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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.
François Gallaire, Alessandro Bongarzone, Alice Evelyne Julienne Marcotte
Véronique Michaud, Baris Çaglar, Helena Luisa Teixido Pedarros