Oscillatory instability in an Ostwald ripening process

Abstract

This paper considers an Ostwald ripening process in which new droplets are injected at a constant rate, with a fixed distribution of radii, and in which droplets are removed when they grow to a specified maximum radius. This process exhibits a transition from a steady state to a limit cycle as a parameter is varied. The instability is shown to be related to the roots of the Laplace transform of a response kernel. A model is described which gives a good approximation of the period of the limit cycle. The model may also exhibit chaotic behaviour. The relevance of the model to atmospheric precipitation is discussed.