Self-organization in the flow of complex fluids (colloid and polymer systems). Part 2: Theoretical models.

Flow induced transitions in complex fluids are usually accompanied by changes in the internal media structure and the flow symmetry. In this review paper, we discuss the theoretical models and approaches that have been used for the analysis of different types of flow instabilities and flow patterns. The main attention is focused on the basic fluid models which reveal vortex and banding flow structures at high shear rates. The Oldroyd-B fluid is one of such models. The Reynolds and the Weissenberg (or Deborah) numbers are the parameters governing its flow behavior. For this model, the secondary flow patterns arising in viscometric flows of different geometries at the bifurcation point are described. Complex fluids which are able to exist in multiple states can form coexisting bands of different structures with different rheological properties and flowing with different shear rates at the same shear stress. Shear banding is typical for fluids demonstrating non-monotonous flow curves described by such models as the diffusive Johnson-Segalman fluid model, for example. Recent progress in exploring this phenomenon is discussed.