Suppression of viscous fluid fingering: a piecewise-constant injection process.

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this Brief Report, we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise-constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.