Propagating fronts and chaotic dynamics in Co(OH)(2) Liesegang systems

This paper presents a study of some features and characteristics of the Co2 +/NH4OH Liesegang system. The pattern of parallel Co(OH)(2) bands displays peculiar properties that are unique among other Liesegang systems. First, t he process of dissolution of bands at the top of the pattern coupled to, th e formation of new ones at the bottom results in a propagating pattern that moves down the tube. Second, the total number of bands N varies erraticall y with time, unlike other Liesegang systems in which N increases monotonica lly with time. These random oscillations in the variable N are related to t he dissolution/precipitation scenario. New experiments are designed to obta in a rigorous measurement of the total number of bands. Image analysis soft ware (SigmaScan) is used to accurately determine N and the distance of:the: first band from the junction between the two solutions, based on a cutoff z ero absorbance criterion. A time series for N is obtained by monitoring the pattern for 40 consecutive days. This time series is then analyzed numeric ally using a "Chaos Data Analyzer" software. All the characterization tools (such as power spectra, phase portraits, Lyapunov exponents and fractal di mensions) suggest a chaotic behavior of deterministic nature. The distance of the first band from the interface is plotted versus time. The velocity o f dissolution is determined by obtaining a functional fit from the time var iation curve and then calculating a derivative curve of that fit. The deriv ative is particularly evaluated at t = 10 and 15 days (taken as reference d ays), thus yielding the velocity of the dissolution front. A;similar method is used for the distance of the last band from the interface, to determine the velocity of the precipitation front. The measurements are performed fo r five different concentrations (C) of cobalt chloride and the dependence o f the two front velocities on Cis investigated. Both front velocities are f ound to decrease monotonically with increasing C with a linear correlation existing between them.