Local and non local rheology of concentrated particles

In this article, we provide an up-to-date review dealing with the flow of soft glassy materials, that is, concentrated hard and soft particle assemblies. Because of the existence of short range forces, steric forces, and polydispersity, the structure of soft glassy materials remains frustrated and disordered. Their structure explores the energy landscape by thermally overcoming barriers to lower the total energy of the system. As the system ages, the barriers it must overcome become higher. Eventually, the system falls into a steep valley, from which it can no longer escape during the observation time; thus, it becomes non-ergodic. These disordered structures and rearrangements provide the origin of the rheological behavior of soft glassy materials, which give rise to solid behavior at low applied stresses. Rearrangement is a critical process that must be considered in the modeling of the rheological response of soft glassy materials. In this review article, we describe generic laws that relate stress to deformation, a relationship that we call local rheology. We also present the failures of this law that arise from hysteresis, particle migration, finite-size and non-local effects. We show that a generic framework corresponds to all the systems.