New prediction for wave length selection of radial fingering in a Hele-Shaw cell

Existing linear stability analysis of radial fingering in Hele-Shaw cells use Darcy’s law as a model for the fluid motion. Comparison between experiments and theory reveals a large discrepancy at order 1 capillary numbers. In this work we use the so-called Brinkman equations to describe the fluid motion. It becomes apparent that the in-plane stresses play a dominant role in the determination of the most unstable mode as the surface tension gets very small.