Coupling Vortical Bulk Flows to the Air–Water Interface: From Putting Oil on Troubled Waters to Surfactants on Protein Solutions

Abstract

The air–water interface in flowing systems remains a challenge to model, even in cases where the interface is essentially flat. This is because even though each side is governed by the Navier–Stokes equations, the stress balance which provides the boundary conditions for the equations involves properties associated with surfactants that are inevitably present at the air–water interface. Aside from challenges in measuring interfacial properties, either intrinsic or flow-dependent, the two-way coupling of bulk and interfacial flows is non-trivial, even for very simple flow geometries. Here, we present an overview of the physics associated with surfactant monolayers of flowing liquid and describe how the monolayer affects the bulk flow and how the monolayer is transported and deformed by the bulk flow. The emphasis is primarily on cylindrical flow geometries, and both Newtonian and non-Newtonian interfacial responses are considered. We consider interfacial flows that are solenoidal as well as those where the surface velocity is not divergence free.