Spectrophotometric Observations of Gel-Free Reaction Front Kinetics in Confined Geometry
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Spectrophotometric Observations of Gel-Free Reaction Front Kinetics in Confined Geometry Sung Hyun Park*, Stephen Parus*, Raoul Kopelman* and Haim Taitelbaum** * Department of Chemistry, University of Michigan, Ann Arbor, MI 48109, U.S.A. ** Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel ABSTRACT We present a new experimental system to study the kinetics of the reaction front in A + B → C reaction-diffusion systems with initially-separated reactants. The set-up is composed of a CCD camera monitoring the kinetics of the front formed in the reaction-diffusion system Cu2+ + tetra → 1:1 complex (in aqueous, gel-free solution) inside a 150 micron gap between two flat microscope slides. This is basically a two-dimensional system. The results are consistent with the theoretical predictions for the anomalous time dependence of the front’s width, height, and location. INTRODUCTION The kinetics of the reaction front in A + B → C reaction-diffusion systems with initiallyseparated reactants has been studied extensively in the past decade [1-22] and has shown many exotic properties. The initial separation of the reactants is an initial condition that readily enables, in principle, experimental investigations of this system [2,5,16,18]. Indeed, some of the novel characteristics of this system, such as the non-monotonic motion of the reaction front [5], and the split front in the case of competing reactions [16], have been experimentally observed in a series of absorption measurements in a capillary where reactants diffuse and react in a gel solution. However, some of the theoretical predictions that were recently made, such as the doubly non-monotonic motion of the reaction front [17] or the breakdown of the non-monotonic motion have not been obtained yet in experiments due to experimental difficulties, some of which related to problems with the gel solution. In this paper, we present a new experimental system and a set of measurements of the reaction front properties in this system. The experiments are performed in a two-dimensional geometry, where the reaction and diffusion take place within a gap of 150 microns between two flat microscope slides separated by optical fibers. A sketch of the experimental set-up is shown in Figure 1. The simple A + B → C system is assumed to be described for dimensions d ≥ 2 by the mean-field equations for the local concentrations ρa, ρb, dρa / dt = Da ∇ 2ρa – k ρa ρb
(1a)
dρb / dt = Db ∇ 2ρb – k ρa ρb
(1b)
where Da and Db are the diffusion coefficients and k is the microscopic reaction rate constant. For the initially-separated system, the initial condition reads
T7.11.1
Computer
CCD Top view Macro Lens Microscope slides
Side view
Optical Fibers
B
Band-pass Filter Optical Diffuser
Optical fibers
Halogen Lamp Figure 1. Schematic diagram of the experimental setup.
ρa (x, 0) = a0 H(x), ρb (x, 0) = b0 [1-H(x)]
(1c)
where a0, b0 are the initial densities and H(x) is the Heaviside step function. The basic quantities that describe the kinetic behavior of the reacti
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