Speaker
Description
Recent studies have shown that chemical reactions in phase separating systems can lead to growth and division of droplets. The fuel from chemical reactions can lead to a sequence of growth and splitting that mimics the behavior in the transition of protocells from nonliving to living systems. Such systems where energy is externally supplied and the governing equations do not fulfil a free energy inequality are termed active systems. In this talk we provide a mathematical description based on a sharp interface Mullins-Sekerka free boundary problem that can be derived from a Cahn-Hilliard system with source terms. We are interested in analyzing the influence of certain parameters that promote growth of instabilities, leading to topology changes of perturbed stationary solutions, such as droplet splitting and merging. Accompanying numerical simulations show complex dynamical behavior, such as multiple instabilities, splitting of droplets and appearance of shell-type solutions. This is a joint work with Harald Garcke (Regensburg), Robert Nurnberg (Trento) and Andrea Signori (Milan).