Scaling properties of A + B → C reaction-diffusion fronts in finite rectilinear geometries

A + B → C reaction-diffusion fronts are localized reactive zones developing upon diffusive transport and reaction between two zones containing separately the reactants A and B of a bimolecular A+B→C reaction. Gálfi and Rácz have characterized the scalings of these types of reaction fronts in infinitely large systems, showing that the position xf, width w, and maximum production rate R scale as xf∼t1/2, w∼t1/6, and R∼t-2/3, respectively, where t denotes time. In this work, we show theoretically that the properties of these A+B→C reaction-diffusion fronts can be affected in geometries of a finite size. Considering arbitrary finite rectilinear geometry sizes and initial positions of the reactants, we identify the existence of two additional regimes that follow the initial dynamics described by Gálfi and Rácz and are significantly influenced by the geometric constraints of the spatial domain. In the first regime, the observables exhibit an exponential dynamics, while in the second one, the front position remains spatially stationary under certain conditions. We further show that the transition times between regimes depend on the size of the system. We support our calculations with numerical simulations and characterize the dynamics of the front observables as a function of the ratio of initial concentrations.