Arno F. Münster

Oxidation of ascorbic acid by air oxygen catalyzed by copper(II) ions in batch and continuous flow stirred tank reactors: bistability, oscillations and stochastic resonance

We report various nonlinear phenomena observed in the oxidation of ascorbic acid (H2Asc) by molecular oxygen in the presence of copper(II) ions in a continuous flow stirred tank reactor (CSTR) as well as in a batch reactor (closed system). Transient irregular oscillations were observed in a batch reactor by varying the initial concentrations of H2Asc and copper(II) ions. The behavior of the system in a CSTR was studied by varying the flow rate (kf) and the inflow concentrations of H2Asc and copper(II) ions. At low inflow concentrations of copper(II) ions the system exhibits bistability and small amplitude regular oscillations. In a two-dimensional parametric plot with coordinates kf and [Cu2+]0 the regions of bistability and oscillations form a cross-shaped diagram if the inflow concentration of H2Asc is kept constant. For increasing values of kf oscillations emerge ia a Hopf bifurcation and disappear due to a homoclinic orbit. Simultaneously applied small amplitude periodic and stochastic perturbations imposed onto the flow rate close to the bistable region revealed the phenomenon of stochastic resonance, which is confirmed by an analysis of probability distribution functions, power spectra, and singular value decomposition.

Spatial entrainment of patterns during the polymerization of acrylamide in the presence of the methylene blue–sulfide chemical oscillator

Abstract Turing-like patterns formed during the polymerization of acrylamide in the presence of sulfide, methylene blue and molecular oxygen are presented. We propose a chemical model of the polymerization of acrylamide in the presence of sulfide and oxygen. The model explains the formation of Turing patterns in this system. The experimental process of pattern formation becomes light sensitive if methylene blue is added. A space-periodic perturbation may thus be introduced into the system and spatial entrainment effects can be studied. The perturbation was realized by imposing an illumination pattern upon the reactive layer: after mixing the gel components and the MBO system in a Petri dish, a mask made of transparent film was placed between the light source and the dish. At different perturbation wavelengths we observed synchronization with the perturbation as well as irregular responses.

Resonant chaos control by light in a chemiluminescent reaction

Abstract We present the resonant method of chaos control using light as the control parameter. The experiments have been carried out with the chemiluminescent Belousov–Zhabotinsky (BZ) reaction, which is catalyzed by a mixture of cerium and ruthenium (tris(2-2′-bipyridine)ruthenium(II) ([Ru(bpy 3 )] 2+ )) in a continuous-flow stirred tank reactor. The perturbation by light (470 nm) is applied in the form of rectangular light pulses at the absorption wavelength of [Ru(bpy 3 )] 2+ . Several unstable periodic orbits (UPO) of different periodicities (P1, P2 and P3) have been stabilized. It is demonstrated that the UPOs are embedded in the chaotic attractor. For simulations and tracking calculations, we use the 7-variable Montanator model by Gyorgyi and Field.

Periodic and irregular wave patterns in an open tubular gel reactor

Abstract In an open quasi-one-dimensional Belousov-Zhabotinsky reaction-diffusion system we investigated simple periodic, complex and irregular spatiotemporal concentration patterns emerging under oscillatory boundary conditions. Symmetric (identical) feed concentrations were used at each boundary of a tabular gel reactor and the length of the system was varied. For tubes shorter than 11 mm the intrinsic wavelength is larger than half the length of the tube. In this case regular pairs of pulse waves are generated. When the length of the tube was increased we found more complex spatiotemporal behavior. Small inevitable differences in the oscillation frequencies at the boundaries finally lead to irregular patterns. The Karhunen-Loeve decomposition technique was applied for an analysis of the observed patterns.

Complex Behaviour of Spiral Waves Induced by an Alternating Electric Field

An efficient control of chemical waves is desirable in various fields of science and engineering. We present a novel method to control the motion of the spiral tip using an electric field perpendicular to the plane of wave propagation. An alternating field may lead to complex spatio-temporal patterns. Shown in the picture is an example of the destabilising effect of an alternating electric field, in which the wavefront displays fluctuating wrinkles.

Macroscopically structured polymer formation governed by spatial patterns in the Belousov–Zhabotinsky reaction

Abstract We report the formation of macroscopically structured cross-linked polyacrylamide hydrogel in the Belousov–Zhabotinsky (BZ) system (oxidation of malonic acid by bromate catalyzed by ferroin). Here, acrylamide, the cross-linker bis-acrylamide, and polymerization initiator are added into the BZ system. We show that the formation of waves and ripples in the polymer is governed by spatial structures emerging in the BZ system. Without any spatial structures in the BZ system only the formation of a spatially uniform polymer is observed. Without cross-linker, a spatially uniform polymer was observed as well. Structured polymer formation is caused by the interaction of chemical reactions in the BZ system and the polymerization process including gelation and cross-linking of the monomer units.

EXPERIMENTAL COUPLING OF CHEMICAL OSCILLATORS BY AN EXCITABLE MEDIUM

Abstract In this work we report the experimental coupling of two Belousov-Zhabotinsky systems run in stirred flow cells. The coupling is achieved by an excitable BZ-medium connecting both reactors. Pulse waves are triggered by one of the reactors which is in an oscillatory state. The waves perturb the reaction in the second cell which is either in a steady or an oscillatory state. Entertainment as well as irregular behaviour is observed.