Cavitation controls droplet sizes in elastic media

Biomolecular condensates exist in the complex, crowded environments of biological cells. To understand how the elastic properties of the environment affect droplet formation and dynamics, we analyze a particular situation in which decreasing temperatures let droplets form in a soft matrix that can fracture. We show that large droplets only form when they fracture the surrounding matrix in a cavitation event. This cavitation provides an energy barrier for droplet growth, stabilizing small droplets on the mesh size, and diminishing the stochastic effects of nucleation. Consequently, the observed cavitated droplets are monodispersed and have highly correlated positions. In particular, we predict the density of cavitated droplets, which increases with fast temperature changes, similar to recent experiments. We also show how increasing the cooling rate can lead to bimodal droplet distributions, and we speculate on the effect of different stiffnesses. In summary, our theory provides a mechanism to control droplet sizes in elastic media.