Surface viscosity and Marangoni stresses at surfactant laden interfaces

We calculate here the force on a probe at a viscous, compressible interface, laden with soluble surfactant that equilibrates on a finite time scale. The motion of the probe through the interface drives variations in the surfactant concentration at the interface that in turn leads to a Marangoni flow that contributes to the force on the probe. We demonstrate that the Marangoni force on the probe depends non-trivially on the surface shear and dilatational viscosities of the interface indicating the difficulty in extracting these material properties from force measurements at compressible interfaces.