystallites probably by surface diffusion. This process is modeled and compared with experimental observations. Solutions of suggested models with various kinetics are compared with experimental observation enabling to extract parameters like activation energies and rate constants.

Stationary fronts due to weak thermal effects in models of catalytic oxidation

We analyze the possible existence of an infinite number of stationary front solutions in a microkinetic model of a catalytic reaction coupled with weak enthalpy effects in the domain of kinetics bistability. The kinetic model incorporates three steps: dissociative oxygen adsorption, reactant adsorption and desorption, and surface reaction. The infinitude of stationary front solutions emerges due to the lack of intercrystallites communication of surface species in supported catalysts; thermal conductions and gas-phase diffusion are the only means of interaction. Incorporation of surface species diffusion leads to a very slow front motion. We complement this analysis with simulations of stationary states on one- (wire and ring) and two-dimensional (disk) systems which may be subject to control or to fluid flow. These results account for certain experimental results and may have implications for various technological problems.

Spatiotemporal reaction-diffusion patterns emerging on cylindrical surfaces due to global coupling

A condensed polynomial model, that captures the main features of high- or low-pressure catalytic oscillations, is used to simulate spatiotemporal patterns in a cylindrical catalytic surface. This model includes a single autocatalytic variable (activator) and a slow changing and localized inhibitor subject to a global interaction mechanism which maintains the spatial average of the activator at the set point. While for very short (small length L) or very narrow (small perimeter P) cylinders the pattern preserves the structures of the corresponding one-dimensional problems (a ring or a wire), two-dimensional patterns emerge for comparable L and P showing a large multiplicity of spatiotemporal behavior because of a very high sensivity to initial conditions. The effect of kinetic parameters and system size is studied. Approximate solutions for the bifurcation from one- to two-dimension patterns are derived.