About computations of Hele-Shaw flow of non-Newtonian fluids

The flow of a fluid confined between two solid plates (Hele-Shaw cell) is of considerable interest in a variety of applications. Further interest in two phase flow in this geometry stems from the close analogy between the dynamics of fluid-fluid interface and the propagation of the solidification front. While the flow of Newtonian fluids is rather well understood, it is much more complicated to compute flows of non-Newtonian fluids. We find that the dense-branching morphology of Newtonian liquids may be replaced by dendritic fingers with stable tips sidebranches, and discuss resulting length scales.