On a new surfactant-driven fingering phenomenon in a Hele-Shaw cell

According to the Saffman–Taylor criterion there is no instability when a more viscous fluid is displacing a less viscous one in a Hele-Shaw cell. Yet an instability was observed experimentally (Chan et al. 1997) in the same classical set-up but with the inner walls of the cell coated with surfactant solution. Linear stability analysis is applied to reveal the basic mechanism of this new instability. Asymptotic theory for low capillary numbers allows us to predict the long-wave instability, along with the dependence of the critical parameters on the material properties of the surfactant.