Effects of radial injection and solution thickness on the dynamics of confined A + B → C chemical fronts

The spatio-temporal dynamics of an A + B → C front subjected to radial advection is investigated experimentally in a thin solution layer confined between two horizontal plates by radially injecting a solution of potassium thiocyanate (A) into a solution of iron(iii) nitrate (B). The total amount and spatial distribution of the product FeSCN²⁺ (C) are measured for various flow rates Q and solution thicknesses h. The long-time evolution of the total amount of product, n_C, is compared to a scaling obtained theoretically from a one-dimensional reaction-diffusion-advection model with passive advection along the radial coordinate r. We show that, in the experiments, n_C is significantly affected when varying either Q or h but scales as n_C∼Q^-1/2V where V is the volume of injected reactant A provided the solution thickness h between the two confining plates is sufficiently small, in agreement with the theoretical prediction. Our experimental results also evidence that the temporal evolution of the width of the product zone, W_C, follows a power law, the exponent of which varies with both Q and h, in disagreement with the one-dimensional model that predicts W_C∼t^1/2. We show that this experimental observation can be rationalized by taking into account the non-uniform profile of the velocity field of the injected reactant within the cell gap.