Transverse instability of autocatalytic fronts in radial injection

A cubic autocatalytic reaction-diffusion front is a localized reaction zone traveling at a constant speed with a fixed shape [1, 2]. The autocatalytic front properties are affected by the flow rate at early time when the autocatalytic species X is radially injected into a pool of the reactant Y [3]. In the reverse case where the reactant Y is injected at a constant flow rate into X, “frozen fronts” i.e. static fronts maintained at a fixed radius can be obtained since the injection of fresh reactant counterbalances the inward invasion by the autocatalytic species. Analytical solution for concentrations in this stationary regime is obtained, and the theoretical predictions for the front position agree well with experiments [4]. We show numerically that, when the invading reactant Y has a sufficiently larger diffusivity than the displaced autocatalytic species X, a transverse diffusive instability can induce modulated structures with a given number of petals in the θ-direction around the stationary front location. Space-time maps of the dynamics reveal that positions of the crests and troughs of the wavy front vary over time. Simulations also show that an increase in the injection speed and diffusivity coefficient of the invading fluid decreases the transverse modulation’s wavelength.

 

[1] S. K. Scott and K. Showalter, J. Phys. Chem 96, 8702 (1992).

[2] A. De Wit, Phys. Rev. Lett. 87, 054502 (2001).

[3] A. Comolli et al., Phys. Chem. Chem. Phys. 25, 10604 (2023).

[4] L. Negrojević, A. Comolli, F. Brau, A. De Wit (preprint).