Effect of surface rheology on viscous fingering

Surfactants such as fatty acids, alcohols, proteins, and particles generally stabilize fluid interfaces against rupture and coalescence. However, interfacial instabilities occur even in the presence of surfactants. These instabilities are often undesirable and present challenges in common industrial processes involving multiphase flows. We investigate, for the first time, the impact of interfacial rheology on the Saffman-Taylor or viscous fingering problem and demonstrate the stabilizing role of surface viscosity. We use linear stability analysis to show that surface viscosity slows the growth of unstable protrusions and results in thicker fingers. We quantify the growth of the instability in realistic ranges of fluid and geometric parameters, and use these insights to highlight the quantitative changes that are predicted to occur when a typical surface-viscous surfactant is present in a multiphase fluid displacement problem.