THE DYNAMICS AND STABILITY OF CUBIC AUTOCATALYTIC CHEMICAL WAVES IN 3-DIMENSIONAL SYSTEMS

Numerical and theoretical results are presented for planar, cylindrica l and spherical chemical waves with cubic autocatalysis, where the dif fusivities of tie reactant A and the autocatalyst B may differ. The dy namics of the wavefront depend upon the ratio of the diffusivities del ta = D-A/D-B, as well as the system geometry. If delta is less than de lta approximate to 2.3, circular and spherical waves accelerate as th ey spread radially outwards. With larger values of delta, monotonic de celeration is observed. The evolution of perturbations or wrinkles app lied to the wavefront is also discussed. The wrinkle may persist if th e diffusivity ratio exceeds the critical value delta. Such perturbati ons can only grow if their curvature is sufficiently small. In Cartesi an systems this imposes a minimum system size for patterned front form ation. In circular and spherical systems there is an analogous require ment on the radius of the wavefront. Hence, the perturbation may decay initially, only to begin growing again when the front expands beyond a critical radius R(cr). Long-time solutions for the form of the pertu rbation are also obtained in the circular and spherical cases. Net gro wth (geometrical instability) is only observed if the initial radius e xceeds 3(-1/2)R(cr) (approx).