Dynamics and Control of Chemical Waves In Heterogeneous BZ Reaction

Abstract

The Belousov-Zhabotinsky (BZ) reaction is the prototype of a large class of systems that display excitation waves, including the physiological systems such as the heart, brain, and retina. Excitation waves in these systems exhibit similar spatiotemporal patterns, such as expanding target waves or rotating spiral waves. A characteristic feature of the rotating spiral waves is their tendency to pin to heterogeneities in the system. These stable pinned waves can cause fatal cardiac arrhythmias in systems like the heart. Hence the external control of rotating waves is an important requirement. Several studies proposed methods for controlling pinned waves using an external electric field. Field-induced unpinning in the cardiac system is well explored and found to be due to the secondary wave emission from the heterogeneities. The pinned chemical waves can also be unpinned with an electric field. However, secondary wave emission is not observed in the chemical medium. So the mechanism of unpinning is very different for the pinned waves in the BZ reaction as opposed to such waves in the cardiac tissue. This thesis investigates the mechanism of spiral wave unpinning in the BZ reaction using static and rotating electric fields. The unpinning occurs if the applied field strength equals a particular threshold. Using different electric fields, we measured the unpinning phase of the spiral around the obstacle boundary. In a static DC field, independent of the initial phases, the spiral unpins at a fixed unpinning phase for a chosen field strength and chirality. When the initial phase is close to the unpinning phase, the unpinning happens with a fixed delay. Spirals with opposite chirality unpin mirror-symmetrically. In a rotating circularly polarised electric field (CPEF), the unpinning phase changes according to the initial phases and the rotational frequencies of both the field and the spiral. Not only a high-frequency CPEF but also a relatively slow-rotating CPEF or a CPEF with the same frequency as the spiral can induce unpinning if it possesses a threshold amplitude. However, in every case, the spiral unpins as it propagates away from the anode. As the spiral propagates away from the anode, the electric force opposes its natural propagation. If the applied field strength is equal to a particular threshold, the opposition experienced in the spiral propagation leads to unpinning of the tip from the obstacle. The analytical formulae based on this assumption accurately predict the unpinning phase, and the values match wellwith our observations. Such an unpinning by an opposing electric force is not seen in any other excitable medium. We conclude that, in the BZ medium due to the advective motion of the ions the chemical excitation waves interact with an applied electric field uniquely. We hope our work will provide a better understanding of the control of excitation wave dynamics using an external electric field.