Direct link between mechanical stability in gels and percolation of isostatic particles

Colloidal gels have unique mechanical and transport properties that stem from their bicontinous nature, in which a colloidal network is intertwined with a viscous solvent, and have found numerous applications in foods, cosmetics, construction materials, and for medical applications, such as cartilage replacements. So far, our understanding of the process of colloidal gelation is limited to long-time dynamical effects, where gelation is viewed as a phase separation process interrupted by the glass transition. However, this picture neglects two important effects: the influence of hydrodynamic interactions, and the emergence of mechanical stability. With confocal microscopy experiments, here we successfully follow the entire process of gelation with a single-particle resolution, yielding time-resolved measures of internal stress and viscoelasticity from the very beginning of the aggregation process. First, we demonstrate that the incompressible nature of a liquid component constrains the initial stage of phase separation, assisting the formation of a percolated network. Then we show that this network is not mechanically stable and undergoes rearrangements driven by self-generated internal stress. Finally, we show that mechanical metastability is reached only after percolation of locally isostatic environments, proving isostaticity a necessary condition for the stability and load bearing ability of gels rather than the glass transition. Our work reveals the crucial roles of momentum conservation in gelation in addition to the conventional purely out-of-equilibrium thermodynamic picture.