  We derive a general integrodifferential equation for the transient behaviour
of small-amplitude capillary waves on the planar surface of a viscous fluid in
the presence of the Marangoni effect. The equation is solved for an insoluble
surfactant solution in concentration below the critical micelle concentration
(cmc) undergoing convective-diffusive surface transport. The special case of a
diffusion-driven surfactant is considered near the the critical damping
wavelength. The Marangoni effect is shown to contribute to the overall damping
mechanism and a first-order term correction to the critical wavelength with
respect to the surfactant concentration difference and the Schmidt number is
proposed.
