Abstract
Liquid-liquid phase separation (LLPS) is found in many natural systems, ranging from food science to biological organization. In the context of biology, these LLPS condensates typically grow over time by coarsening. Typically, these organelles are embedded in a complex, far-from-equilibrium environment such as the cell cytoplasm. There, condensates are transported with a complex, active, turbulent flow, for which the framework for coarsening droplets is not well understood. Here, we design an experimental composite system composed of DNA nanostars, which mimics the phase behavior of membraneless organelles, and a microtubule-kinesin 3D active fluid, which mimics the complex advection behavior of the cytoplasmic environment. We compare how this composite system directs “active coarsening” and compare it to how droplets coarsen in a passive fluid with no advection. We find that the number of droplets decrease much more rapidly in active coarsening compared to passive coarsening, characterized by the number scaling exponent N. The average droplet radius scaling behavior, characterized by the average radius scaling exponent r, remains unchanged between active and passive coarsening. While the droplet radius distribution in passive coarsening reaches self-similarity, the active coarsening radius distribution shows an increasing polydispersity over time, characterized by the width parameter r. We also design a simulation to recreate the coarsening experiments we conducted, and find the same scaling and radius distribution behavior as we find in the experiments. We also measured coarsening of self-propelled active droplets with no spatial correlation, and find that removing spatial correlation in droplet motility does not change the coarsening dynamics. Ultimately, we find that droplet coarsening dynamics are set by droplet binary collision statistics, characterized by the collision kernel ij, regardless of whether droplets are in an active or passive fluid. These findings illuminate the generic principles that determine coarsening dynamics, and provide a framework for understanding measured organelle size distributions. This work might also allow future experiments to exert direct control over the collision kernel such that we can program droplet radius distributions and localize droplets in space.