Rheological instability in a simple shear thickening model

We study the strain response to steady imposed stress in a spatially homogeneous, scalar model for shear thickening, in which the local rate of yielding Gamma(l) of mesoscopic `elastic elements is not monotonic in the local strain l. Despite this, the macroscopic, steady-state flow curve (stress vs. strain rate) is monotonic. However, for a broad class of Gamma(l), the response to steady stress is not in fact steady flow, but spontaneous oscillation. We discuss this finding in relation to other theoretical and experimental flow instabilities. Within the parameter ranges we studied, the model does not exhibit rheo-chaos.