Strong, tough, or fragile: Brownian motion and the osmotic pressure of colloidal gels

We interrogate via dynamic simulation the role played by the osmotic pressure in non-equilibrium phase separation in colloidal gels. In colloidal suspensions, attractive interparticle forces of order several kT lead to arrested phase separation and the formation of a bi-continuous network of reversibly bonded particles condensed into thick, glassy strands. The durable but temporary nature of the bonds permits ongoing structural age-coarsening that lowers the average potential energy of the gel: particles migrate from areas of fewer contacts to regions of more contacts, but thus migrate from regions of higher to lower hydrodynamic mobility. Particles thus undergo a Smoluchowski ratcheting to progressively deeper arrest. Concomitantly, the osmotic pressure evolves during quiescent aging from a more negative to a less negative value, indicating that the driver for further condensation or phase separation weakens continuously. These soft solids, also described as yield-stress fluids, yield mechanically under application of an external stress, force, or flow. Our recent work revealed that mechanical yield can be viewed as a non-equilibrium phase transition, where the liquid-to-solid transition sometimes re-arrests into a re-entrant solid material. To deepen our understanding of this as non-equilibrium phase behavior, we conduct a detailed examination of the role played by osmotic pressure in gels yielding under three modes: fixed stress, fixes strain-rate, and gravitational forcing, and show that an interplay between external perturbation and osmotic pressure temporarily release the gel from kinetic arrest, advancing it toward more complete phase separation. A theoretical model is advanced.