The simplest microscopic model of a complex fluid: flow phenomena and   constitutive relation
  It was shown in [PRL 114, 138301 (2015)] that a remarkably simple dynamical model exhibits many of the complex flow regimes and non-equilibrium phase transitions characteristic of complex fluids. By removing extraneous detail, this simplest microscopic model of non-Newtonian flow can reveal the universal physics relevant to all complex fluids. Here we present more detailed results and a full derivation of the model's compact mean-field constitutive relation, with great potential scope for insights into universality and tractable mathematics. By enforcing local conservation of angular momentum, the one-dimensional (1D) XY-model (originally used for equilibrium magnetic systems) can be driven into various flow regimes, including simple Newtonian behaviour, shear banding, solid-liquid coexistence and slip-plane motion. The model demonstrates that the phenomenon of shear banding does not rely on details of tensorial stress fields, but can exist in 1D. 
R. M. L. Evans, Craig A. Hall, R. Aditi Simha and Tom Welsh
cond-mat.soft cond-mat.stat-mech