Delayed yield in colloidal gels: Creep, flow, and re-entrant solid regimes

We investigate the phenomenon of delayed yield in reversible colloidal gels via dynamic simulation, with a view toward revealing the microscopic particle dynamics and structural transformations that underlie the rheological behavior before, during, and after yield. Prior experimental studies reveal a pronounced delay period between application of a fixed shear stress and the onset of liquidlike flow, a so-called “delay time.” Catastrophic network failure—with sudden, cascading rupture of particle clusters or strands—is the primary model proposed for the structural evolution underlying rheological yield. However, no direct observation of such evolution has been made, owing to the difficulty of obtaining detailed microstructural information during the rapid yield event. Here, we utilize dynamic simulation to examine the microstructural mechanics and rheology of delayed yield. A moderately concentrated dispersion of Brownian hard spheres interacts via a short-range attractive potential of O(kT) that leads to arrested phase separation and the formation of a bicontinuous network of reversibly bonded particles. The linear-response rheology and coarsening dynamics of this system were characterized in our recent work. In the present study, a step shear stress is imposed on the gel, and its bulk deformation, as well as detailed positions and dynamics of all particles, are monitored over time. Immediately after the stress is imposed, the gel undergoes solidlike creep regardless of the strength of the applied stress. However, a minimum or “critical stress” is required to initiate yield: When the imposed stress is weak compared to the Brownian stress, the gel continues to undergo slow creeping deformation with no transition to liquidlike flow. Under stronger stress, creep is followed by a sudden increase in the strain rate, signaling yield, which then gives way to liquidlike viscous flow. The duration of the creep regime prior to yield is consistent with the delay time identified in prior experimental studies, decreasing monotonically with increasing applied stress. However, when the deformation rate is interrogated as a function of strain (rather than time), we find that a critical strain emerges: Yield occurs at the same extent of deformation regardless of the magnitude of the applied stress. Surprisingly, the gel network can remain fully connected throughout yield, with as few as 0.1% of particle bonds lost during yield, which relieve local glassy frustration and create localized liquidlike regions that enable yield. Brownian motion plays a central role in this behavior: When thermal motion is “frozen out,” both the delay time and the critical yield stress increase, showing that Brownian motion facilitates yield. Beyond yield, the long-time behavior depends qualitatively on the strength of the applied stress. In particular, at intermediate stresses, a “re-entrant solid” regime emerges, whereupon a flowing gel resolidifies, owing to flow-enhanced structural coarsening. A nonequilibrium phase diagram is presented that categorizes, and can be used to predict, the ultimate gel fate as a function of imposed stress. We make a connection between these behaviors and the process of ongoing phase separation in arrested colloidal gels.