Chemical waves on spherical surfaces

Abstract

THE concentric-circular and spiral patterns exhibited by the Belousov–Zhabotinsky (BZ) reaction in thin films of solution are representative of spatiotemporal behaviour in a two-dimensional, planar excitable medium^1–6. Here we report BZ chemical waves propagating on the two-dimensional surface of a sphere. A wave on the surface of a single cation-exchange bead, loaded with ferroin and bathed in BZ reaction mixture containing no catalyst, develops to form a rotating spiral. Unlike spiral waves in thin films of solution, which typically wind out to connect with a twin rotating in the opposite direction, these waves rotate from pole to pole in a single direction. The spiral winds outward from a meandering source at one pole, crosses the equator, and undergoes self-annihilation as it winds into itself at the other pole. This behaviour, which is not possible in a two-dimensional planar configuration, arises from qualitative (negative to positive) and quantitative changes in wavefront curvature as the wave traverses the spherical surface. These observations of a single spiral wave contrast with theoretical predictions^7,8 of counter-rotating spirals in this geometry.