The presence of non-Newtonian fluids is one of the two main causes of nonlinear behavior during single-phase flow (inertial effects being the other). Significant advances have been made in this area during the past few years, with good progress toward quantitative modeling. Research in this area has highlighted the limitations of traditional networks and thus has spurred work on advanced network-generation techniques and specialized algorithms for fluid-flow modeling. These developments are valuable for other types of nonlinear flow modeling.

The images above depict the flow of a yield-stress fluid in a packed bed. On the left is the single flow path that is established at the minimum yield stress (For clarity, the rest of the network structure is not shown). The subsequent images are at higher applied pressure gradients, which results in a larger fraction of the fluid yielding and moving through the pore space (black color indicates flowing fluid).