Band Propagation, Scaling Laws, and Phase Transition in a Precipitate System. 2. Computational Study.

Abstract

In this second paper, we introduce a chemical kinetic model that investigates the dynamics of the experimental Ni(2+)/NH3-OH(-) Liesegang system characterized by a pattern of β-nickel hydroxide bands led by a growing pulse of α-nickel hydroxide. The model is based on a system of reaction-diffusion equations describing the precipitation reaction and dissolution of the nickel hydroxide polymorphs by ammonia. The hydroxide ions are assumed to be static whereas ammonia serves as a diffusing "vehicle" that supplies the hydroxide ions along the precipitation zone, and these ions in turn react with the static Ni(2+) ions. The precipitation-diffusion equations are coupled to nucleation, polymorphic transition, and growth rate equations, each of which is characterized by a critical constant specific to the solid phase dynamics. In the proposed model, priority is given to polymorphic transition rather than nucleation. This implies that the critical constants must be subject to a constraint different than that derived for the Lifshitz-Slyozov instability encountered in classical Liesegang patterns. Numerical simulations confirm the validity of our model and the derived constraint. The pulse position and width are found to scale in time as t(α) with α ≃ 0.5, in agreement with the experimental results. Finally, the mass of the bands is shown to oscillate in time, suggesting competition between growth and polymorphic transition on one side and dissolution on the other.