Bifurcation of the Ostwald-Liesegang supersaturation-nucleation-depletion cycle

Abstract

A new formulation of the Ostwald supersaturation-nucleation-depletion cycle is adopted to model precipitate banding in rocks. In a special limiting case, the system is shown to support a propagating steady deposition pulse. The limit of existence is determined analytically for a simple model analogue of a pyrite/goethite system. Using numerical simulations, an unsteady pulse of mineral deposition is obtained and is shown to develop a variety of patterns with an appropriate change in the system parameters-apparently showing that the steady pulse obtained analytically is unstable. The domains of existence of unsteady pulse, undulatory patterns and discrete bands are determined.