Asymmetric steady states revisited

Alternative steady states of a multistable kinetic system can be attained at different locations along a catalytic surface. Propagation of resulting sharp concentration and/or temperature fronts leads to restoration of uniformity, unless special mechanisms come into action to preserve the emerging pattern. Two mechanisms leading to stabilization of asymmetric steady states are described here. The first one, called a global regulator, involves rapid pattern generation due to isothermal kinetics with forward inhibition or backward activation and freezing of propagating concentration fronts into steady inhomogeneities due to slow thermal interactions. Oscillatory solutions (swinging waves) with undulating motion of concentration fronts can be also generated this way. Another mechanism, called a landscape variegator, is based on modification of a catalyst under the influence of local reaction conditions corresponding to alternative homogeneous steady states which results in preservation of these states on stretches of the surface where they once have emerged.     

Inhomogeneities and surface structures in oscillatory catalytic kinetics

The existence of inhomogeneous surface states is investigated for three oscillatory kinetic models, using realistic values of rate and communication parameters. The analysis shows that local oscillators are effectively synchronized if the autocatalytic variable is a gas-phase concentration. If a surface concentration is the autocatalytic variable and the second variable is a gas-phase reactant, the system will admit an inhomogeneous solution in the form of two surface regions separated by a stationary or undulating front. Oscillations may be translated into either a train of trigger waves or into a stationary inhomogeneous state in a system including two surface reactants.The emergence of inhomogeneous surface states leads to falsification of the apparent reaction kinetics, and may induce dependence of the reaction rate on geometrical factors. It may also facilitate formation of permanent surface structures thereby strongly influencing evolution of the clalyst under the influence of reaction conditions.     

Electrochemical impedance spectroscopy of patterned steady states on electrode surfaces

In this work we report modelling of electrochemical impedance spectra for the CO bulk electrooxidation on Pt, an electrochemical system with an S-shaped current-potential curve (S-NDR (negative differential resistance) system). Galvanostatic control and parameter ranges, in which self-organized stationary CO-coverage patterns exist on the electrode surface are considered. The patterns consist of two stationary domains with different CO coverages. The simulations show that at very low frequencies the applied current modulation imposes a domain size modulation which occurs at nearly constant electrode potential. Consequently, the interface impedance modulus tends to zero at very low frequencies and no negative real impedance can be observed in the simulated impedance spectra. For higher modulation frequencies, the faster current modulation affects the domain size expansion and contraction processes, inducing an increase of the interface impedance modulus and a dependence of its phase on the frequency. These results demonstrate that the dynamics of pattern formation affects considerably the linear response of an electrochemical system. Furthermore, they suggest that measurements of impedance spectra can offer valuable information on the dynamics of pattern formation and of the electrochemical processes involved.     

Pattern formation in models of fixed-bed reactors

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.     

A Quasi-steady-state analysis of the dynamics of two-species heterogeneous catalytic reactions

This study demonstrates how low-order algebraic non-linearities that exist in a simple two-component Langmuir-Hinshelwood type reaction kinetics (CO oxidation) are sufficient to produce rate multiplicities and oscillatory steady states (periodic solutions). A singular perturbation analysis is employed wherein certain quasi-steady-state considerations are made which lead to the definition of system manifolds and invariants along which the large-time dynamics of the system can be discerned without recourse to numerical integration. New results, confirmed by simulation, include an explanation for such experimentally observed pathological phenomena as the coexistence of oscillatory and stationary steady states and multi-peak oscillations. It is shown how the existence of oscillatory states and a plausible “buffering” physisorption surface reaction mechanism causing a periodic switching between these states and coexisting stationary ones can give rise to these multi-peak oscillations.     

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Formation of transversal patterns in a 3D cylindrical reactor is studied with a catalytic reactor model in which an exothermic first‐order reaction of Arrhenius kinetics occurs with a variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution with the front position oscillating in the axial direction. Three types of patterns were simulated in the 3D system: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating–oscillating fronts. These solutions coexist with the planar front solution and require special initial conditions. We map bifurcation diagrams showing domains of different modes using the reactor radius as a bifurcation parameter. The possible reduction of the 3D model to the 2D cylindrical shell model is discussed. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Stationary and traveling hot spots in the catalytic combustion of hydrogen in monoliths

In the course of catalytic combustion of hydrogen (1-5% H₂ in air) in monolith reactors, strongly localized stationary and traveling hot spots arise in response to a sudden and persistent rise of gas flow velocity. Such hot spots may occur, e.g. in a catalytic converter following the acceleration of a car or in a catalytic combustor as a result of a load increase. This phenomenon is illustrated by simulations using a two-phase reactor model. The temperature overshoot of the adiabatic limit is typically of the order of the adiabatic temperature rise itself.The following mechanism underlies this behavior. Light fuel is supplied to the catalytic wall by fast diffusion (in the direction perpendicular to flow), while the heat released by reaction is removed from the wall by the slower, mixture-averaged heat conduction. This leads to accumulation of heat at the catalytic surface that eventually saturates at high temperatures. The hot spots may exhibit intricate dynamics, propagating downstream or upstream, or they may remain stationary. The direction of propagation depends on the relative strength of convective downstream and conductive upstream contributions to the overall displacement of reaction fronts. Generally, the hot spot tends to drift downstream at low flow velocities, remain stationary at intermediate flow velocities, and drift upstream at high flow velocities.     

DIFFERENTIATION OF DEACTIVATION DISGUISED KINETICS IN TRANSPORT REACTORS BY WAVEFRONT ANALYSIS

The deactivation disguised kinetic schemes in an isothermal transport reactor are differentiated theoretically by wave front analysis. Riemann's integration method is applied to the linearised hyperbolic partial differential equations describing the reactor dynamics for a small step change in inlet concentration. It is shown that the front of the outlet concentration wave is different for deactivation disguised kinetic schemes even though the final steady states are the same. For the startup condition, where the linearised model is not valid, the wave front is obtained by solving numerically the original partial differential equations. @KEYWORDS: Transport reactors, Deactivation disguised kinetics, Wave front analysis.     

Dynamic behavior of splitting flames in a heated channel

Flame-propagation dynamics with dual peaks in a heated microchannel is predicted by employing a thermal-diffusive model taking into account two reactants. After auto-ignition, the flame immediately splits into two reaction fronts with different luminosities. One front propagates upstream, whereas the other moves downstream, and finally they both extinguish. After some delay, the process is repeated, and reignition of the fuel-air mixture is induced by hot walls. It is also shown that the commonly used infinitely thin reaction zone model, which has no reactant concentration dependence, is not capable of capturing this phenomenon. The splitting flame dynamics with dual fronts is confirmed by photographs taken with a high-speed digital video camera in experimental investigations with a propane-air mixture. The experiments reveal interesting details, namely, coexistence of triple reaction peaks during the process of propagation of splitting flames is observed, and the flame splitting phenomenon occurs twice in one extinction-ignition period. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 12–18, May–June, 2009.     

Phase dynamics and wetting layer formation mechanisms of pattern-directed phase separation in binary polymer mixture films with asymmetry compositions

Focusing on the binary polymer mixture films under the off-critical condition, the phase dynamics and wetting layer formation mechanisms of pattern-directed phase separation are numerically investigated. The simulated results demonstrate that, for different compositions, the polymer mixtures on the strip patterned surface can exhibit various phase morphologies in the strips of the bulk, which can be used to tailor the microscopic structures of films. The evolutions of these phase structures in the strips of the bulk obey almost the same power law with an exponent of 1/3, i.e., the Lifshitz-Slyozov growth law for the films with various off-critical degrees. It is found that the wetting layer thickness near the patterned surface grows logarithmically at the initial stages, just like the wetting layer formation mechanism of the polymer mixture near the surface with an isotropic potential. This revels that only patterning the surface potential may not change the growth law of the wetting layer. The simulated results also indicate that the diffusion of the component in the direction parallel to the surface originates from the edge of the strips.     

Hydrodynamical instability of spatially extended bistable chemical systems

Hydrodynamical density fingering of chemical fronts separating two miscible, stable steady states of different chemical composition, and hence density, can lead to complex spatio-temporal dynamics. The most striking feature of such dynamics is the disconnection of droplets of one stable steady state from fingers invading the other stable steady state. Such disconnected droplets do not exist in pure density fingering and are thus the result of the bistable kinetics. We study such dynamics by direct numerical simulations of Darcy's law for flow in Hele-Shaw cells coupled to the kinetic equation for the concentration of a chemically reacting solute controlling the density of the miscible solutions. The concentration of this solute obeys a simple cubic model leading to bistability. Experimental realization of such dynamics in spatially extended Hele-Shaw cells calls for the use of the concept of spatial bistability which implies construction of new continuously fed open reactors.     

Velocity of flame propagation upon development of hydrodynamic instability

On the basis of a theoretical analysis and numerical calculations, it has been shown that the dynamics of a flame surface under conditions of hydrodynamic instability can be represented as the interaction of a finite number of nonlinear configurations of the flame front. Their number is defined by the physical size of the system in which the flame propagates. It has been shown that the development of an initial plane front leads to a stationary regime at which the propagation velocity of the curved flame tends asymptotically to its limiting value independent of the size of the system in which burning takes place. This conclusion is based on the exact solution of the nonlinear equation describing hydrodynamic instability of flame. Institute of Thermophysics, Novosibirsk. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 6, pp. 19–25, November–December, 1993.     

Velocity of the simplest solid-phase chemical reaction front and internal mechanical stresses

The theory of thermal and mass elasticity is the basis for deriving equations for describing the stationary front of chemical transformations in a deformable medium. Approximate formulas are obtained for the case of a zero-order reaction for calculating the stationary velocity in different particular cases. An increase in the front velocity is shown to be possible, in particular, as a result of direct activation of the chemical reaction at the expense of the work done by the deformation forces. Estimates for the characteristic temperature of the front and combustion are presented. The first value is due to fracture in the front and is defined by the condition of stationary propagation of cracks. In this case, there exist two stationary front velocities. This corresponds to different temperature profiles.V. V. Kuibyshev Tomsk State University, Tomsk. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 1, pp. 44–54, January–February, 1994.     

Formation of structural defects and strain in electrodegraded Fe‐doped SrTiO3 crystals due to oxygen vacancy migration

We report on our investigation of structural defect and strain formation in electrodegraded reduced and oxidized, Fe‐doped SrTiO₃ (Fe:STO) single crystals using optical second harmonic generation (SHG) and confocal Raman spectroscopy. SHG and Raman spectra reveal structural and electrochemical inhomogeneity resulting from the formation of Fe⁴⁺/oxygen ion and Fe³⁺/oxygen vacancy aggregation sites along the degraded anode and cathode interfaces, respectively. We show that mixed Fe³⁺/Fe⁴⁺ states and structural strain gradients are generated across the color fronts. These results, as well as oxygen sublattice differences between the anodic and cathodic bulk, present the color front as an interface between two dominant oxygen bonding distortions. The strain near the color front shows a strong dependence on oxygen vacancy concentration and diffusion within the crystals. Our characterization of structural and electrochemical changes due to electric field‐induced strain and oxygen vacancy migration advances knowledge of electrodegradation in perovskite‐based titanate single crystals.     

Dynamics of catalytic reactions on microdesigned surfaces

We report experimental and computational studies of reaction dynamics on Pt/Rh and Pt/TiO₂ microcomposite catalytic surfaces. Reaction fronts initiated at the material interface dominate both steady and dynamic behavior of the composite catalytic material. Our analysis links the transient phenomenon of front initiation to the bifurcations of reaction–diffusion systems with active boundaries.     

Catalytic Membrane Reactor Model as a Laboratory for Pattern Emergence in Reaction-diffusion-advection Media

Reaction-diffusion-advection media on semi-infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling waves and stationary periodic states, we review results obtained using a membrane reactor as a case model. Such solutions coexist in overlapping parameter regimes and their temporal stability is determined by the boundary conditions which either preserve or destroy the translational symmetry, i. e., selection mechanisms under realistic Danckwerts boundary conditions. A brief outlook is given at the end.     

Development of a Surface‐Active Coating for Promoted Gas Hydrate Formation

This work deals with the influences of surface‐active coatings made by silanization with an increasing hydrophobicity on methane hydrate formation in view of induction times, gas uptake, and rate of gas consumption. Hydrate formation was performed in a stirred pressure autoclave under stationary and transient conditions in presence of different coatings made from diverse silanes. With increasing carbon chain length of the silanes, promoting effects were observed while using stationary formation conditions.     

Studies of liquid-induced crystallization of bisphenol a polycarbonate

The course of liquid-induced crystallization of a bisphenol A-derived polycarbonate was investigated using acetone, methyl propyl ketone, methyl isobutyl ketone, and xylene as swelling agents. It was found that above a certain temperature, characteristic of a given polycarbonate–swelling agent system, the diffusion process takes place with the formation of a sharp boundary. The velocity of motion of the diffusion front was determined at various temperatures, and these data were then used to calculate the apparent diffusion coefficients and diffusion activation energies for the different swelling liquids employed. Moreover, a distinct separation of the diffusion and crystallization fronts was observed in the systems investigated, changes in the distance between these two fronts having been determined for various swelling temperatures. The above phenomenon was used to determine the experimental conditions making possible the characterization of a crystallization process not controlled by the diffusion of the swelling agent into the sample. The dependence of half-times of crystallization on temperature was determined based on crystallization kinetics studies performed by means of a light depolarization technique.     

The external-pulse introduced pattern in a system with a closer reference electrode and a quasi-one-dimensional ribbon working electrode

In the present work the electrochemical pattern formation was investigated during electro-oxidation of formic acid on platinum electrode. The working electrode is quasi-one-dimensional ribbon polycrystalline platinum. The stationary domains (sDs) have been successfully captured after an external pulse was triggered. At a relatively high conductivity a new kind of electrochemical pattern was found and it is named as cyclopean pattern. In a nonlinear electrochemical system with an N-type negative differential resistance, the theoretical simulation of the spatial temporal structure is able to predict the existence of stationary domains. Increasing the electrolyte conductivity promotes the formation of stationary domains and cyclopean pattern. The difference of the potential amplitudes in two phases (domains) becomes smaller in an electrolyte with a higher conductivity.     

Failure modes in organic coatings studied by scanning acoustic microscopy

Scanning acoustic microscopy (SAM) has been found to be well suited to study physically and chemically induced changes and defects in polymer coatings exposed to corrosive environments. In this work, SAM was used to investigate sub-surface migration and blister formation in polymer coatings of different layer structure after exposure to a corrosive solution. Two model systems consisting of base coat and clear coat on steel substrates where studied. The time evolution of sub-surface migration fronts and blister initiation and their growth were investigated by analysing SAM images after different exposure times. Depending on the layer structure, it was possible to differentiate between transport of the electrolyte solution (i) through the coating and (ii) along the coating/substrate interface. Samples without clear coat typically showed randomly distributed blisters at the coating/substrate interface, irrespective of the location of initial defects. The random distribution of blisters is related to diffusion of the electrolyte solution through the coating layer followed by “nucleation” at weak spots of the substrate, at the interface between polymer and substrate or within the polymer. In contrast, samples with a clear coat acting as a diffusion barrier showed a sub-surface migration front of 2–4 μm height, propagating along the coating/substrate interface, starting at initial defects. The linear propagation of this front cannot be explained by Fickian diffusion and is discussed in terms of an accelerated diffusion or crack growth kinetics. Since blistering started only at regions, where the migration front has already passed, the presence of electrolyte solution or water at the coating/substrate interface was found to be a prerequisite for the nucleation of blisters.