1
|
Taylor AF. Mechanism and Phenomenology of an Oscillating Chemical Reaction. PROGRESS IN REACTION KINETICS AND MECHANISM 2019. [DOI: 10.3184/007967402103165414] [Citation(s) in RCA: 97] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Chemical reactions, which are far from equilibrium, are capable of displaying oscillations in species concentrations and hence in colour, electrode potential, pH and/or temperature. The oscillations arise from the interplay between positive and negative kinetic feedback. Mechanisms for such reactions are presented, along with the rich phenomenology that these systems exhibit, from complex oscillations and chemical waves, to stationary concentration patterns. This review will focus on the Belousov-Zhabotinksy reaction but reference to other reactions will be made where appropriate.
Collapse
|
2
|
Gambino G, Lombardo MC, Sammartino M, Sciacca V. Turing pattern formation in the Brusselator system with nonlinear diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042925. [PMID: 24229267 DOI: 10.1103/physreve.88.042925] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Indexed: 05/03/2023]
Abstract
In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.
Collapse
Affiliation(s)
- G Gambino
- University of Palermo, Department of Mathematics, Via Archirafi, 34, 90123 Palermo, Italy
| | | | | | | |
Collapse
|
3
|
Pojman JA, Viner V, Binici B, Lavergne S, Winsper M, Golovaty D, Gross L. Snell's law of refraction observed in thermal frontal polymerization. CHAOS (WOODBURY, N.Y.) 2007; 17:033125. [PMID: 17903007 DOI: 10.1063/1.2784386] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
We demonstrate that Snell's law of refraction can be applied to thermal fronts propagating through a boundary between regions that support distinct frontal velocities. We use the free-radical frontal polymerization of a triacrylate with clay filler that allows for two domains containing two different concentrations of a peroxide initiator to be molded together. Because the polymerization reaction rates depend on the initiator concentration, the propagation speed is different in each domain. We study fronts propagating in two parallel strips in which the incident angle is 90 degrees. Our data fit Snell's law v(r)/v(i)=sin theta(r)/sin theta(i), where v(r) is the refracted velocity, v(i) is the incident velocity, theta(r) is the angle of refraction, and theta(i) is the incident angle. Further, we study circular fronts propagating radially from an initiation point in a high-velocity region into a low-velocity region (and vice versa). We demonstrate the close resemblance between the numerically simulated and experimentally observed thermal reaction fronts. By measuring the normal velocity and the angle of refraction of both simulated and experimental fronts, we establish that Snell's law holds for thermal frontal polymerization in our experimental system. Finally we discuss the regimes in which Snell's law may not be valid.
Collapse
Affiliation(s)
- John A Pojman
- Department of Chemistry and Biochemistry, The University of Southern Mississippi, Hattiesburg, Mississippi 39406, USA
| | | | | | | | | | | | | |
Collapse
|
4
|
Volford A, Noszticzius Z, Krinsky V, Dupont C, Lázár A, Försterling HD. Amplitude Control of Chemical Waves in Catalytic Membranes. Asymmetric Wave Propagation between Zones Loaded with Different Catalyst Concentrations. J Phys Chem A 1998. [DOI: 10.1021/jp9824609] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- András Volford
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| | - Zoltán Noszticzius
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| | - Valentin Krinsky
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| | - Christophe Dupont
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| | - Attila Lázár
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| | - Horst-Dieter Försterling
- Center for Complex and Nonlinear Systems and the Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary, Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France, and Fachbereich Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg/Lahn, Germany
| |
Collapse
|
5
|
Hegedus L, Kirschner N, Wittmann M, Noszticzius Z. Electrolyte Transistors: Ionic Reaction−Diffusion Systems with Amplifying Properties. J Phys Chem A 1998. [DOI: 10.1021/jp981488h] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- László Hegedus
- Center for Complex and Nonlinear Systems and The Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary
| | - Norbert Kirschner
- Center for Complex and Nonlinear Systems and The Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary
| | - Mária Wittmann
- Center for Complex and Nonlinear Systems and The Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary
| | - Zoltán Noszticzius
- Center for Complex and Nonlinear Systems and The Department of Chemical Physics, Technical University of Budapest, H-1521 Budapest, Hungary
| |
Collapse
|
6
|
Lazar A, Forsterling HD, Farkas H, Simon P, Volford A, Noszticzius Z. Waves of excitation on nonuniform membrane rings, caustics, and reverse involutes. CHAOS (WOODBURY, N.Y.) 1997; 7:731-737. [PMID: 12779698 DOI: 10.1063/1.166270] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Chemical wave experiments on concentric nonuniform membrane rings are presented together with their theoretical description. A new technique is applied to create a slow inner and a fast outer zone in an annular membrane. An abrupt qualitative change of the wave profile was observed while decreasing the wave velocity in the inner zone. This phenomenon and all the experimental wave profiles can be adequately described by assuming that waves are involutes of a relevant caustic. A possible connection with recent models of atrial flutter is also set forth. (c) 1997 American Institute of Physics.
Collapse
Affiliation(s)
- Attila Lazar
- Fachbereich Physikalische Chemie, Philipps Universitat Marburg, D-35032, Marburg/Lahn, Germany
| | | | | | | | | | | |
Collapse
|