  Electrokinetic effects offer a method of choice to control flows in micro and
nanofluidic systems. While a rather clear picture of these phenomena exists now
for the liquid-solid interfaces, the case of liquid-air interfaces remains
largely unexplored. Here we investigate at the molecular level electrokinetic
transport in a liquid film covered with ionic surfactants. We find that the
zeta potential, quantifying the amplitude of electrokinetic effects, depends on
the surfactant coverage in an unexpected way. First, it increases upon lowering
surfactant coverage from saturation. Second, it does not vanish in the limit of
low coverage, but instead approaches a finite value. This behavior is
rationalized by taking into account the key role of interfacial hydrodynamics,
together with an ion-binding mechanism. We point out implications of these
results for the strongly debated measurements of zeta potential at free
interfaces, and for electrokinetic transport in liquid foams.
