Scaling laws for phase coexistence in multicomponent mixtures

Liquid mixtures of many interacting components often exhibit numerous coexisting types of droplets. An exciting example is the cytosol of biological cells, where diverse droplets, known as condensates, enable cellular functions. However, how much their formation is constrained by thermodynamics is currently unclear because we lack predictions for generic multicomponent fluids. Linear stability analysis suggests that homogeneous mixtures become more robust to fluctuations as the number of components increases, so droplets might not form easily in multicomponent mixtures. In contrast, we show through numerical simulations and analytical scaling laws that the number of coexisting phases typically increases with the number of components in equilibrium. The combination of both results suggests that generic multicomponent mixtures can maintain many metastable states with various droplets, generalizing the nucleation-and-growth regime of binary mixtures. Our scaling laws also indicate why cells exhibit much fewer condensates than components and how they could exploit multistability to form various condensates independently.