Experimental study of a ternary A+2B-->C reaction-diffusion system with a propagating reaction front: Scaling exponents
TL;DR: In this article, the authors compared with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate, the location of the reaction center, the front's width, and the local production rate.
Abstract: We study experimentally the $A+2B\ensuremath{\rightarrow}C$ reaction-diffusion process with initially separated reagents in a capillary using an inorganic chemical reaction. We measure and compare with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate $R(t),$ the location of the reaction center ${x}_{f}(t),$ the front's width $w(t),$ and the local production rate ${R(x}_{f},t).$ We demonstrate the nonclassical phenomena of reactant segregation and depletion-zone formation for this reaction-diffusion process. The experimental results are in good agreement with theory and simulation and quite different from the exponents for the elementary binary $A+B\ensuremath{\rightarrow}C$ reaction. The time exponents are 0.27 for the width, -0.48 for the global reaction rate, and -0.75 for the local reaction rate, compared to theoretical values of 0.25, -0.5, and -0.75, respectively.
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TL;DR: In this paper, the authors studied the propagation of a reaction front in an immiscible liquid-liquid system under the condition of a mass transfer across the interface accompanied by a neutralization reaction.
37 citations
TL;DR: In this paper, the long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R ( ρ A, ρ B ) = kρ A m ρ b n.
33 citations
TL;DR: In this article, a simple A + B → C reaction takes place and reaction-diffusion profiles develop due to the coupling of reaction and diffusion, and both the leading order large-time and small-time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically.
Abstract: If two initially separated solutions of reactants are put in contact and a simple A + B → C reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large-time and small-time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like t1/2 and the width of the reaction front scales with t1/6. In the large Péclet number limit the large-time asymptotic properties of the radial reaction front are found to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is 1/ √ 2 of the distance that a planar reaction front travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of 21/6 and √ 2, respectively, compared to the planar reaction front.
10 citations
TL;DR: In this paper, a deterministic rate equation of three-species in the reaction diffusion system was proposed and the particle density and the global reaction rate were analyzed analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions.
Abstract: We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The particle density and the global reaction rate are also shown analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions. Especially, the crossover of the global reaction rate is discussed in both early-time and long-time regimes.
6 citations