Pattern Dynamics by Interaction of Chemical Waves and Hydrodynamic Flows

Abstract

Chemical reactions evolving under far from equilibrium conditions may exhibit self-organization in time and in space, such as oscillations in homogeneous solution or waves, that is concentration gradients travelling through space (Field and Burger, 1985; Ross et al., 1988). One of the classical systems in which such nonlinear phenomena have been investigated in much detail is the Belousov-Zhabotinskii reaction having oscillatory reaction kinetics (Zhabotinskii, 1964; Field et al., 1972, Bornmann et al., 1973). When choosing an appropriate chemical composition, this reaction can be prepared such that it remains in an excitable state when a small volume is placed into a petri dish, resulting in a liquid layer of thickness of 1 mm or less. Then, a local stimulus (e.g. a hot wire or just a dust particle) produces an excited state which propagates into the outer regions of the medium as a circular wave of excitation. Breaking a wave front leads to the formation of rotating spiral-shaped waves (Winfree, 1972; Müller et al., 1985a). Both geometric forms appear in the experiment shown in Fig. 1. Several authors have treated these structures theoretically by modelling the nonlinear coupling of the complex kinetics of this reaction and diffusion (Tyson and Keener, 1988, and references therein; Zykov, 1988).