Isolating the yield stress in thixotropic fibrillar gels

Yielding in disordered materials is often characterized by a characteristic yield stress that marks the transition between solid-like and liquid-like responses. Despite the importance of yielding to the behavior of many soft materials, identifying the yield stress often requires arbitrary definitions of non-linear behavior, resulting in orders of magnitude differences between measurement techniques. These differences are further exaggerated for thixotropic fluids whose shear history affects their behavior. Here we propose a rheological strategy to quantify the yield stress in thixotropic materials. We measure the compliance of gels comprised of TEMPO-oxidized cellulose nanofibrils (CNFs) and identify a stress-controlled bifurcation in the yielding response as the gels age. For low stresses, the time to yield diverges with increasing sample age while at high stresses, it plateaus at a finite value. A critical stress bifurcates this response and leads to a power-law evolution of the yield time with sample age, similar to the Winter-Chambon criterion characterizing the gel transition. Separating the elastic solid-like and viscous liquid-like responses of the gel, this critical stress serves as an unambiguous measurement of the yield stress for thixotropic fluids.