Networks of aggregated colloidal particles are solidlike and can sustain an applied shear stress while exhibiting little or no creep; however, ultimately they will catastrophically fail. We show that the time delay for this yielding decreases in two distinct exponential regimes with applied stress. This behavior is universal and found for a variety of colloidal gel systems. We present a bond-rupture model that quantitatively describes this behavior and highlights the role of mesoscopic structures. Our result gives new insight into the nature of yielding in these soft solid materials.

A model for flexible fibers in viscous fluid flow is proposed, and its predictions compared with experiments found in the literature. The incompressible three-dimensional Navier–Stokes equations are employed to describe the fluid motion, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous and dynamic drag forces. Fiber segments, from the same or from different fibers, interact with each other through normal, frictional, and lubrication forces. Momentum conservation is enforced on the system to capture the two-way coupling between phases. Quantitative predictions could be made, and showed good agreement with experimental data, for the period of Jeffery orbits in shear flow, as well as for the amount of bending of flexible fibers in shear flow. Simulations, using the proposed model, also successfully reproduced the different regimes of motion for threadlike particles, ranging from rigid fiber motion to complicated orbiting behavior, including coiling and self-entanglement.

We study the geometry of biopolymer networks and effects of the geometry on bulk mechanical properties. It is shown numerically that the physical network geometry can be quantified statistically and regenerated from its statistical description, so that the regenerated network exhibits the same network mechanics as the physical network in the elastic regime. A collagen-I biopolymer network is used for validation. The method enables parametric studies of the network geometry, whose parameters are often difficult to vary independently in experiments.

Sample-spanning networks of aggregated colloidal particles have a finite stiffness and deform elastically when subjected to a small shear stress. After some period of creep, these gels ultimately suffer catastrophic failure. This delayed yielding is governed by the association and dissociation dynamics of interparticle bonds and the strand structure of the gel. We derive a model which connects the kinetics of the colloids to the erosion of the strand structure and ultimately to macroscopic failure. Importantly, this model relates time-to-failure of the gel to an applied static stress. Model predictions are in quantitative agreement with experiments. It is predicted that the strand structure, characterized by its mesh size and strand coarseness, has a significant impact on delay time. Decreasing the mesh size or increasing the strand thickness makes colloidal gels more resilient to delayed yielding. The quench and flow history of gels modifies their microstructures. Our experiments show that a slow quenching increases the delay time due to the coarsening of the strands; by contrast, preshear reduces the delay time, which we explain by the increased mesh size as a result of shear-induced fracture of strands.