Model for the fingering instability of spreading surfactant drops

We show that the Marangoni effect drives the fingering instability observed at the edge of an aqueous surfactant drop spreading on a thin film of water. A calculation of the unperturbed flow profile demonstrates that the spreading of the drop is controlled by the dynamics of a thin layer which develops in front of the drop. The surface-tension gradient in this region leads to the fingering instability via a mechanism mathematically similar to that in Hele-Shaw flow despite the very different underlying physics.