Phase separation by polar active transport

We propose an active Cahn-Hilliard theory for the dynamics of a new type of phase transition where the driving force is not the direct interactions between the two separating components, but their active sorting by a third polar species. This third species can transport the other two along its polarity in opposite directions, thus separating them. Inspired by recent experiments where molecular motors that walk in opposite directions along microtubules are sorted into separated domains, our theoretical description of this process introduces a new mechanism for active phase separation and could serve as a model for the organization of biological material in space inside cells. We predict the formation of motor domains, and further show that they can either coarsen to form macroscopic phases or reach a finite micro- or mesoscopic steady state size, these latter due to an arrest of coarsening through activity.