Scientific Computation and Applied & Industrial Mathematics: Iain Moyles

Many chemical systems exhibit a regular pattern of precipitate bands known as Liesegang rings in tribute to the chemist Raphael E. Liesegang who demonstrated them using a reaction of silver nitrate and potassium dichromate. A variety of theories have been studied to try and understand how these patterns develop and one of the most seminal papers on the topic was a mathematical model developed by Keller and Rubinow using a supersaturation framework. This model predicted the formation of primary and secondary bands using heuristic arguments and assumptions about the underlying equations. In this talk we present the Keller-Rubinow model from a formal asymptotic perspective and discuss the dynamics and formation of the primary precipitation band. Furthermore we show that secondary bands are infeasible under the model as posed thus necessitating the development of a new model. We will provide preliminary insights into such a new model and its resolution towards secondary bands.