Frozen autocatalytic fronts in a radial flow

Autocatalytic reaction-diffusion fronts are localized reaction zones propagating at a constant speed with a constant width. We show both theoretically and experimentally that, if the reactant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>Y</a:mi></a:math> of the autocatalytic reaction is injected radially at a constant flow rate in a sea of the autocatalytic species <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>X</b:mi></b:math>, a stationary front can be maintained at a fixed position that scales linearly with the flow rate. When this reaction front is about to reach a stationary state, a second outward traveling front emerges to adapt the outer concentration of the autocatalytic species to the stoichiometry ratio between <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>X</c:mi></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>Y</d:mi></d:math>. Simple analytical solutions to the reaction-diffusion-advection equations governing the dynamics are computed for both fronts. The analytical predictions for the stationary front position and moving front dynamics as a function of injection flow rate, reactant concentration, and gap of the quasi-two-dimensional reactor agree well with experimental results obtained with the autocatalytic chlorite-tetrathionate reaction. Published by the American Physical Society 2024