Competing Elementary Reactions in a Capillary - Two Reaction Fronts Moving in Opposite Directions
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=
Db V
2
b - kab
at where the local concentrations of the reactants A and B are denoted by a and b, respectively, Da and Db are the corresponding diffusion constants, and k is the microscopic reaction constant. The equations must satisfy the following initial conditions to properly represent the initially separated reactants along the separation axis x. a = aoH(x),
b = b.[1I-H(x)]
(2)
where H(x) is the Heaviside step function. By applying scaling arguments, Galfi and Racz could derive analytically the power law of three major properties of a reaction front in the long-time limit. Namely, in the asymptotic regime, the center of the reaction front (xf) and the width of the 249
Mat. Res. Soc. Symp. Proc. Vol. 543 c 1999 Materials Research Society
reaction front (w) scale with time as xj - t"2 and w - t"6 , while the production rate of C at xf, R(xf, t), is proportional to t-213. The monotonous asymptotic time behavior of the center of the reaction front, xf - t11 2 , can be understood intuitively in terms of the diffusive nature of the reaction-diffusion system in the long-time limit. However, the movement of the reaction front in the early-time limit has been shown to be very exotic and nontrivial. The early-time behavior of the reaction front has been studied first by Taitelbaum et al.." Using the approach of perturbation theory, they found that, unlike for the long-time limit studied by Galfi and Racz using scaling arguments, the system parameters play a crucial role in determining the kinetic properties of the reaction front. Their theoretical results predict various nontrivial crossovers and four different universality classes for the dynamics of the reaction front center. In particular, they showed that under appropriate choices of the diffusion constants and initial densities of the reactants, the front exhibits a change of its direction of movement. Experimental results from a xylenol orange (XO) - Cr3 system with appropriate diffusion constants and initial concentrations confirmed the change of direction for the front motion, i.e., the existence of the extremum. Later, Taitelbaum et al. presented another interesting behavior of the reaction front in the initially separated A+B--+C reaction-diffusion system"2 , namely the possibility of two directional changes during its motion, as well as a stationary front after a single switch of direction. These phenomena resulted from the argument that three different parameters of the system determine the direction of motion of the reaction front. In this paper, we report the experimental observation of the reaction front splitting and the motion of its two parts in opposite directions. We focus on the dynamic behavior of the position of each reaction front, showing that both fronts independently follow the long-time limit behavior predicted by Galfi and Racz. EXPERIMENTAL We observed an inorganic complex formation reaction between XO and Cr3 + in a capillary reactor. We used CrCl3 as the source of Cr3 +and a sodium salt of xylenol orange as the source of XO. A
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