Chemical complexity: Spontaneous and engineered structures

Kiss, István Z.; Hudson, John L.

doi:10.1002/aic.690490902

Cited by 46 publications

(29 citation statements)

References 51 publications

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“…The boundary conditions effect becomes insignificant at distance f^0.2 before the front, where the dimensionless temperature and concentrations do not exceed 10 À8 using BC's (11). So, the simulations in a moving frame were conducted with the Danckwerts BC (11) and we verified, that the length L is sufficiently long to neglect the BC effect.…”

Section: Planar Front and Its Linear Stability Analysissupporting

confidence: 38%

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Nekhamkina

Sheintuch

2011

AIChE Journal

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We derive a new criterion for transversal instability of planar fronts based on the bifurcation condition dV f /dK| K¼0 ¼ 0, where V f and K are the front velocity and its curvature, respectively. This refines our previously obtained condition, which was formulated as a ¼ (DT ad Pe T )/(DT m Pe C ) [ 1 to a [ 1 þ |d|, where DT ad and DT m are the adiabatic and maximal temperature rise, respectively, Pe C and Pe T are the axial mass and the heat Pe numbers, respectively, and d is a small parameter. The criterion is based on approximate relations for DT m and V f , which account for the local curvature of a propagating front in a packed bed reactor with a first-order activated kinetics. The obtained relations are verified by linear stability analysis of planar fronts. Simulations of a simplified 2D model in the form of a thin cylindrical shell are in good agreement with the critical parameters predicted by dispersion relations. Three types of patterns were detected in simulations: ''frozen'' multiwave patterns, spinning waves, and complex rotating-oscillating patterns. We map bifurcation diagrams showing domains of different modes using the shell radius as the bifurcation parameter. The possible translation of the 2D cylindrical shell model results to the 3D case is discussed. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: 735-748, 2011 Keywords: reactor analysis, simulation, process, fronts, bifurcations, transversal patterns IntroductionHeterogeneous catalysts are extensively used in the chemical and petrochemical industry and for pollution abatement purposes. It is usually assumed that the temperature and concentrations of the reactants at any transversal cross section of an adiabatic packed-bed reactor are uniform. However, various industrial and laboratory experimental observations revealed formation of nonuniform temperature in the reactor cross section. Such patterns may pose severe safety hazards by altering the wall strength and inducing cracks. Ignoring such patterns in design and simulations may lead to erroneous results. Understanding which kinetics may lead to spatiotemporal pattern formation is essential for the development of design and control strategies that circumvent them.Symmetry-breaking leading to either spatial and/or spatiotemporal pattern formation has been observed in many biological, physiological, chemical, and electro-chemical systems [1][2][3][4][5][6][7][8] governed by the interaction of diffusion and reaction processes. Majority of the studies of pattern formation in chemically reacting systems are of homogeneous systems. Pattern formation in heterogeneous catalytic and electrochemical systems, like wires, pellets, and packed bed reactors has been known for 20 years. Recent reviews of the and Krischer. 12 The current knowledge and understanding about the formation of transversal temperature patterns has been reviewed by Viswanathan et al. 13The obtained results are kinetics-dependent 14 and in the present study we focus on kinetics that admits multiple steady sta...

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Section: Planar Front and Its Linear Stability Analysissupporting

confidence: 38%

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Nekhamkina

Sheintuch

2011

AIChE Journal

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“…Nonlinear chemistry [1][2][3][4], engineered complexity [5], biological analogies, and possible analytical applications [6] motivated the research initiated in the past few years in the field of the electrolyte diodes and transistors [3,4,[6][7][8][9][10]. The "building block" of these devices is a hydrogel cylinder connecting reservoirs of two different electrolytes.…”

Section: A Background Of the Researchmentioning

confidence: 39%

Electrolyte diodes and hydrogels: Determination of concentration andpKvalue of fixed acidic groups in a weakly charged hydrogel

et al. 2004

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Current-voltage (CV) characteristics of polyvinyl alcohol (PVA)-glutardialdehyde hydrogel cylinders were measured in aqueous KCl solutions. To this end a new special apparatus was constructed where the gel cylinder connects two electrolyte reservoirs. The measured quantities are the electric current flowing through the gel and the potential difference between the two reservoirs. Concentration polarization near the gel-liquid interfaces is decreased considerably by applying an intense mechanical stirring in both reservoirs. Under these conditions below 1 V concentration polarization is negligible, and the CV curves are nearly straight lines. It was found that the gel applied here is a weakly charged anionic hydrogel. Concentration of fixed anions was determined from the slope of these lines measured in 0.001 and 0.01 molar KCl solutions. Fixed anion concentration of the same piece of gel was measured also with a different method, when the gel was used in an acid-base diode. In this case one reservoir contained 0.1 molar HCl, and the other 0.1 molar KOH. From the results of the two measurements, the concentration (4.45 x 10(-3) M) and the pK value (4.03) of the fixed acid groups responsible for the anionic character of the gel was calculated. The pK value is compatible with fixed carboxylic acid groups contaminating the PVA gel. Furthermore, concentration polarization phenomena in the boundary layers nearby the gel were studied in 0.001 M KCl solutions, measuring the diodelike CV characteristic of a gel cylinder, when stirring was applied only at one side of the gel. Boundary layers facing the cathode or the anode responded in a different way to stirring. The difference cannot be explained completely with the hypothesis of electroconvection suggested previously.

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“…By combining eqn (2) and (3) we obtain differential equations for the dynamical evolution of the electrode potentials:…”

Section: Equivalent Circuit Analysismentioning

confidence: 48%

Dynamics of electrochemical oscillators with electrode size disparity: asymmetrical coupling and anomalous phase synchronization

Wickramasinghe

Mrugacz

Kiss

2011

Phys. Chem. Chem. Phys.

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Experiments are carried out in dual electrode oscillatory Ni electrodissolution in which the two electrodes have different surface areas. The transition to phase synchronization is analyzed as asymmetrical coupling strength, induced by placing a cross resistance between the electrodes, is varied. It is shown that because of nonisochronicity (phase shear, i.e., strong dependence of period on amplitude) of the oscillators, anomalous phase synchronization effects can be observed: advanced/delayed synchronization and, to a lesser extent, frequency difference enhancement. The type of synchronization is strongly affected by the underlying heterogeneities of the oscillators; in the experiments with a slow driver (large surface area) electrode the synchronization is advanced, with a fast driver electrode the synchronization is delayed with respect to symmetrical coupling. The findings thus reveal that the interplay of asymmetrical coupling with the types of inherent heterogeneities plays an important role for the interpretation of size effects in the dynamical behavior of a nonlinear chemical reaction.

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Chemical complexity: Spontaneous and engineered structures

Cited by 46 publications

References 51 publications

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

Electrolyte diodes and hydrogels: Determination of concentration andpKvalue of fixed acidic groups in a weakly charged hydrogel

Dynamics of electrochemical oscillators with electrode size disparity: asymmetrical coupling and anomalous phase synchronization

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