The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent

Abstract

Rotating waves of activity are seen in various biological phenomena and in chemical mixtures. In thin layers of these media, the waves often appear as spirals spinning around a pivot point, but actually they are scroll-shaped waves rotating around curved filament in three-space. The filament about which the scroll rotates is not stationary, but rather moves through space until it achieves a stable configuration or disappears altogether. Some features of the temporal evolution of a planar scroll wave filament can be understood in terms of the simple equation N = Dκ, where N is the velocity of the filament in the direction of its principal normal, κ is the curvature of the filament, and D is the diffusion coefficient of the active chemical species. This equation of motion implies that a scroll ring shrinks in size and collapses in finite time, that an elongated spiral evolves into a symmetric spiral, and that an elongated target pattern becomes more symmetrical and vanishes in finite time. Characteristic times for these processes are estimated. In each case, good quantitative agreement is found between implications of the model and observations of scroll-wave evolution in shallow layers of the Belousov-Zhabotinsky reagent.