Spatial structure formation in precipitation reactions

We analyze selected experiments on spatial structure formation in the presence and the absence of imposed gradients of concentrations, with emphasis on length scales, time scales, initial degree of supersaturation, and initial concentration differences of the ions forming the precipitate. In relation to these experiments, we discuss two major proposed models. The first is the Ostwald-Prager model of Liesegang bands for systems with imposed concentration gradients (diffusion of ions occurs and at a given degree of supersaturation, nucleation and precipitation to form bands take place discontinuously but repeatedly in space) The other model, known by various designations (Ostwald ripening, competitive growth model, Turing instability) for systems with and without imposed gradients, supposes nucleation to occur continuously in a region of space, followed by the competitive and autocatalytic growth of larger particles at the expense of the dissolution of smaller particles within that region of space. This process coupled to diffusion may lead to macroscopic Turing structures. We find extensive experimental evidence for the second model over a large range of initial concentrations of electrolytes as well as some theoretical evidence, and we find the experimental evidence presented for the validity of the first model alone to be insufficient.