Shear thickening rheology: analogy to a phase transition

The lubricated-to-frictional rheological transition in suspensions [1], associated with stress-induced frictional contacts, includes an apparent critical point on the flow curve for the critical solid fraction, for which the fluctuations in stress at a specific shear rate become extremely large. At larger solid fraction, the suspension undergoes a discontinuous change in stress at a particular shear rate, i.e. discontinuous shear thickening (DST), as well as shear jamming (SJ). These behaviors are reminiscent of second-order and first-order phase transitions, and here we explore a mapping of the DST behavior to a phase transition. We find it useful to consider the DST and SJ transitions in terms of two coupled order parameters. The first of these measures the fraction of frictional contacts and the other the fraction of particles in rigid clusters. We will discuss mapping to a minimal statistical mechanical model that incorporates this description of the material, as well as the insight it provides regarding the conditions defining the onset of DST as well as the behavior approaching SJ.

1. J. F. Morris 2018 The lubricated-to-frictional shear thickening scenario in dense suspensions. Phys. Rev. Fluids. 3, 110508.