Bubble phases in active emulsions

A very general model for non-equilibrium phase transitions is the Active model B+ model which is an active generalisation of the classical active model B for the dynamics of phase transitions with a conserved order parameter. The field theoretical version of the model predicts various exotic phases including a "bubble phase" where one phase forms finite size droplets in a continuum of the other phase. But inside the droplet bubbles of the external phase appear and disappear. A simpler approach of the model is to focuses on the activity of the interface between the two phases that we describe by an Onsager theory. In this language, we try to describe theoretically the bubble phase as a double nucleation process where the bubbles of the external phase nucleates in the droplets. The theory follows the classical theory of Ostwald ripening. This work has been realised under the supervision of Professor Jean-François Joanny and Dr. Julien Brémont during a stage of four months at Collége de France, Paris.